Tg Eapcet 2022 20th July Evening Shift Question Paper Question Paper with Solutions | TG EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQfunctions

+1 / -0

If $[𝑥]$ represents the greatest integer function, then the set of all real values of $𝑥$ for which $𝑓 (𝑥) = \sqrt{\sqrt \frac{[𝑥] - 𝑥}{𝑥 - [𝑥]}}$ is real is

$𝜙$

Incorrect

$𝑅$

Incorrect

$𝑍$

Incorrect

$𝑅 - 𝑍$

Incorrect

Q 2MathematicsSection A • MCQfunctions

+1 / -0

If $[𝑥]$ denotes the greatest integer $\leq 𝑥$ , then the range of the real valued function $𝑓 (𝑥) = \frac{1}{\sqrt{\sqrt 𝑥 - [𝑥]}}$ is

$[0, 1)$

Incorrect

$(0, 1)$

Incorrect

$(1, \infty)$

Incorrect

$[1, \infty)$

Incorrect

Q 3MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴$ is a $2 \times 2$ matrix such that $\det 𝐴 = - 21$ and trace of $𝐴^{3}$ is 2024 , then the trace of $𝐴$ is

6

Incorrect

11

Incorrect

12

Incorrect

13

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $⎡⎣⎢ \begin{matrix} 𝑎 & 𝑏 & 𝑐 \\ 𝑑 & 𝑒 & 𝑓 \\ 𝑔 & ℎ & 𝑖 \end{matrix} ⎤⎦⎥$ is a skew-symmetric matrix and $𝑏, 𝑐$ and $𝑓$ are non-zero real numbers, then $\frac{𝑏}{𝑐} =$

$\frac{𝑑 ℎ}{𝑓 𝑔}$

Incorrect

$\frac{𝑑 𝑓}{𝑔 ℎ}$

Incorrect

$\frac{- 𝑑 𝑓}{𝑔 ℎ}$

Incorrect

$\frac{- 𝑑 ℎ}{𝑓 𝑔}$

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

In the matrix $⎡⎣⎢ \begin{matrix} - 1 & 𝑥 & 3 \\ - 4 & - 5 & - 6 \\ - 7 & 𝑦 & 9 \end{matrix} ⎤⎦⎥$ , if the cofactors of -6 and -7 are respectively 22 and 27 , then $5 𝑥 + 𝑦 =$

0

Incorrect

-1

Incorrect

-2

Incorrect

-4

Incorrect

Q 6MathematicsSection A • MCQmatrices and determinants

+1 / -0

Consider the simultaneous linear equations $𝛽 𝑥 + 𝛼 𝑦 - 𝑧 = - 1, 3 𝑥 - 𝛽 𝑦 + 𝛼 𝑧 = 0 𝛼 𝑥 + 𝛽 𝑦 + 𝑧 = 1$ , In the usual notation used in Crammer's rule, given that $\frac{Δ_{1}}{Δ} = - 1, \frac{Δ_{2}}{Δ} = 1, \frac{Δ_{3}}{Δ} = 2$ , then $(𝛼, 𝛽) =$

$(1, 2)$

Incorrect

$(2, 1)$

Incorrect

$(- 1, 2)$

Incorrect

$(1, - 2)$

Incorrect

Q 7MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $∣ \begin{matrix} 2 + 3 𝑖 & 𝑖 \\ 1 - 2 𝑖 & - 𝑖 \end{matrix} ∣ = 𝑥 + 𝑖 𝑦$ , then $𝑥 + 𝑦 =$

-2

Incorrect

-4

Incorrect

-8

Incorrect

4

Incorrect

Q 8MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝛼$ and $𝛽$ are the roots of the equation $𝑥^{2} - 2 𝑥 + 2 = 0$ , then $𝛼^{2020} + 𝛽^{2020} =$

$2^{1011}$

Incorrect

$- 2^{1011}$

Incorrect

$2^{2021}$

Incorrect

$2^{- 2021}$

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑧 = \frac{- 1 - 𝑖 \sqrt{\sqrt 3}}{2}$ , then $\sum_{2022}^{𝑘 = 1} {(𝑧^{𝑘} + \frac{1}{𝑧^{𝑘}})}^{2} =$

0

Incorrect

2022

Incorrect

4044

Incorrect

1011

Incorrect

Q 10MathematicsSection A • MCQquadratic equations

+1 / -0

Statement I The set of solutions of $| 𝑥 |^{2} - 4 | 𝑥 | + 3 < 0$ is the interval $(- 3, 3)$

Statement II If $𝑥 < 3$ or $𝑥 > 5$ , then $𝑥^{2} - 8 𝑥 + 15 > 0$

Which of the above statements is (are) true?

Statement I is true, but Statement II is false

Incorrect

Statement II is true, but Statement I is false

Incorrect

Both Statement I and Statement II are true

Incorrect

Both Statement I and Statement II are false

Incorrect

Q 11MathematicsSection A • MCQquadratic equations

+1 / -0

If $6 𝑥 - 𝑥^{2} + 12$ attains its extreme value $𝛽$ at $𝑥 = 𝛼$ , then $𝛽 =$

$7 𝛼$

Incorrect

$5 𝛼$

Incorrect

$3 𝛼$

Incorrect

$𝛼$

Incorrect

Q 12MathematicsSection A • MCQquadratic equations

+1 / -0

Let $𝑎$ be a common root of the equations $𝑥^{3} - 2 𝑥 - 25 𝜆 = 0, 3 𝑥^{3} - 8 𝑥 - \frac{175}{3} 𝜆 = 0$ and $𝜆 > 0$ . Then, $𝜆 =$

$\frac{3}{\sqrt{\sqrt 5}}$

Incorrect

$\frac{\sqrt{\sqrt 3}}{5 \sqrt{\sqrt 5}}$

Incorrect

$\frac{3}{5 \sqrt{\sqrt 5}}$

Incorrect

$\frac{3 \sqrt{\sqrt 5}}{5}$

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If the sum of two roots of the equation $𝑥^{3} - 7 𝑝 𝑥^{2} + 5 𝑞 𝑥 - 6 𝑟 = 0$ is zero, then

$5 𝑝 = \frac{6 𝑞}{7 𝑟}$

Incorrect

$5 𝑞 = \frac{6 𝑟}{7 𝑝}$

Incorrect

$5 𝑟 = \frac{6 𝑝}{7 𝑞}$

Incorrect

$𝑝 𝑞 𝑟 = 35$

Incorrect

Q 14MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼$ and $𝛽$ are the irrational roots of the equation $3 𝑝^{2} 𝑥^{3} + 𝑝 𝑥^{2} + 𝑞 𝑥 + 3 = 0$ when $𝑝 = 1$ and $𝑞 = - 7$ , then $| 𝛼 - 𝛽 | =$

$\frac{3 \sqrt{\sqrt 13}}{2}$

Incorrect

$\frac{\sqrt{\sqrt 3}}{2}$

Incorrect

$\frac{2 \sqrt{\sqrt 13}}{3}$

Incorrect

4

Incorrect

Q 15MathematicsSection A • MCQquadratic equations

+1 / -0

The roots of a cubic equation $𝑓 (𝑥) = 0$ are diminished by $\frac{- 3}{2}$ so, as to remove the term containing $𝑥^{2}$ and the transformed equation is $8 𝑥^{3} - 54 𝑥 - 78 = 0$ . Then, the equation $𝑓 (𝑥) = 0$ is

$2 𝑥^{3} - 9 𝑥^{2} - 6 = 0$

Incorrect

$2 𝑥^{3} - 9 𝑥^{2} - 27 𝑥 - 6 = 0$

Incorrect

$8 𝑥^{3} + 3 𝑥^{2} - 6 = 0$

Incorrect

$8 𝑥^{3} - 9 𝑥^{2} + 12 𝑥 - 15 = 0$

Incorrect

Q 16MathematicsSection A • MCQpermutations and combinations

+1 / -0

If $^{𝑚} 𝑃_{𝑟} -^{(𝑚 - 1)} 𝑝_{𝑟} = 𝑎 \cdot^{(𝑚 - 1)} 𝑃_{𝑠}$ , then $𝑎 - 𝑠 =$

1

Incorrect

0

Incorrect

$𝑚 - 1$

Incorrect

$𝑚 - 𝑟$

Incorrect

Q 17MathematicsSection A • MCQpermutations and combinations

+1 / -0

The total number of ways of selecting 4 letters from all the letters of the word TSEAMCET is

12

Incorrect

13

Incorrect

26

Incorrect

36

Incorrect

Q 18MathematicsSection A • MCQbinomial theorem

+1 / -0

Numerically greatest term in the expansion of $(2 𝑥 - 3 𝑦)^{11}$ when $𝑥 = \frac{1}{3}$ and $𝑦 = \frac{1}{2}$ is

$^{11} 𝐶_{8} {(\frac{2}{3})}^{5}$

Incorrect

$^{11} 𝐶_{3} {(\frac{3}{2})}^{5}$

Incorrect

$^{11} 𝐶_{2} {(\frac{3}{2})}^{7}$

Incorrect

$^{11} 𝐶_{2} {(\frac{2}{3})}^{7}$

Incorrect

Q 19MathematicsSection A • MCQindefinite integration

+1 / -0

If $\frac{𝑥 - 2}{𝑥^{2} (2 𝑥 - 3)} = \frac{𝐴}{𝑥} + \frac{𝐵}{𝑥^{2}} + \frac{𝐶}{2 𝑥 - 3}$ , then $2 (𝐴 - 𝐶) =$

$3 𝐵$

Incorrect

$2 𝐵$

Incorrect

0

Incorrect

$𝐵$

Incorrect

Q 20MathematicsSection A • MCQindefinite integration

+1 / -0

If $\frac{𝑥^{2} - 𝑥 + 1}{(𝑥^{2} + 1) (𝑥^{2} + 𝑥 + 1)} = \frac{𝐴 𝑥 + 𝐵}{𝑥^{2} + 1} + \frac{𝐶 𝑥 + 𝐷}{𝑥^{2} + 𝑥 + 1}$ , then $𝐴 + 2 𝐵 + 𝐶 + 2 𝐷 =$

0

Incorrect

1

Incorrect

-1

Incorrect

2

Incorrect

Q 21MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\sin 𝐴 = \frac{- 7}{25}, \cos 𝐵 = \frac{8}{17}, 𝐴$ does not lie in the 3rd quadrant and $𝐵$ does not lie in the 1st quadrant, then $8 \tan 𝐴 - 5 \cot 𝐵 =$

0

Incorrect

$\frac{1}{3}$

Incorrect

$\frac{1}{2}$

Incorrect

1

Incorrect

Q 22MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\sin 𝜃 - \cos 𝜃 = \frac{1}{\sqrt{\sqrt 3}}$ , then $\sin (2 𝜃) + \cos (4 𝜃) + \sin (6 𝜃) =$

$\frac{37}{27}$

Incorrect

$\frac{- 37}{27}$

Incorrect

$\frac{- 43}{27}$

Incorrect

$\frac{43}{27}$

Incorrect

Q 23MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $𝑎 \tan 𝛼 + 𝑏 \tan 𝛽 = (𝑎 + 𝑏) \tan (\frac{𝛼 + 𝛽}{2})$ and $𝛼 - 𝛽 \neq 2 𝑛 𝜋$ then $\frac{\cos 𝛽}{\cos 𝛼} =$

$\frac{𝑎}{𝑏}$

Incorrect

$\frac{𝑎 + 𝑏}{𝑎 - 𝑏}$

Incorrect

$\frac{𝑎^{2} - 𝑏^{2}}{𝑎^{2} + 𝑏^{2}}$

Incorrect

$\frac{𝑏}{𝑎}$

Incorrect

Q 24MathematicsSection A • MCQfunctions

+1 / -0

Assertion (A) $\coth 𝑥 = \frac{1 - 𝑘}{1 + 𝑘} (0 < 𝑘 < 2)$ .

