Tg Eapcet 2022 18th July Evening Shift Question Paper Question Paper with Solutions | TG EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQfunctions

+1 / -0

Let $𝑅$ be the set of all real number

Statement I The function $𝑓 : (- \frac{𝜋}{2}, \frac{𝜋}{2}) \to 𝑅$ defined by $𝑓 (𝑥) = \sec 𝑥 + \tan 𝑥$ is one-one function.

Statement II The function $𝑓 : [0, \infty) \to 𝑅$ defined by $𝑓 (𝑥) = 𝑥^{2}$ is a one-one function

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 2MathematicsSection A • MCQfunctions

+1 / -0

Let $𝑅$ be the set of all real numbers. Let $𝑓 : 𝑅 \to 𝑅$ be a function defined by

$𝑓 (𝑥) = ⎧⎩⎨⎪⎪ \begin{matrix} 2 𝑥 - 5, & if & 𝑥 < - 3 \\ 𝑥 + 2, & if & - 3 \leq 𝑥 < 5 \\ 3 𝑥 + 1, & if & 𝑥 \geq 5 \end{matrix}$

Match the following

$\begin{matrix} List I & List II \\ A & 𝑓 (- 5) + 𝑓 (0) + 𝑓 (- 1) = & I & 16 \\ B & 𝑓 (𝑓 (5) + 10 𝑓 (- 3)) = & II & 40 \\ C & 𝑓 (| 𝑓 (- 4) |) = & III & - 32 \\ D & 𝑓 (𝑓 (𝑓 (1))) = & IV & - 12 \\ V & 19 \end{matrix}$

A	B	C	D
III	II	V	I

Incorrect

A	B	C	D
V	IV	I	III

Incorrect

A	B	C	D
IV	V	II	I

Incorrect

A	B	C	D
IV	V	III	I

Incorrect

Q 3MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴 + 𝐵 = ⎡⎣⎢ \begin{matrix} 2 & 1 & 2 \\ 1 & 2 & 0 \\ 0 & 2 & 2 \end{matrix} ⎤⎦⎥, 𝐴 𝐵 = ⎡⎣⎢ \begin{matrix} 1 & 2 & 2 \\ 1 & 1 & 0 \\ 1 & 2 & 1 \end{matrix} ⎤⎦⎥$ , then $𝐴^{2} + 𝐵 (𝐴 + 𝐵) =$

$⎡⎣⎢ \begin{matrix} 4 & 6 & 6 \\ 3 & 4 & 2 \\ 1 & 6 & 3 \end{matrix} ⎤⎦⎥$

Incorrect

$⎡⎣⎢ \begin{matrix} 4 & 9 & 6 \\ 3 & 3 & 2 \\ 4 & 7 & 4 \end{matrix} ⎤⎦⎥$

Incorrect

$⎡⎣⎢ \begin{matrix} 6 & 10 & 8 \\ 4 & 5 & 2 \\ 4 & 9 & 6 \end{matrix} ⎤⎦⎥$

Incorrect

$⎡⎣⎢ \begin{matrix} 3 & 4 & 4 \\ 2 & 3 & 2 \\ 0 & 4 & 2 \end{matrix} ⎤⎦⎥$

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴, 𝑃, 𝐵$ are $3 \times 3$ matrices. If $| - 𝐵 | = 5, ∣ 𝐵 𝐴^{𝑇} ∣ = 15$ , $∣ 𝑃^{𝑇} 𝐴 𝑃 ∣ = - 27$ , then one of the values of $| 𝑃 |$ is

3

Incorrect

-5

Incorrect

9

Incorrect

6

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴$ is a $3 \times 3$ matrix and $| 𝐴 | = \frac{1}{2}$ , then ${∣ 𝐴^{- 1} (Adj (Adj 𝐴)) ∣}^{- 1} =$

8

Incorrect

$\frac{1}{8}$

Incorrect

$\frac{1}{2}$

Incorrect

2

Incorrect

Q 6MathematicsSection A • MCQmatrices and determinants

+1 / -0

Let $𝑥 = 𝛼, 𝑦 = 𝛽, 𝑧 = 𝛾$ be the unique solution of the system of simultaneous linear equations $2 𝑥 + 3 𝑦 - 2 𝑧 + 4 = 0, 3 𝑥 - 4 𝑦 + 3 𝑧 + 5 = 0$ , $𝑘 𝑥 - 2 𝑦 + 𝑧 + 3 = 0$ . If $𝛼 = - 2$ , then $𝑘 =$