Reason (R) The graph of $𝑦 = \tanh 𝑥$ always lies between the lines $𝑦 = - 1$ and $𝑦 = 1$

The correct option among the following is

(A) is true, (R) is true and (R) is the correct explanation for (A).

Incorrect

(A) is true, (R) is true but (R) is not the correct explanation for (A).

Incorrect

(A) is true but (R) is false.

Incorrect

(A) is false but (R) is true.

Incorrect

Q 25MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\frac{5 \sinh 2 𝑥}{7 + 6 \cosh 2 𝑥} = \frac{3}{2}$ , then $3 \tanh^{2} 𝑥 + 20 \tanh 𝑥 =$

13

Incorrect

26

Incorrect

39

Incorrect

$\frac{13}{2}$

Incorrect

Q 26MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $𝑎 = 7, 𝑏 = 8, \tan 𝐶 = \frac{3 \sqrt{\sqrt 5}}{2}$ and $𝐶$ is an acute angle, then $𝑐 =$

$\sqrt{\sqrt 145}$

Incorrect

5

Incorrect

11

Incorrect

9

Incorrect

Q 27MathematicsSection A • MCQproperties of triangles

+1 / -0

In a $△ 𝐴 𝐵 𝐶$ , if $\frac{𝑎}{\tan 𝐴} = \frac{𝑏}{\tan 𝐵} = \frac{𝑐}{\tan 𝐶}$ , then $\cos^{2} 𝐴 + \cos^{2} 𝐵 + \cos^{2} 𝐶 =$

$\sqrt{\sqrt 2}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{\sqrt{\sqrt 3} + 1}{2}$

Incorrect

$\frac{2 \sqrt{\sqrt 3} - 1}{2}$

Incorrect

Q 28MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $𝑎 = 7, 𝑏 = 10$ and $𝑐 = 11$ , then $\frac{𝑅}{𝑟} =$

14

Incorrect

77

Incorrect

$\frac{24}{11}$

Incorrect

$\frac{55}{24}$

Incorrect

Q 29MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐴 𝐵 𝐶$ be a triangle and $𝐚, 𝐛$ and $𝐜$ be the position vectors of $𝐴, 𝐵$ and $𝐶$ , respectively. Let $𝐷$ divides $𝐵 𝐶$ in the ratio $3 : 1$ internally and $𝐸$ divides $𝐴 𝐷$ in the ratio $4 : 1$ internally. Let $𝐵 𝐸$ meet $𝐴 𝐶$ in $𝐹$ . If $𝐸$ divides $𝐵 𝐹$ in the ratio $3 : 2$ internally, then the position vector of $𝐹$ is

$\frac{𝐚 + 𝐛 + 𝐜}{3}$

Incorrect

$\frac{𝐚 - 2 𝐛 + 3 𝐜}{2}$

Incorrect

$\frac{𝐚 + 2 𝐛 + 3 𝐜}{2}$

Incorrect

$\frac{𝐚 - 𝐛 + 3 𝐜}{3}$

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

If $𝛼, 𝛽$ and $𝛾$ are real numebrs such that

$\begin{matrix} (\frac{7}{3} + 𝛽) \hat{𝐢} - \hat{𝐣} + (𝛼 + 𝛾) \hat{𝐤} \\ = \frac{5}{3} (𝛼 \hat{𝐢} + \hat{𝐣} - \hat{𝐤}) + 𝛽 (2 \hat{𝐣} + \hat{𝐤}) + (\hat{𝐢} + 𝛾 \hat{𝐣} + 3 \hat{𝐤}), then \\ 5 𝛼 - 9 𝛽 + 13 𝛾 = \end{matrix}$

4

Incorrect

12

Incorrect

0

Incorrect

15

Incorrect

Q 31MathematicsSection A • MCQ3d geometry

+1 / -0

If $𝐫 = (2 - 𝜆 + 𝜇) \hat{𝐢} + (1 - 𝜇) \hat{𝐣} + (2 - 3 𝜆 + 2 𝜇) \hat{𝐤}$ is the vector equation of a plane, then the equivalent cartesian equation of the plane is

$3 𝑥 + 𝑦 - 𝑧 = 5$

Incorrect

$3 𝑥 - 𝑦 + 𝑧 = 5$

Incorrect

$- 3 𝑥 + 𝑦 + 𝑧 = 5$

Incorrect

$3 𝑥 - 𝑦 - 𝑧 = 5$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚 = 2 \hat{𝐢} + \hat{𝐣} - \hat{𝐤}, 𝐛 = \hat{𝐢} - \hat{𝐣} + 3 \hat{𝐤}, 𝐱 = (\frac{𝐚 𝐛}{| 𝐛 |^{2}}) 𝐛, 𝐲 = (\frac{𝐚 𝐛}{| 𝐚 |^{2}}) 𝐚$ and $𝜃$ is angle between $𝐚$ and $𝐛$ , then $𝑥^{2} + 𝑦^{2} =$

$17 \cos^{2} 𝜃$

Incorrect

$(\sqrt{\sqrt 6} + \sqrt{\sqrt 11}) \cos^{2} 𝜃$

Incorrect

$17 \cos 2 𝜃$

Incorrect

$17 \sin^{2} 𝜃$

Incorrect

Q 33MathematicsSection A • MCQ3d geometry

+1 / -0

Let $𝜋_{1}$ be a plane passing through the point $\hat{𝐢} + \hat{𝐣} + \hat{𝐤}$ and perpendicular to the vector $- \hat{𝐣} + 2 \hat{𝐤}$ . Let the line $𝐿$ passing through the points $3 \hat{𝐢} - 2 \hat{𝐣} + \hat{𝐤}$ and $- \hat{𝐢} + 3 \hat{𝐣} + \hat{𝐤}$ be a normal to the plane $𝜋_{2}$ . If the angle between the planes $𝜋_{1}$ and $𝜋_{2}$ is $𝜃$ , then $\cos 𝜃 =$

$\sqrt{\sqrt \frac{5}{41}}$

Incorrect

$\frac{- 14}{\sqrt{\sqrt 205}}$

Incorrect

$\frac{𝜋}{4}$

Incorrect

$\frac{𝜋}{2}$

Incorrect

Q 34MathematicsSection A • MCQvector algebra

+1 / -0

Three non-coplanar vectors $𝐚, 𝐛$ and $𝐜$ are the coterminous edges of a parallelopiped. If $𝐚$ and $𝐛$ determine the base of the parallelopiped, then its height is

$\frac{| [abc] |}{| b \times c |}$

Incorrect

$\frac{| [abc] |}{| a \times b |}$

Incorrect

$\frac{| [abc] |}{| a \times c |}$

Incorrect

$\frac{| [abc] |}{| b + c |}$

Incorrect

Q 35MathematicsSection A • MCQstatistics

+1 / -0

Statement I The range of the ungrouped data does not change even if certain intermediate observations are removed

Statement II The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency

Statement III For a grouped data, range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class

Statements I and II are true but Statement III is false

Incorrect

Statements II and III are true but Statement I is false

Incorrect

Statement III and I are true but Statement II is false

Incorrect

Statements I, II and III are true

Incorrect

Q 36MathematicsSection A • MCQprobability

+1 / -0

The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of 52 playing card is

$\frac{1}{26}$

Incorrect

$\frac{8}{221}$

Incorrect

$\frac{2}{51}$

Incorrect

$\frac{1}{52}$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

Two cards are drawn from a pack of 52 playing cards one after the other. If $𝑝_{1}$ is the probability of getting a queen in the first draw and a diamond card in the second draw when the first card drawn is replaced and $𝑝_{2}$ is the probability of the same event when the first card drawn is not replaced. Then $\frac{𝑝_{1}}{𝑝_{2}} =$

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

Bag $𝐴$ contains 4 white and 2 black balls, bag $𝐵$ contains 3 white and 3 black balls and bag $𝐶$ contains 2 white and 4 black balls. If a bag is chosen at random and a ball is chosen at random from it, then the probability that the ball drawn is black is

$\frac{1}{3}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{1}{2}$

Incorrect

$\frac{2}{3}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

A random variable $𝑋$ has the following probability distribution

$\begin{matrix} 𝑋 = 𝐱_{𝑖} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 𝑃 (𝑋 = 𝐱_{𝑖}) & 10 𝑘 & 9 𝑘 & 8 𝑘 & 8 𝑘 & 6 𝑘 & 5 𝑘 & 4 𝑘 & 3 𝑘 & 𝑘 \end{matrix}$

where $𝑘$ is a real number.

If $𝐴 = {𝑥_{𝑖} ∣ 𝑥_{𝑖}$ is a prime number $}$ and $𝐵 = {𝑥_{𝑖} ∣ 𝑥_{𝑖} > 5}$ are two events, then $𝑃 (𝐴 \cup 𝐵) =$

$\frac{2}{3}$

Incorrect

$\frac{4}{9}$

Incorrect

$\frac{1}{27}$

Incorrect

$\frac{5}{6}$

Incorrect

Q 40MathematicsSection A • MCQprobability

+1 / -0

If $𝑋$ is a Poisson variate such that $\frac{5}{3} 𝑘 = 𝑃 (𝑋 = 2) = 𝑃 (𝑋 = 3)$ , then $𝑃 (𝑋 = 5) =$

$𝑘$

Incorrect

$\frac{1}{4} 𝑘$

Incorrect

$\frac{1}{2} 𝑘$

Incorrect

$\frac{3}{4} 𝑘$

Incorrect

Q 41MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

$𝐴 (- 4, 0)$ and $𝐵 (4, 0)$ are two fixed points. $𝐶$ and $𝐷$ are two points on $𝑌$ - axis such that $𝐶 𝐷 = 4$ and $𝐶$ is a point below $𝐷$ . Then, the locus of the point of intersection of the lines $𝐴 𝐶$ and $𝐵 𝐷$ is

$𝑥^{2} - 𝑦^{2} - 𝑥 𝑦 = 0$

Incorrect

$𝑥^{2} + 2 𝑥 𝑦 - 16 = 0$

Incorrect

$(𝑥 + 𝑦)^{2} - 16 = 0$

Incorrect

$2 𝑥 𝑦 = 16 + 𝑦^{2} + 𝑥^{2}$

Incorrect

Q 42MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

By rotating the axes through an angle of $30^{\circ}$ in the anti-clockwise direction about the origin, the equation $4 𝑥^{2} + 12 𝑥 𝑦 + 9 𝑦^{2} + 6 𝑥 + 9 𝑦 + 2 = 0$ becomes $𝑎 𝑥^{2} + 2 ℎ 𝑥 𝑦 + 𝑏 𝑦^{2} + 2 𝑔 𝑥 + 2 𝑓 𝑦 + 𝑐 = 0$ becomes, then

$𝑎 = 21 - 6 \sqrt{\sqrt 3}$

Incorrect

$𝑔 / 𝑓 = \frac{3 + 2 \sqrt{\sqrt 3}}{3 \sqrt{\sqrt 3} - 2}$

Incorrect

$𝑏 = 31 + 6 \sqrt{\sqrt 3}$

Incorrect

$𝑐 = 6$

Incorrect

Q 43MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

In an isosceles triangle the ends of its base are $(2 𝑎, 0), (0, 𝑎)$ and one of its two other sides is a horizontal line other than $𝑋$ -axis. If the third vertex is $(𝑥_{1}, 𝑦_{1})$ , then $𝑥_{1} + 𝑦_{1} =$

$\frac{9 𝑎}{2}$

Incorrect

$3 𝑎$

Incorrect

$\frac{9 𝑎}{4}$

Incorrect

$5 𝑎$

Incorrect

Q 44MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

If the lines $𝐿_{1} \equiv 𝑥 - 2 𝑦 + 3 = 0, 𝐿_{2} \equiv 2 𝑥 + 𝑦 + 1 = 0$ and $𝐿_{3} \equiv 3 𝑥 + 𝑦 + 𝑐 = 0$ are concurrent and $𝜃$ is the acute angle between the lines $𝐿_{1} = 0$ and $𝐿_{3} = 0$ , then $\tan 𝜃 =$

$𝑐 + 2$

Incorrect

$𝑐 - 5$

Incorrect

$𝑐 + 5$

Incorrect

$c - 2$

Incorrect

Q 45MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

If the lengths of the perpendiculars drawn from a point $(𝑎, 𝑏)$ to the lines $2 𝑥 + 3 𝑦 + 4 = 0$ and $3 𝑥 - 2 𝑦 + 4 = 0$ are same, then the point $(𝑎, 𝑏)$ lies on the line

$𝑥 - 5 𝑦 + 8 = 0$ or $5 𝑥 + 𝑦 = 0$

Incorrect

$𝑥 + 5 𝑦 + 8 = 0$ or $5 𝑥 - 𝑦 + 8 = 0$

Incorrect

$𝑥 - 5 𝑦 = 0$ or $5 𝑥 + 𝑦 + 8 = 0$

Incorrect

$𝑥 + 5 𝑦 = 0$ or $5 𝑥 - 𝑦 + 8 = 0$

Incorrect

Q 46MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

If $3 𝑥 + 6 𝑦 + 2 = 0, 𝑥 + 𝑦 + 1 = 0, 2 𝑥 - 𝑦 + 3 = 0$ are three given lines, then the point $(\frac{- 4}{3}, \frac{1}{3})$ is

the orthocentre of the triangle formed by the lines

Incorrect

the point of concurrence of the lines

Incorrect

the circumcentre of the triangle formed by the lines

Incorrect

the incentre of the triangle formed by the lines

Incorrect

Q 47MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

If $𝜃$ is the acute angle between the pair of lines $12 𝑥^{2} + 2 ℎ 𝑥 𝑦 + 7 𝑦^{2} = 0$ and $\tan 𝜃 = \frac{8}{19}$ , then $ℎ =$

$\pm 6$

Incorrect

$\pm 7$

Incorrect

$\pm 8$

Incorrect

$\pm 10$

Incorrect

Q 48MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

The number of real values of $𝛼$ for which the pair of lines represented by $(𝛼^{2} + 12 | 𝛼 |) 𝑥^{2} + 6 𝑥 𝑦 + (18 - 21 | 𝛼 |) 𝑦^{2} = 0$ are at right angles to each other, is

0

Incorrect

1

Incorrect

2

Incorrect

4

Incorrect

Q 49MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

The line $𝑥 + 2 𝑦 - 𝑐 = 0$ meets the curve $𝑥^{2} + 𝑦^{2} - 3 𝑥 - 6 𝑦 + 3 = 0$ at two points $𝑃$ and $𝑄$ and $∠ 𝑃 𝑂 𝑄 = \frac{𝜋}{2}$ , where $𝑂$ is the origin. Then, $2 𝑐^{2} - 15 𝑐 =$

15

Incorrect

-15

Incorrect

2

Incorrect

-2

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

The line $4 𝑥 + 3 𝑦 - 4 = 0$ divides the circumference of a circle in the ratio $1 : 2$ . If $𝐶 (5, 3)$ is the centre of that circle, then equation of the circle is

$(𝑥 - 5)^{2} + (𝑦 - 3)^{2} = (10)^{2}$

Incorrect

$(𝑥 - 5)^{2} + (𝑦 - 3)^{2} = (12)^{2}$

Incorrect

$(𝑥 - 5)^{2} + (𝑦 - 3)^{2} = 7^{2}$

Incorrect

$(𝑥 - 5)^{2} + (𝑦 - 3)^{2} = 8^{2}$

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

Two sides of a square are along the lines $𝑥 = - 5$ and $𝑦 = 4$ . The point of intersection of the diagonals is $(3, - 4)$ . The point of intersection of the tangents drawn to the circumcircle of the square at the two consecutive vertices lying on $𝑥 = - 5$ is

$(- 4, - 4)$

Incorrect

$(- 13, - 4)$

Incorrect

$(- 4, - 13)$

Incorrect

$(- 4, - 10)$

Incorrect

Q 52MathematicsSection A • MCQcircle

+1 / -0

If $𝐿_{1}, 𝐿_{2}$ and $𝐿_{3}$ are the chords of contact of the three points $(2, 0), (1, - 2)$ and $(4, 4)$ respectively with respect to the circle $𝑥^{2} + 𝑦^{2} = 3$ , then $𝐿_{1}, 𝐿_{2}$ and $𝐿_{3}$ are

concurrent lines

Incorrect

sides of a right-angled triangle

Incorrect

sides of an equilateral triangle

Incorrect

parallel lines

Incorrect

Q 53MathematicsSection A • MCQcircle

+1 / -0

The combined equation of the direct common tangents of the circles $𝑥^{2} + 𝑦^{2} + 2 𝑥 = 0$ and $𝑥^{2} + 𝑦^{2} - 2 𝑦 - 3 = 0$

$𝑥 𝑦 + 𝑥 + 2 𝑦 + 2 = 0$

Incorrect

$𝑥^{2} - 𝑥 𝑦 - 2 𝑦^{2} + 3 𝑥 - 6 𝑦 = 0$

Incorrect

$2 𝑥^{2} + 5 𝑥 𝑦 + 2 𝑦^{2} + 13 𝑥 + 14 𝑦 + 20 = 0$

Incorrect

$2 𝑥^{2} - 9 𝑥 𝑦 + 9 𝑦^{2} + 3 𝑥 - 6 𝑦 + 1 = 0$

Incorrect

Q 54MathematicsSection A • MCQcircle

+1 / -0

If $(ℎ, 𝑘)$ is the centre of the circle which passes through the origin and cuts the circles $𝑥^{2} + 𝑦^{2} + 4 𝑥 + 6 𝑦 + 12 = 0$ and $𝑥^{2} + 𝑦^{2} + 4 𝑥 - 6 𝑦 + 9 = 0$ orthogonally, then $𝑘 - 2 ℎ =$

0

Incorrect

1

Incorrect

-1

Incorrect

5

Incorrect

Q 55MathematicsSection A • MCQcircle

+1 / -0

If $(- 1, - 1)$ is the radical centre of the circles $𝑥^{2} + 𝑦^{2} + 2 𝑔 𝑥 - 4 𝑦 + 4 = 0, 𝑥^{2} + 𝑦^{2} + 6 𝑥 + 2 𝑓 𝑦 + 12 = 0$ and $𝑥^{2} + 𝑦^{2} + 10 𝑦 + 20 = 0$ , then $𝑔 - 𝑓 =$

0

Incorrect

-1

Incorrect

1

Incorrect

2

Incorrect

Q 56MathematicsSection A • MCQparabola

+1 / -0

The equation of the given curve is $𝑥^{2} - 4 𝑥 + 4 𝑦 - 8 = 0$ . Match the following

$\begin{matrix} List I & List II \\ (A) & Focus & (I) (4, 2) \\ (B) & Vertex & (II) (3, 2) \\ (C) & \begin{matrix} One end of the \\ latusrectum \end{matrix} & (III) (2, 3) \\ (D) & \begin{matrix} point of intersection of the \\ axis and directrix \end{matrix} & (IV) (2, 4) \\ (V) (2, 2) \end{matrix}$

$The correct match is$

A	B	C	D
II	III	I	IV

Incorrect

A	B	C	D
IV	III	I	V

Incorrect

A	B	C	D
V	III	IV	I

Incorrect

A	B	C	D
V	III	I	IV

Incorrect

Q 57MathematicsSection A • MCQparabola

+1 / -0

If one end of a focal chord of the parabola $𝑦^{2} = \frac{8}{𝑎} \times (𝑎 > 0)$ is at $(1, 4)$ , then the length of this focal chord is

$\frac{25}{8}$

Incorrect

$\frac{25}{2}$

Incorrect

$\frac{25}{4}$

Incorrect

25

Incorrect

Q 58MathematicsSection A • MCQellipse

+1 / -0

If $𝑚$ is the length of the latusrectum and $𝑛$ is the length of the major-axis of the ellipse $25 𝑥^{2} + 16 𝑦^{2} - 150 𝑥 - 64 𝑦 - 111 = 0$ , then the ordered pair $(𝑚, 𝑛) =$

$(\frac{16}{5}, 10)$

Incorrect

$(\frac{32}{5}, 10)$

Incorrect

$(\frac{25}{2}, 8)$

Incorrect

$(\frac{25}{4}, 8)$

Incorrect

Q 59MathematicsSection A • MCQellipse

+1 / -0

If $𝑃 (𝜃)$ and $𝑄 (\frac{𝜋}{2} + 𝜃)$ are two points on the ellipse $\frac{𝑥^{2}}{𝑎^{2}} + \frac{𝑦^{2}}{𝑏^{2}} = 1$ and the locus of mid-point of $𝑃 𝑄$ is $\frac{𝑥^{2}}{𝛼^{2}} + \frac{𝑦^{2}}{𝛽^{2}} = 1$ , then $\frac{𝑎 + 𝑏}{𝛼 + 𝛽} =$

$\frac{1}{\sqrt{\sqrt 2}}$

Incorrect

$\sqrt{\sqrt 3}$

Incorrect

$\frac{1}{\sqrt{\sqrt 3}}$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

Q 60MathematicsSection A • MCQhyperbola

+1 / -0

Let $𝑆$ be the focus of the hyperbola $𝑥^{2} - 2 𝑦^{2} = 1$ lying on the positive $𝑋$ -axis. Let $𝑃 (- 1, 1)$ be a given point. Then, the area of the triangle formed by the line $𝑃 𝑆$ with the coordinate axes is (in sq. units)

$\frac{\sqrt{\sqrt 2}}{2 (\sqrt{\sqrt 2} + 3)}$

Incorrect

$\frac{\sqrt{\sqrt 6}}{2 (2 + \sqrt{\sqrt 6})}$

Incorrect

$\frac{3}{2 (2 + \sqrt{\sqrt 6})}$

Incorrect

$\frac{\sqrt{\sqrt 3}}{2 (\sqrt{\sqrt 2} + \sqrt{\sqrt 3})}$

Incorrect

Q 61MathematicsSection A • MCQhyperbola

+1 / -0

If $𝑃 (\frac{𝜋}{6})$ is a point on the hyperbola $\frac{𝑥^{2}}{𝑎^{2}} - \frac{𝑦^{2}}{𝑏^{2}} = 1, 𝑆, 𝑆$ are its foci and $𝑆 𝑃 + 𝑆 𝑃 = 2 | 𝑆 𝑃 - 𝑆 𝑃$ |, then $𝑒 =$

$\sqrt{\sqrt 2}$

Incorrect

2

Incorrect

$\sqrt{\sqrt 3}$

Incorrect

3

Incorrect

Q 62MathematicsSection A • MCQ3d geometry

+1 / -0

Let $𝐴 = (1, 2, 0), 𝐵 = (2, 0, - 1), 𝐶 = (0, - 2, 3)$ and $𝐷 = (- 1, 2, - 3)$ be four points in the space. Let $𝐺_{1}$ be the centroid of $△ 𝐴 𝐵 𝐶$ and $𝐺_{2}$ be the centroid of tetrahedron $𝐴 𝐵 𝐶 𝐷$ . If $𝑃$ divides, $𝐺_{1} 𝐺_{2}$ in the ratio $4 : 3$ internally, then $𝑃 =$

$(\frac{5}{7}, \frac{2}{7}, \frac{1}{7})$

Incorrect

$(\frac{1}{7}, \frac{2}{7}, \frac{3}{7})$

Incorrect

$(\frac{4}{7}, \frac{- 2}{7}, \frac{1}{7})$

Incorrect

$(\frac{1}{7}, \frac{- 3}{7}, \frac{5}{7})$

Incorrect

Q 63MathematicsSection A • MCQ3d geometry

+1 / -0

If the d.r.'s of two lines are connected by the relations $𝑎 - 𝑏 + 𝑐 = 0, 𝑎^{2} - 𝑏^{2} + 2 𝑐^{2} = 0$ and $𝜃$ is the angle between these lines, then $\cos 𝜃 =$

$\frac{2}{\sqrt{\sqrt 7}}$

Incorrect

$\frac{3}{2 \sqrt{\sqrt 7}}$

Incorrect

$\frac{3}{4 \sqrt{\sqrt 2}}$

Incorrect

$\frac{1}{3 \sqrt{\sqrt 2}}$

Incorrect

Official Correct Answer:Option (A)

Step-by-Step Solution:

Given, $𝑎 - 𝑏 + 𝑐 = 0$

$\begin{matrix} \Rightarrow & 𝑏 = 𝑎 + 𝑐 . . . (𝑖) \\ and & 𝑎^{2} - 𝑏^{2} + 2 𝑐^{2} = 0 \\ \Rightarrow & 𝑎^{2} - (𝑎 + 𝑐)^{2} + 2 𝑐^{2} = 0 \end{matrix}$

[using Eq. (i)]

$\begin{matrix} \Rightarrow & 𝑎^{2} - 𝑎^{2} - 𝑐^{2} - 2 𝑎 𝑐 + 2 𝑐^{2} = 0 \\ \Rightarrow & 𝑐^{2} - 2 𝑎 𝑐 = 0 \\ \Rightarrow & 𝑐 (𝑐 - 2 𝑎) = 0 \\ \Rightarrow & 𝑐 = 0 or 𝑐 = 2 𝑎 \end{matrix}$

When $𝑐 = 0$ , then $𝑏 = 𝑎$ and when $𝑐 = 2 𝑎$ , then $𝑏 = 3 𝑎$

$\begin{matrix} 𝑎 = 𝑎, 𝑏 = 𝑎, 𝑐 = 0 \\ \frac{𝑎}{𝑎} = \frac{𝑏}{𝑎} = \frac{𝑐}{0} \dots (ii) \end{matrix}$	$\begin{matrix} 𝑎 = 𝑎, 𝑏 = 3 𝑎, 𝑐 = 2 𝑎 \\ \frac{𝑎}{𝑎} = \frac{𝑏}{3 𝑎} = \frac{𝑐}{2 𝑎} \dots (iii) \end{matrix}$

∴ Direction ratios of Eq. (ii) are $(1, 1, 0)$ and direction ratios of (iii) are ( $1, 3, 2$ ).

$\begin{matrix} ∴ \cos 𝜃 & = \frac{1 \times 1 + 1 \times 3 + 0 \times 2}{\sqrt{\sqrt 1^{1} + 1^{2} + 0} \sqrt{\sqrt 1^{2} + 3^{2} + 2^{2}}} \\ = \frac{4}{\sqrt{\sqrt 2} \sqrt{\sqrt 14}} = \frac{2}{\sqrt{\sqrt 7}} \end{matrix}$

Q 64MathematicsSection A • MCQ3d geometry

+1 / -0

If $𝑙, 𝑚$ and $𝑛$ are the d.c.'s of a normal to the plane passing through the points $(0, 1, 2)$ , $(3, 0, 2)$ and $(4, 5, 0)$ , then $| 𝐼 | + | 𝑚 | + | 𝑛 | =$

$\frac{13}{\sqrt{\sqrt 91}}$

Incorrect

$\frac{11}{\sqrt{\sqrt 57}}$

Incorrect

$\frac{13}{\sqrt{\sqrt 77}}$

Incorrect

$\frac{12}{\sqrt{\sqrt 74}}$

Incorrect

Q 65MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

$lim_{𝑥 \to 2} \frac{𝑥^{3} - 𝑥^{2} - 𝑥 - 2}{2 𝑥^{3} - 3 𝑥^{2} - 3 𝑥 + 2} =$

0

Incorrect

$\infty$

Incorrect

$\frac{5}{7}$

Incorrect

$\frac{7}{9}$

Incorrect

Q 66MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

$lim_{𝑥 \to 0} \frac{4 [\sin (2022 𝑥) - \sin (2020 𝑥)]}{𝑥 [\cos (2022 𝑥) + 2 \cos (2021 𝑥) + \cos (2020 𝑥)]} =$

1

Incorrect

2

Incorrect

2020

Incorrect

2021

Incorrect

Q 67MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑓 (𝑥) = \sum_{7}^{𝑝 = 1} 𝑝^{2} \sin^{- 1} (\frac{4}{5} \sin (𝑝 𝑥) - \frac{3}{5} \cos (𝑝 𝑥))$ , then the value of $\frac{𝑑 𝑓}{𝑑 𝑥}$ at $𝑥 = 1$ is [given that $\sin^{- 1} (\sin 𝑥) = 𝑥$ ])

0

Incorrect

628

Incorrect

1140

Incorrect

784

Incorrect

Q 68MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑦 = \frac{𝑎 𝑥 + 𝑏}{𝑐 𝑥 + 𝑑}$ , then $\frac{𝑑 𝑥}{𝑑 𝑦} =$

$\frac{𝑎 𝑑 - 𝑏 𝑐}{(𝑎 𝑥 + 𝑏)^{2}}$

Incorrect

$\frac{𝑎 𝑑 - 𝑏 𝑐}{(𝑎 - 𝑐 𝑦)^{2}}$

Incorrect

$\frac{𝑎 𝑑 + 𝑏 𝑐}{(𝑐 𝑥 + 𝑑)^{2}}$

Incorrect

$\frac{𝑎 𝑑 + 𝑏 𝑐}{(𝑎 + 𝑐 𝑦)^{2}}$

Incorrect

Q 69MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑥^{2} + 𝑦^{2} = 𝑡 - \frac{1}{𝑡}, 𝑥^{4} + 𝑦^{4} = 𝑡^{2} + \frac{1}{𝑡^{2}}$ , then $\frac{𝑑 𝑦}{𝑑 𝑥} =$

$\frac{𝑥}{𝑦}$

Incorrect

$\frac{- 𝑥}{𝑦}$

Incorrect

$\frac{𝑦}{𝑥}$

Incorrect

$\frac{- 𝑦}{𝑥}$

Incorrect

Q 70MathematicsSection A • MCQapplication of derivatives

+1 / -0

The equation of the tangent to the curve $𝑥^{2} + 𝑦 - 7 = 4 𝑥$ at the point $(1, 10)$ is

$𝑦 = 2 𝑥 + 8$

Incorrect

$𝑦 = 𝑥 + 8$

Incorrect

$𝑦 = - 2 𝑥 - 14$

Incorrect

$𝑦 = 𝑥 - 4$

Incorrect

Q 71MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝜃$ is the angle between the curves $𝑥^{2} - 𝑦^{2} = 4$ and $𝑦^{2} = 3 𝑥$ , then $\tan 𝜃 =$

$\frac{5}{3 \sqrt{\sqrt 3}}$

Incorrect

$\frac{5}{6 \sqrt{\sqrt 3}}$

Incorrect

$\frac{5}{18}$

Incorrect

$\frac{5}{6}$

Incorrect

Q 72MathematicsSection A • MCQapplication of derivatives

+1 / -0

The absolute maximum value of the function $𝑓 (𝑥) = 2 𝑥^{3} - 3 𝑥^{2} - 36 𝑥 + 9$ defined on $[- 3, 3]$ is

36

Incorrect

53

Incorrect

63

Incorrect

72

Incorrect

Q 73MathematicsSection A • MCQindefinite integration

+1 / -0

If $𝑓 (𝑥) = \int \frac{2 - 3 \sin^{2} 𝑥}{1 + \cos 2 𝑥} 𝑑 𝑥$ and $𝑓 (\frac{𝜋}{4}) = 1$ , then $𝑓 (0) =$

$\frac{3}{8} (4 - 𝜋)$

Incorrect

$3 - \frac{𝜋}{4}$

Incorrect

0

Incorrect

1

Incorrect

Q 74MathematicsSection A • MCQindefinite integration

+1 / -0

If $𝑥 \neq (2 𝑛 + 1) \frac{𝜋}{2}, 𝑛 \in 𝑍$ and $\cos 𝑥 \neq \frac{- 1}{2}$ , then

$\int {(\frac{\sin 𝑥 + \sin 2 𝑥}{1 + \cos 𝑥 + \cos 2 𝑥})}^{2} 𝑑 𝑥 =$

$\frac{\tan^{3} 𝑥}{3} - 𝑥 + 𝑐$

Incorrect

$\frac{\sec^{3} 𝑥}{3} - 𝑥 + 𝑐$

Incorrect

$\cot 𝑥 - 𝑥 + 𝑐$

Incorrect

$\tan 𝑥 - 𝑥 + 𝑐$

Incorrect

Q 75MathematicsSection A • MCQindefinite integration

+1 / -0

Given that $\int \frac{1}{𝑥^{2} + 𝑎^{2}} 𝑑 𝑥 = \frac{1}{𝑎} \tan^{- 1} (\frac{𝑥}{𝑎}) + 𝑐$ .

$\begin{matrix} If \int \frac{1}{𝑥^{4} + 3 𝑥^{2} + 1} 𝑑 𝑥 = 𝑎 \tan^{- 1} (\frac{𝑏 (𝑥^{2} - 1)}{𝑥}) \\ + 𝑐 \tan^{- 1} (\frac{𝑑 (𝑥^{2} + 1)}{𝑥}) + 𝑘 \end{matrix}$

where $𝑘$ is a constant of integration, then $5 (𝑐 + 𝑑 + 𝑎 𝑏) =$

3

Incorrect

5

Incorrect

8

Incorrect

10

Incorrect

Q 76MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{4}^{0} | | 𝑥 - 2 | - 𝑥 | 𝑑 𝑥 =$

2

Incorrect

3

Incorrect

6

Incorrect

12

Incorrect

Q 77MathematicsSection A • MCQdefinite integration

+1 / -0

If $\int_{𝑎}^{- 𝑎} 𝑓 (𝑥) 𝑑 𝑥 = \int_{𝑎}^{0} 𝑓 (𝑥) 𝑑 𝑥 + \int_{𝑎}^{0} 𝑔 (𝑥) 𝑑 𝑥$ , then $𝑔 (𝑥) =$

$- 𝑓 (𝑥)$

Incorrect

$𝑓 (𝑥)$

Incorrect

$𝑓 (- 𝑥)$

Incorrect

$𝑓 (𝑥) + 𝑓 (- 𝑥)$ .

Incorrect

Q 78MathematicsSection A • MCQdifferential equations

+1 / -0

$𝑓 (𝑥, 𝑦, 𝑐_{1}, 𝑐_{2}) = 0$ is an equation containing two arbitrary constants $𝑐_{1}$ and $𝑐_{2}$ . If the differential equation having $𝑓 (𝑥, 𝑦, 𝑐_{1}, 𝑐_{2}) = 0$ as its general solution is of $𝑘$ th order, then the differential equation corresponding to $𝑥^{𝑘} + 𝑦^{𝑘} = 𝑐^{2}$ ( $𝑐$ is an arbitrary constant) is

$\frac{𝑑 𝑦}{𝑑 𝑥} + \frac{𝑥}{𝑦} = 0$

Incorrect

$\frac{𝑑 𝑦}{𝑑 𝑥} + \frac{𝑦}{𝑥} = 0$

Incorrect

$\frac{𝑑 𝑦}{𝑑 𝑥} - \frac{𝑥}{𝑦} = 0$

Incorrect

$\frac{𝑑 𝑦}{𝑑 𝑥} - \frac{𝑦}{𝑥} = 0$

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

If $𝑙$ and $𝑚$ are respectively the order and the degree of the differential equation $𝑓 (𝑥) 𝑦^{''} + 𝑔 (𝑥) 𝑦^{'} = \frac{4 𝑦}{𝑥}$ whose general solution is $𝑦 = 𝑎 𝑥^{2} + 𝑏 𝑥^{2} \log 𝑥$ , then $𝑓 (𝑚) + 𝑔 (𝑚) =$

21

Incorrect

1

Incorrect

$3 𝑚$

Incorrect

$𝐼 + 𝑚$

Incorrect

Q 80MathematicsSection A • MCQdifferential equations

+1 / -0

The general solution of the differential equation $𝑑 𝑥 = (2 𝑥 + 3 𝑦 - 4) 𝑑 𝑦$ is

$2 𝑥 + 6 𝑦 - 3 \log | 4 𝑥 + 6 𝑦 - 5 | = 𝑐$

Incorrect

$6 𝑦 - 3 \log | 4 𝑥 + 6 𝑦 - 5 | = 𝑐$

Incorrect

$2 𝑥 + 6 𝑦 - 8 - 3 \log | 4 𝑥 + 6 𝑦 - 5 | = 𝑐$

Incorrect

$6 𝑥 + 6 𝑦 - 3 \log | 4 𝑥 + 6 𝑦 - 5 | = 𝑐$

Incorrect

Q 81PhysicsSection A • MCQatoms and nuclei

+1 / -0

Among the fundamental forces, which one of the following is the strongest force?

Electromagnetic force

Incorrect

Strong Nuclear force

Incorrect

Gravitational force

Incorrect

Weak nuclear force

Incorrect

Q 82PhysicsSection A • MCQcurrent electricity

+1 / -0

Which of the following is the unit of mobility of a electron in a conductor?

${kg}^{- 1} s^{2} A^{- 1}$

Incorrect

${kg}^{- 1} s^{2} A$

Incorrect

${kg}^{- 1} {ms}^{2} A^{- 1}$

Incorrect

$kg - {ms}^{- 1} A^{- 1}$

Incorrect

Q 83PhysicsSection A • MCQmotion in a straight line

+1 / -0

A car starts at time $𝑡 = 0$ from an initial speed of $10 m / s$ and accelerates uniformly with $2 m / s^{2}$ on a straight road for time $0 \leq 𝑡 \leq 10 s$ . Let $𝑠_{1}$ and $𝑠_{2}$ be the distance covered by the car in time $3 \leq 𝑡 \leq 4 s$ and $4 \leq 𝑡 \leq 5 s$ , respectively. The ratio $\frac{𝑠_{2}}{𝑠_{1}}$ is

1

Incorrect

$\frac{19}{7}$

Incorrect

$\frac{9}{7}$

Incorrect

$\frac{5}{3}$

Incorrect

Q 84PhysicsSection A • MCQmotion in a plane

+1 / -0

Particle $𝐴$ (which was located at the origin at time $𝑡 = 0$ ) is moving along the $𝑋$ -axis with a constant speed of $1 m / s$ . Location of particle $𝐵$ which is moving along the $𝑌$ -axis is given by $𝑦 = 𝑐 𝑡^{2}$ , where $𝑐 = 1 m / s^{2}$ . Find the speed of particle $𝐴$ relative to particle $𝐵$ at $𝑡 = 1 s$

$\sqrt{\sqrt 5} m / s$

Incorrect

$2 m / s$

Incorrect

$1 m / s$

Incorrect

$0 m / s$

Incorrect

Q 85PhysicsSection A • MCQmotion in a plane

+1 / -0

A particle is moving in $𝑋 𝑌$ -plane as $𝐱 = (4 𝑡 + 𝑡^{2}) \hat{𝐢}$ , $𝐲 = (2 𝑡 + \frac{𝑡^{2}}{2}) \hat{𝐣}$ , where $𝐱$ and $𝐲$ are displacements measured along $𝑋$ and $𝑌$ -axes respectively, in metres and $𝑡$ in seconds, What is the velocity of the particle?

$𝐯 = (4 + 𝑡) \hat{𝐢} + (2 + 𝑡) \hat{𝐣} m / s$

Incorrect

$𝐯 = (4 + 2 𝑡) \hat{𝐢} + (2 + 𝑡) \hat{𝐣} m / s$

Incorrect

$𝐯 = (4 + 2 𝑡) \hat{𝐢} + (2 + \frac{𝑡}{2}) \hat{𝐣} m / s$

Incorrect

$𝐯 = (4 + 𝑡) \hat{𝐢} + (2 + \frac{𝑡}{2}) \hat{𝐣} m / s$

Incorrect

Q 86PhysicsSection A • MCQmotion in a plane

+1 / -0

The surface of a hill inclined at an angle $30^{\circ}$ to the horizontal. A stone is thrown from the summit of the hill (point $𝐴$ ) at an initial speed $10 m / s$ at angle $60^{\circ}$ to the vertical. If the stone strikes the hill at point $𝐵$ as shown in the figure, the distance between $𝐴$ and $𝐵$ is (take, $𝑔 = 10 m / s^{2}$ )

qImage--motion-in-a-plane-mechanics-Jeemate

10 m

Incorrect

15 m

Incorrect

20 m

Incorrect

30 m

Incorrect

Q 87PhysicsSection A • MCQcircular motion

+1 / -0

A spherical bob of mass 250 g is attached to the end of a string having length 50 cm . The bob is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is 72 N . The maximum possible value of angular velocity of bob (in $rad / s$ ) is

18

Incorrect

24

Incorrect

28

Incorrect

32

Incorrect

Q 88PhysicsSection A • MCQwork power and energy

+1 / -0

A boat of mass 1000 kg goes from rest to speed 20.0 $m / s$ in 5.0 s . The water exerts a constant drag force and the acceleration of the boat is constant. If the average power required by the boat is 45000 W , then the magnitude of the drag force is

500 N

Incorrect

750 N

Incorrect

250 N

Incorrect

1000 N

Incorrect

Q 89PhysicsSection A • MCQwork power and energy

+1 / -0

A pump on the ground floor of a building can pump up water to fill a tank of volume $36 m^{3}$ in 30 min . If the tank is 50 m above the ground, and the electric power consumed by the pump is 40 k W , the efficiency of the pump is

(use $𝑔 = 10 m / s^{2}$ and density of water $= 1000 kg / m^{3}$ )

$30 %$

Incorrect

$25 %$

Incorrect

$33 %$

Incorrect

$40 %$

Incorrect

Q 90PhysicsSection A • MCQcircular motion

+1 / -0

A cyclist is riding with a speed of $36 km / h$ . As he approaches a circular turn on the road of radius 50 m , he applies brakes and reduces his speed at the constant rate of $0.5 m / s$ every second. The magnitude and direction of the net acceleration of the cyclist on the circular turn respectively, are

$\frac{\sqrt{\sqrt 3}}{2} {ms}^{- 2}, \tan^{- 1} (4)$

Incorrect

$\frac{\sqrt{\sqrt 3}}{2} {ms}^{- 2}, \tan^{- 1} (\frac{1}{4})$

Incorrect

$\sqrt{\sqrt 17} {ms}^{- 2}, \tan^{- 1} (\frac{1}{4})$

Incorrect

$\frac{\sqrt{\sqrt 17}}{2} {ms}^{- 2}, \tan^{- 1} (4)$

Incorrect

Q 91PhysicsSection A • MCQsimple harmonic motion

+1 / -0

A block is in simple harmonic motion (SHM) on the end of the spring with position given by $𝑥 = 5 \cos (𝜔 𝑡 + \frac{𝜋}{4}) cm$ . If the total mechanical energy used is 100 J to achieve maximum displacement, then the potential energy at time, $𝑡 = 0$ is

75 J

Incorrect

50 J

Incorrect

20 J

Incorrect

80 J

Incorrect

Q 92PhysicsSection A • MCQgravitation

+1 / -0

Statement I The force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it is always positive.

Statement II The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is same just as, if the entire mass of the shell is at the centre of the shell.

Which of the following is correct?

Both statement I and statement II are true

Incorrect

Statement I is true, but statement II is false

Incorrect

Statement II is true, but statement I is false

Incorrect

Both statements I and II are false

Incorrect

Q 93PhysicsSection A • MCQelasticity

+1 / -0

What is the work done in stretching a uniform metal wire of length from 2 m to 2.004 m with an area of cross-section $10^{- 6} m^{2}$ ?

[Young's modulus of the wire $= 2 \times 10^{11} N / m^{2}$ ]

1.6 J

Incorrect

0.8 J

Incorrect

8 J

Incorrect

16 J

Incorrect

Q 94PhysicsSection A • MCQfluid mechanics

+1 / -0

A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible. Find at what height from the bottom of the vessel a small hole should be made for the water jet coming out of it to hit the surface of the table at the maximum horizontal distance from the vessel

15 cm

Incorrect

35 cm

Incorrect

25 cm

Incorrect

10 cm

Incorrect

Q 95PhysicsSection A • MCQfluid mechanics

+1 / -0

A spherical drop of radius $𝑟$ is divided into 8 equal droplets. If the surface tension is $𝑆$ , then the work done in the process will be

$2 𝜋 𝑟^{2} 𝑆$

Incorrect

$3 𝜋 𝑟^{2} 𝑆$

Incorrect

$4 𝜋 𝑟^{2} 𝑆$

Incorrect

$4 𝜋 𝑟^{2} 𝑆^{2}$

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A circular copper ring at $30^{\circ} C$ has a hole with an area of $9.98 {cm}^{2}$ . It is made to slip onto a steel rod of cross-sectional area of $10 {cm}^{2}$ , by raising the temperature of both ring and rod simultaneously by an amount $Δ 𝑇$ . If the coefficient of linear expansion of copper and steel are $17 \times 10^{- 6} 𝜌 C$ and $11 \times 10^{- 6} 𝜌 C$ , then minimum value of $Δ 𝑇$ should be

${167.6}^{\circ} C$

Incorrect

${133.3}^{\circ} C$

Incorrect

${83.3}^{\circ} C$

Incorrect

${249.9}^{\circ} C$

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Statement I A device in which heat measurement can be made is called calorimeter.

Statement II Skating is possible on snow due to the formation of water below the skates. Water is formed due to the increase of temperature and ice melts.

Statement III Two bodies at different temperature are mixed in a calorimeter. Total internal energy of the two bodies remains conserved.

Which of the following is correct?

Statement I, II and III are true

Incorrect

Statement I is true, but statements II and III are false

Incorrect

Both statements I and II are true, but statement III is false

Incorrect

both statements I, III are true, but statement II is false

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Which of the following statements is not true?

Specific heat capacity is dependent on nature of substance but independent of its quantity.

Incorrect

Specific heat capacity depends on temperature.

Incorrect

Specific heat capacity of water doesn't vary with temperature.

Incorrect

The SI unit of specific heat capacity is ${JK}^{- 1} {kg}^{- 1}$ .

Incorrect

Q 99PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A gas system is taken through the thermodynamic cyclic process $1 \to 2 \to 3 \to 1$ as shown below. The amount of heat released by the system is

qImage--heat-and-thermodynamics-mechanics-Jeemate

$- 𝑝 \frac{𝑉}{2}$

Incorrect

$𝑝 𝑉$

Incorrect

$\frac{𝑝 𝑉}{2}$

Incorrect

$\frac{- 3 𝑝 𝑉}{2}$

Incorrect

Q 100PhysicsSection A • MCQheat and thermodynamics

+1 / -0

An ideal gas at pressure $𝑝$ is enclosed in a container that is placed in a reservoir at temperature $𝑇$ . If the volume of the gas is increased to two times its original value, then the new pressure $𝑝^{'} =$ $____$ $𝑝$

$1 / 2$

Incorrect

2

Incorrect

1

Incorrect

Cannot be determined

Incorrect

Q 101PhysicsSection A • MCQwaves

+1 / -0

A cylindrical tube open at both ends has a fundamental frequency $𝑓$ in air. The tube is dipped vertically in water, so that half of it is in water. The new fundamental frequency is

$𝑓$

Incorrect

$\frac{𝑓}{2}$

Incorrect

$2 𝑓$

Incorrect

$4 𝑓$

Incorrect

Q 102PhysicsSection A • MCQray optics

+1 / -0

A convex lens of focal length 25 cm and made of glass with refractive index 1.5 is immersed in water. the absolute change in focal length of the glass is [use refractive index of water $= 4 / 3$ ]

100 cm

Incorrect

37.5 cm

Incorrect

75 cm

Incorrect

12.5 cm

Incorrect

Q 103PhysicsSection A • MCQwave optics

+1 / -0

In a Young's double slit experiment, if the distance between two slits is reduced by a factor of 2 and the wavelength of light is increased 4 times then the distance between two maxima will become $____$ times the original value

2

Incorrect

4

Incorrect

8

Incorrect

16

Incorrect

Q 104PhysicsSection A • MCQelectrostatics

+1 / -0

A small block of mass 5 g and charge $5 𝜇 C$ is placed on insulated, frictionless, inclined plane of angle $60^{\circ}$ . An electric field is applied parallel to the inclined plane. If the block remains at rest, then the magnitude of electric field is (take, $𝑔 = 10 m / s^{2}$ )

$\frac{10^{5}}{\sqrt{\sqrt 3}} N / C$

Incorrect

$\frac{5}{\sqrt{\sqrt 3}} \times 10^{4} N / C$

Incorrect

$\sqrt{\sqrt 3} \times 10^{4} N / C$

Incorrect

$2 \times 10^{4} N / C$

Incorrect

Q 105PhysicsSection A • MCQelectrostatics

+1 / -0

Two metal spheres have their radii in the ratio of $4 : 7$ . They are put in contact and a charge $8.8 \times 10^{- 7} C$ is given to the system. Then they are separated, so that each can exert no influence on the other. The potential due to the smaller sphere at 60 m from it in V is

85

Incorrect

76

Incorrect

48

Incorrect

66

Incorrect

Q 106PhysicsSection A • MCQcurrent electricity

+1 / -0

The time required to raise the temperature 3 litre of water from $0^{\circ} C$ to $80^{\circ} C$ by a heater operated under 200 V having resistance of $50 Ω$ is [specific heat capacity of water is $4200 J {kg}^{- 1} K^{- 1}$ ] [density of water $= 1000 kg / m^{3}$ ]

12 min

Incorrect

18 min

Incorrect

21 min

Incorrect

24 min

Incorrect

Q 107PhysicsSection A • MCQcurrent electricity

+1 / -0

The current density in a circular wire is given by $𝐽 (𝑟) = (1 \times 10^{5} A / m^{3}) 𝑟$ , where $𝑟$ is the radial distance and the wire's radius is 2 mm . If the potential applied across the wire is 70 V , then the energy consumed by the wire in 1000 s is

25 kJ

Incorrect

$30 𝜋 kJ$

Incorrect

$18 𝜋 kJ$

Incorrect

88 kJ

Incorrect

Q 108PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

Two infinitely long thin wires are placed at $(1 cm, 0 cm)$ and $(2 cm, 0 cm)$ as shown in the figure.

qImage--moving-charges-and-magnetism-electromagnetism-Jeemate

The same current $𝑖$ flows in both the wires in the same direction, say, into the page. Let the magnetic field at the origin due to these wires is $𝐁$ . If $𝐵_{0}$ is the magnitude of the magnetic field, if only the wire at $(1 cm, 0 cm)$ was present, then the value of $\frac{𝐵}{𝐵_{0}}$ is

$3 / 2$

Incorrect

$2 / 3$

Incorrect

$1 / 2$

Incorrect

2

Incorrect

Q 109PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A toroid core has inner radius of 0.24 m and outer radius of 0.26 m . A current of 10 A flows through the wire having 2500 turns around it. Find the magnetic field inside the core of the toroid

$𝜋 \times 10^{- 2} T$

Incorrect

$2 𝜋 \times 10^{- 2} T$

Incorrect

$2 \times 10^{- 2} T$

Incorrect

$20 \times 10^{- 2} T$

Incorrect

Q 110PhysicsSection A • MCQmagnetism and matter

+1 / -0

In the magnetic meridian of a certain place, the horizontal component of the earth's magnetic field is 86.6 G (Gauss) and the magnetic field of earth is 100 G (Gauss). The the dip angle is

$45^{\circ}$

Incorrect

$60^{\circ}$

Incorrect

$30^{\circ}$

Incorrect

$75^{\circ}$

Incorrect

Q 111PhysicsSection A • MCQelectromagnetic induction

+1 / -0

A wheel of 20 metallic spokes each 40 cm long is rotated with a speed of $180 rev / \min$ in a plane normal to the horizontal component of earth's magnetic field $𝐻_{𝑐}$ at a place. If $𝐻_{𝑐} = 0.4 G$ (Gauss) at that place, the induced emf between the axle and the rim of the wheel is

$192 𝜋 \times 10^{- 7} V$

Incorrect

$256 𝜋 \times 10^{- 7} V$

Incorrect

$148 𝜋 \times 10^{- 7} V$

Incorrect

$110 𝜋 \times 10^{- 7} V$

Incorrect

Q 112PhysicsSection A • MCQalternating current

+1 / -0

A generator produces a current of 100 A at 4000 V . The voltage is stepped up to $2 \times 10^{5} V$ by a transformer before being sent on a high voltage transmission line of resistance $50 Ω$ . The percentage of power loss in the transmission line is

$0.25 %$

Incorrect

$0.05 %$

Incorrect

$1.25 %$

Incorrect

$0.02 %$

Incorrect

Q 113PhysicsSection A • MCQelectromagnetic waves

+1 / -0

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of 30 MHz and amplitude $150 V / m$ , Identify the correct expression of $𝐁$ assuming the wave is propagating along $𝑋$ -axis and is oscillating along $𝑌$ -axis.

$5 \times 10^{- 7} \sin [\frac{𝑥}{3} - 6 \times 10^{+ 7} 𝑡] \hat{𝑧} 𝑇$

Incorrect

$5 \times 10^{- 7} \sin [𝜋 (\frac{𝑥}{5} - 6 \times 10^{+ 7} 𝑡)] \hat{𝐳} 𝑇$

Incorrect

$5 \times 10^{- 7} \sin [𝜋 (\frac{𝑥}{10} - 3 \times 10^{+ 7} 𝑡)] \hat{𝑧} 𝑇$

Incorrect

$5 \times 10^{- 7} \sin [𝜋 (\frac{2 𝑥}{5} - 6 \times 10^{+ 8} 𝑡)] \hat{𝐳} 𝑇$

Incorrect

Q 114PhysicsSection A • MCQdual nature of radiation

+1 / -0

When monochromatic light falls on a photo sensitive metal, an electron is emitted with maximum velocity $1.6 \times 10^{6} m / s$ . Find the stopping potential.

[charge of electron $= 1.6 \times 10^{- 19} C$ , mass of electron $= 9 \times 10^{- 31} kg]$

7.2 V

Incorrect

14.4 V

Incorrect

21.6 V

Incorrect

28.8 V

Incorrect

Q 115PhysicsSection A • MCQdual nature of radiation

+1 / -0

A lamp of power 942 W radiates energy uniformly in all direction. The wavelength of radiation is 660 nm .The photon flux on a small screen 5.0 m from the lamp in units of photon $/ m^{2} s 𝑄$ is

(take Planck's constant, $ℎ = 6.6 \times 10^{- 34}$ SI unit)

$5 \times 10^{20}$

Incorrect

$2 𝜋 \times 10^{19}$

Incorrect

$\frac{6}{𝜋} \times 10^{18}$

Incorrect

$1 \times 10^{19}$

Incorrect

Q 116PhysicsSection A • MCQatoms and nuclei

+1 / -0

The shortest wavelength in Balmer series of hydrogen atom spectrum is approximately equal to (use $𝑅_{𝐻} = 1.097 \times 10^{7} m^{- 1}$ )

3646 A

Incorrect

912 A

Incorrect

364.6 A

Incorrect

91.2 A

Incorrect

Q 117PhysicsSection A • MCQatoms and nuclei

+1 / -0

What will be the energy released in joule, in the process of fission by 1 mg of $_{240}^{92} U$ . Assume energy release per fission is 200 MeV .

[use Avogadro's number as $6 \times 10^{23}$ and 1 eV $= 1.6 \times 10^{- 19} J$ ]

$62 \times 10^{7} J$

Incorrect

$7.0 \times 10^{7} J$

Incorrect

$8.0 \times 10^{7} J$

Incorrect

$82 \times 10^{7} J$

Incorrect

Q 118PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

The band gap in a semiconductor is 0.6 eV . The maximum wavelength of electromagnetic radiation which can create a hole electron pair in the semiconductor is equal to

[use $ℎ 𝑐 = 1242 eV - nm$ ]

2450 nm

Incorrect

1150 nm

Incorrect

2070 nm

Incorrect

1050 nm

Incorrect

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

Identify the logic gate from the following with the same truth table characteristics of the logic circuit below

qImage--semiconductor-devices-and-logic-gates-modern-physics-Jeemate

NAND

Incorrect

NOR

Incorrect

AND

Incorrect

$𝑂 𝑅$

Incorrect

Q 120PhysicsSection A • MCQcommunication systems

+1 / -0

For an amplitude modulated wave, the modulation index is found to be 0.5 . If the maximum amplitude is found to be 10.0 V , then the minimum amplitude is

5.0 V

Incorrect

3.33 V

Incorrect

2.5 V

Incorrect

6.66 V

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

Choose the correct statements in reference to the photoelectric effect.

(A) There is no time lag between the striking of light and ejection of electrons from the metal surface.

(B) The number of electrons ejected is independent of the intensity of light.

(C) The elements $K, Rb$ and Cs can show photoelectric effect when exposed to the beam of light.

A and B only

Incorrect

A and C only

Incorrect

$𝐴, 𝐵, 𝐶$

Incorrect

B and C only

Incorrect

Q 122ChemistrySection A • MCQd and f block elements

+1 / -0

Assertion (A) Mo has the ground state electronic configuration $4 𝑑^{5} 5 𝑠^{1}$ .

Reason (R) Mo has the highest exchange energy among the second row transition elements.

The correct option among the following is

(A) is true, (R) is true and (R) is the correct explanation for (A).

Incorrect

(A) is true, (R) is true but (R) is not the correct explanation for (A).

Incorrect

(A) is true but (R) is false.

Incorrect

(A) is false but (R) is true.

Incorrect

Q 123ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Which of the following sequence is correct for decreasing order of ionic radius?

$I^{-} > {Se}^{2 -} > {Br}^{-} > O^{2 -} > F^{-}$

Incorrect

${Se}^{2 -} > I^{-} > {Br}^{-} > F^{-} > O^{2 -}$

Incorrect

$I^{-} > {Se}^{2 -} > O^{2 -} > {Br}^{-} > F^{-}$

Incorrect

${Se}^{2 -} > I^{-} > {Br}^{-} > O^{2 -} > F^{-}$

Incorrect

Q 124ChemistrySection A • MCQperiodic classification of elements

+1 / -0

The successive ionisation energies (starting from the 1 st ) of an element are $801, 2430, 3660, 25, 000$ and $32, 800 kJ {mol}^{- 1}$ , respectively. The element is

B

Incorrect

C

Incorrect

O

Incorrect

N

Incorrect

Q 125ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

The compounds with $𝑠 𝑝^{2}$ hybridised central atom among the following are

(A) $H_{2} {CO}_{3}$

(B) ${SiF}_{4}$

(C) ${BF}_{3}$

(D) ${HClO}_{2}$

A and C only

Incorrect

A and B only

Incorrect

C and D only

Incorrect

A, B, C and D

Incorrect

Q 126ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

The hybridisation and shape of $𝐼_{-}^{3}$ ion, respectively, are

$𝑠 𝑝^{3} 𝑑^{2}$ , distorted octahedral

Incorrect

$𝑠 𝑝^{3} 𝑑$ , linear

Incorrect

$𝑠 𝑝^{3} 𝑑$ , trigonal bipyramid

Incorrect

$𝑑 𝑠 𝑝^{3}$ , square pyramidal

Incorrect

Q 127ChemistrySection A • MCQstates of matter

+1 / -0

1 mole of a real gas is kept at high pressure of 100 bar at 300 K . If van der Waals' constant $𝑏$ is $0.005 L / mol$ , what are the values of compressibility factor $𝑍$ of the gas and \% deviation of volume from ideality?

Z	$% deviation$
1.10	10

Incorrect

Z	$% deviation$
1.2	20

Incorrect

Z	$% deviation$
1.02	2

Incorrect

Z	$% deviation$
1.2	15

Incorrect

Q 128ChemistrySection A • MCQstates of matter

+1 / -0

1 L closed flask contains a mixture of 4 g of methane and 4.4 g of carbon dioxide. The pressure inside the flask at $27^{\circ} C$ is

[assume ideal behaviour of gases].

8.6 atm

Incorrect

2.2 atm

Incorrect

4.2 atm

Incorrect

6.1 atm

Incorrect

Q 129ChemistrySection A • MCQsome basic concepts of chemistry

+1 / -0

Round the number 234555359 to 3 significant figure.

234000000

Incorrect

234000

Incorrect

235000000

Incorrect

234500000

Incorrect

Q 130ChemistrySection A • MCQredox reactions

+1 / -0

Which of the following are disproportionation reactions?

(A) ${Cl}_{2} + 2 NaOH ⟶ NaCl + NaOCl + H_{2} O$

(B) $H_{2} O_{2} ⟶ 2 H_{2} O + O_{2}$

(C) $2 {KMnO}_{4} \to K_{2} {MnO}_{4} + {MnO}_{2} + O_{2}$

(D) $3 {MnO}_{2 -}^{4} + 4 H^{+} ⟶ 2 {MnO}_{-}^{4} + {MnO}_{2} + 2 H_{2} O$

A, B, C only

Incorrect

A, B, D only

Incorrect

A, C only

Incorrect

A, B, C, D

Incorrect

Q 131ChemistrySection A • MCQthermodynamics

+1 / -0

The bond enthalpies of heavy hydrogen, $O - O$ and $D - O$ are $+ 400, + 498$ and $+ 490 {kJmol}^{- 1}$ , respectively. The $Δ_{𝑟} 𝐻^{\circ}$ of the reaction to produce $D_{2} O$ is

$- 300 kJ {mol}^{- 1}$

Incorrect

$- 331 kJ {mol}^{- 1}$

Incorrect

$29.1 kJ {mol}^{- 1}$

Incorrect

$2.91 kJ {mol}^{- 1}$

Incorrect

Q 132ChemistrySection A • MCQchemical equilibrium

+1 / -0

Calculate the value of the equilibrium constant $(𝐾_{𝑝})$ for the reaction of oxygen gas oxidising ammonia gas to nitric oxide and water vapour. The pressure of each gas at equilibrium is 0.5 atm .

1.5 atm

Incorrect

0.5 atm

Incorrect

1 atm

Incorrect

2.5 atm

Incorrect

Q 133ChemistrySection A • MCQionic equilibrium

+1 / -0

Ammonia is a Lewis base because it is

electron pair donor

Incorrect

electron pair acceptor

Incorrect

proton donor

Incorrect

proton acceptor

Incorrect

Q 134ChemistrySection A • MCQhydrogen

+1 / -0

${CaC}_{2} + 2 D_{2} O ⟶'' 𝑃^{''} + Ca (OD)_{2}$

In the above reaction, product " $𝑃$ " is

$C_{2} H_{2}$

Incorrect

$C_{2} H_{4}$

Incorrect

${CD}_{4}$

Incorrect

$C_{2} D_{2}$

Incorrect

Q 135ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Assertion (A) The ionic radii of the alkaline earth metals are smaller than those of alkali metals in the same period.

Reason (R) Alkali metals have higher nuclear charge than that of the alkaline earth metals.

The correct option among the following is

(A) is true, (R) is true and (R) is the correct explanation for (A).

Incorrect

(A) is true, (R) is true but (R) is not the correct explanation for (A).

Incorrect

(A) is true but (R) is false.

Incorrect

(A) is false but (R) is true.

Incorrect

Q 136ChemistrySection A • MCQp block elements

+1 / -0

A black coloured element with $𝑛 𝑠^{2} 𝑛 𝑝^{1}$ outer electronic configuration cannot react with air in its crystalline form. However, in amorphous form, it gives an oxide in air which is acidic in nature. Identify the element.

Boron

Incorrect

Aluminium

Incorrect

Gallium

Incorrect

Indium

Incorrect

Q 137ChemistrySection A • MCQp block elements

+1 / -0

The element that does not show catenation is

C

Incorrect

Ge

Incorrect

Sn

Incorrect

Pb

Incorrect

Q 138ChemistrySection A • MCQgeneral organic chemistry

+1 / -0

From the following compounds, the ones which contain both $𝑠 𝑝$ and $𝑠 𝑝^{2}$ hybridised carbons are

qImage--general-organic-chemistry-organic-chemistry-Jeemate

I, II and III

Incorrect

II, III and IV

Incorrect

I, III and VI

Incorrect

I, III and V

Incorrect

Q 139ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

1-chloro-3- methylbutane on reaction with zinc and dilute hydrochloric acid gives $____$ product. as the major

2-methylbutane

Incorrect

2-methylbutene

Incorrect

n-pentane

Incorrect

$𝑛$ -pentene

Incorrect

Q 140ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

The major products $𝑌$ and $𝑍$ in the following reactions are

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

Q 141ChemistrySection A • MCQsolid state

+1 / -0

A solid has a structure in which ' W ' atoms are located at the corners of a cubic lattice, oxygen atoms at the edge centre and

Na atom at the body centre. The formula of the compound is

${NaWO}_{2}$

Incorrect

${Na}_{2} {WO}_{3}$

Incorrect

${NaWO}_{3}$

Incorrect

${NaWO}_{4}$

Incorrect

Q 142ChemistrySection A • MCQsolutions

+1 / -0

If 2 g of NaOH is dissolved to make 200 mL solution at $25^{\circ} C$ , the molarity ( $𝑀$ ) at $90^{\circ} C$ is

$𝑀 < 0.25$

Incorrect

$0.5 > 𝑀 > 0.25$

Incorrect

$𝑀 = 0.25$

Incorrect

$0.5<M<1.0$

Incorrect

Q 143ChemistrySection A • MCQsolutions

+1 / -0

A solvent freezes at $17^{\circ} C$ and its latent heat of fusion is $180 {Jg}^{- 1}$ . The molal depression constant of the solvent is [units of $𝐾_{𝑓} = K kg {mol}^{- 1}$ ]

3.88

Incorrect

3.55

Incorrect

3.70

Incorrect

4.77

Incorrect

Q 144ChemistrySection A • MCQelectrochemistry

+1 / -0

The $𝐸^{\circ}$ of ${Ce}^{4 +} / {Ce}^{3 +} = 1.6 V, {Fe}^{3 +} / {Fe}^{2 +} = 0.76 V$ the $𝐸^{\circ}$ of ${Fe}^{3 +}$ oxidising ${Ce}^{3 +}$ is

+0.84 V

Incorrect

-0.84 V

Incorrect

-2.32 V

Incorrect

+1.5 V

Incorrect

Q 145ChemistrySection A • MCQchemical kinetics

+1 / -0

For a reaction, the threshold energy is $75 kJ /$ mole. If the internal energy of the reactants is 20 $kJ /$ mole, the activation energy (in $kJ /$ mole) is

55

Incorrect

20

Incorrect

75

Incorrect

95

Incorrect

Q 146ChemistrySection A • MCQsurface chemistry

+1 / -0

The process in which colloids, when subjected to DC electric field move towards an electrode is

brownian movement

Incorrect

Tyndall effect

Incorrect

peptisation

Incorrect

electrophoresis

Incorrect

Q 147ChemistrySection A • MCQcoordination compounds

+1 / -0

$Match the following$

Column -I (Reaction)		Column - II (Colour of the product or nature)
(A)	${FeCl}_{3} (aq) + {NH}_{3} (aq) ⟶$	(l)	Green ppt.
(B)	$AgCl (aq) + {NH}_{3} (aq) ⟶$	(II)	Deep blue
(C)	${Cu}^{2 +} (aq) + {NH}_{3} (aq) ⟶$	(III)	Brown ppt.
		(IV)	Colourless

$The correct match$

A	B	C
I	II	III

Incorrect

A	B	C
I	III	IV

Incorrect

A	B	C
III	IV	II

Incorrect

A	B	C
III	I	IV

Incorrect

Q 148ChemistrySection A • MCQp block elements

+1 / -0

In the following, the oxoacid with a peroxy bond is

$H_{2} S_{2} O_{5}$

Incorrect

$H_{2} S_{2} O_{6}$

Incorrect

$H_{2} S_{2} O_{7}$

Incorrect

$H_{2} S_{2} O_{8}$

Incorrect

Q 149ChemistrySection A • MCQp block elements

+1 / -0

Chlorine is allowed to react with excess of ammonia. In this, 1 mole of chlorine can oxidise ' $𝑍$ ' moles of ${NH}_{3}$ . ' $𝑍$ ' is

$3 / 8$

Incorrect

$8 / 3$

Incorrect

$2 / 3$

Incorrect

$3 / 2$

Incorrect

Q 150ChemistrySection A • MCQp block elements

+1 / -0

The correct order of enthalpy of vaporisation of noble gases is

$Xe > Kr > Ar > Ne > He$

Incorrect

$He > Ne > Kr > Ar > Xe$

Incorrect

$Xe > Ar > He > Ne > Kr$

Incorrect

$Ne > Xe > Kr > He > Ar$

Incorrect

Q 151ChemistrySection A • MCQd and f block elements

+1 / -0

Choose the correct statement.

${Fe}^{3 +}$ ion is more stable than ${Fe}^{2 +}$ ion because

more the charge on the atom, more is its stability.

Incorrect

electronic configuration of ${Fe}^{2 +}$ is $3 𝑑^{6}$ while that of ${Fe}^{3 +}$ is $3 𝑑^{5}$ .

Incorrect

${Fe}^{2 +}$ has a larger size than that of ${Fe}^{3 +}$ .

Incorrect

${Fe}^{3 +}$ ions are coloured.

Incorrect

Q 152ChemistrySection A • MCQcoordination compounds

+1 / -0

Secondary valences of the following complexes based on their reactions with excess ${AgNO}_{3}$ are

\begin{matrix} \begin{matrix} Formula of the \\ complexes \end{matrix} & \begin{matrix} Moles of AgCl precipitated \\ per mole of complex \end{matrix} \\ (I) & {CoCl}_{3} \cdot 6 H_{2} O & 3 \\ (II) & {NiCl}_{3} \cdot 6 H_{2} O & 2 \\ (III) & Co ({SO}_{4}) Br \cdot 5 {NH}_{3} & 1 \end{matrix}

I	II	III
4	6	6

Incorrect

I	II	III
6	4	4

Incorrect

I	II	III
6	4	6

Incorrect

I	II	III
6	6	6

Incorrect

Q 153ChemistrySection A • MCQbiomolecules

+1 / -0

Assertion (A) In aqueous solution, amino acids exist in dipolar ion form.

Reason (R) Most of the naturally occurring amino acids have $𝐿$ -configuration.

The correct option among the following is

(A) is true, (R) is true and (R) is the correct explanation for (A).

Incorrect

(A) is true, (R) is true but (R) is not the correct explanation for (A).

Incorrect

(A) is true but (R) is false.

Incorrect

(A) is false but (R) is true.

Incorrect

Q 154ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

$Match the following.$

$\begin{matrix} (A) & {CH}_{3} {CH}_{2} {CH}_{2} \overset{Aq . KOH}{\to\leftarrow} & I & S_{N} 1 \\ (B) & {({CH}_{3})}_{3} Cl \overset{H_{2} O}{\to\leftarrow} & II & E 2 \\ (C) & {CH}_{3} {CH}_{2} {CH}_{2} \overset{Alc. KOH}{\to\leftarrow} & III & E 1 \\ (D) & {({CH}_{3})}_{3} COH \overset{H^{+}}{\to\leftarrow} & IV & S_{N} 2 \end{matrix}$

$The correct match is$

A	B	C	D
I	II	III	IV

Incorrect

A	B	C	D
IV	II	III	I

Incorrect

A	B	C	D
IV	I	II	III

Incorrect

A	B	C	D
IV	II	I	III

Incorrect

Q 155ChemistrySection A • MCQaldehyde and ketone

+1 / -0

$The major product in the following transformation is$

qImage--aldehyde-and-ketone-organic-chemistry-Jeemate

Incorrect

qImage--aldehyde-and-ketone-organic-chemistry-Jeemate

Incorrect

qImage--aldehyde-and-ketone-organic-chemistry-Jeemate

Incorrect

qImage--aldehyde-and-ketone-organic-chemistry-Jeemate

Incorrect

Q 156ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

$The major product of the following reaction is$

qImage--compounds-containing-nitrogen-organic-chemistry-Jeemate

Incorrect

qImage--compounds-containing-nitrogen-organic-chemistry-Jeemate

Incorrect

qImage--compounds-containing-nitrogen-organic-chemistry-Jeemate

Incorrect

qImage--compounds-containing-nitrogen-organic-chemistry-Jeemate

Incorrect

Q 157ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

$The major product of the following reaction is$

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

Incorrect

Q 158ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

Suitable reagents $𝑋$ and $𝑌$ , respectively, in the following reactions are

qImage--haloalkanes-and-haloarenes-organic-chemistry-Jeemate

aq. KOH, ${CrO}_{3}$

Incorrect

alc. $KOH, \frac{Cu}{Δ}$

Incorrect

aq. ${NaHCO}_{3} \cdot {KMnO}_{4}$

Incorrect

alc. $KOH, NaOI$

Incorrect

Q 159ChemistrySection A • MCQgeneral organic chemistry

+1 / -0

Among the compounds

(i) $H - C \equiv C - COOH$

(ii) ${CH}_{2} = CH - COOH$

(iii) ${CH}_{3} - {CH}_{2} COOH$ and

(iv) ${CH}_{3} - {CH}_{2} - OH$

The correct order of acid strength is

(i) $>$ (ii) $>$ (iii) $>$ (iv)

Incorrect

(iv) $>$ (iii) $>$ (ii) $>$ (i)

Incorrect

(ii) $>$ (i) $>$ (iv) $>$ (iii)

Incorrect

(iii) $>$ (ii) $>$ (i) $>$ (iv)

Incorrect

Q 160ChemistrySection A • MCQiupac nomenclature

+1 / -0

What is the IUPAC name of the below given compound?

qImage--iupac-nomenclature-organic-chemistry-Jeemate

N-methyl-N-ethylbenzenamine

Incorrect

N -methyl- N -phenylethanamine

Incorrect

N -ethyl- N -methylbenzenamine

Incorrect

N-ethyl-N-phenylmethanamine

Incorrect

TG EAPCET 2022 20th July Evening Shift Question Paper with Solutions