$∣ \begin{matrix} 1 & 2 \\ 3 & 5 \end{matrix} ∣$

Incorrect

$∣ \begin{matrix} 5 & 3 \\ 1 & 2 \end{matrix} ∣$

Incorrect

$∣ \begin{matrix} 3 & 5 \\ 1 & 2 \end{matrix} ∣$

Incorrect

$∣ \begin{matrix} 3 & 5 \\ 2 & 1 \end{matrix} ∣$

Incorrect

Q 7MathematicsSection A • MCQcomplex numbers

+1 / -0

If the point $(𝑥, 𝑦)$ satisfies the equation $\frac{𝑥 + 𝑖 (𝑥 - 2)}{3 + 𝑖} - 𝑖 = \frac{2 𝑦 + 𝑖 (1 - 3 𝑦)}{𝑖 - 3}$ , then $𝑥 + 𝑦 =$

4

Incorrect

2

Incorrect

0

Incorrect

-2

Incorrect

Q 8MathematicsSection A • MCQcomplex numbers

+1 / -0

If $\cos 𝛼 + \cos 𝛽 + \cos 𝛾 = 0$ and $\sin 𝛼 + \sin 𝛽 + \sin 𝛾 = 0$ then $\cos 2 𝛼 + \cos 2 𝛽 + \cos 2 𝛾 =$

$\frac{3}{2}$

Incorrect

$\cos^{2} \frac{𝛼}{2} + \cos^{2} \frac{𝛽}{2} + \cos^{2} \frac{𝛾}{2}$

Incorrect

$3 \sin (𝛼 + 𝛽 + 𝛾)$

Incorrect

$\cos (𝛼 + 𝛽) + \cos (𝛽 + 𝛾) + \cos (𝛾 + 𝛼)$

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

One of the values of $(- 32 𝑖)^{\frac{2}{5}}$ is

$4 cis \frac{2 𝜋}{5}$

Incorrect

$4 cis \frac{3 𝜋}{5}$

Incorrect

$4 cis \frac{4 𝜋}{5}$

Incorrect

$4 cis \frac{6 𝜋}{5}$

Incorrect

Q 10MathematicsSection A • MCQquadratic equations

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If the quadratic equations $𝑥^{2} - 7 𝑥 + 3 𝑐 = 0$ and $𝑥^{2} + 𝑥 - 5 𝑐 = 0$ have a common root, then for non-zero real value of $𝑐$ the sign of the expression $𝑥^{2} - 3 𝑥 + 𝑐$ is

negative for all $𝑥 \in 𝑅$

Incorrect

positive for all $𝑥 \in (1, 3)$

Incorrect

negative for all $𝑥 \in (1, 3)$

Incorrect

positive for all $𝑥 \in 𝑅$

Incorrect

Q 11MathematicsSection A • MCQquadratic equations

+1 / -0

II. Let $𝑓 (𝑥) = \frac{6 𝑥^{2} - 18 𝑥 + 21}{6 𝑥^{2} - 18 𝑥 + 17}$ . If $𝑚$ is the maximum value of $𝑓 (𝑥)$ and $𝑓 (𝑥) > 𝑛 \forall 𝑥 \in 𝑅$ . Then, $14 𝑚 - 7 𝑛 =$

-1

Incorrect

23

Incorrect

35

Incorrect

42

Incorrect

Q 12MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼, 𝛽, 𝛾$ are the roots of the equation $𝑥^{3} + 𝑥^{2} + 𝑥 + 𝑟 = 0$ and $𝛼^{3} + 𝛽^{3} + 𝛾^{3} = 5$ , then $𝑟 =$

$\frac{- 1}{2}$

Incorrect

1

Incorrect

-1

Incorrect

$\frac{1}{2}$

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If $\frac{5}{2}$ is the sum of two roots of the equation $6 𝑥^{6} - 25 𝑥^{5} + 31 𝑥^{4} - 31 𝑥^{2} + 25 𝑥 - 6 = 0$ then the sum of all non-real roots of the equation is

does not exist

Incorrect

0

Incorrect

$\frac{5}{3}$

Incorrect

$\frac{2}{5}$

Incorrect

Q 14MathematicsSection A • MCQquadratic equations

+1 / -0

If $1 - \sqrt{\sqrt 2}$ and $2 + 𝑖$ are the roots of the equation $𝑥^{4} + 𝑏 𝑥^{3} + 𝑐 𝑥^{2} + 𝑑 𝑥 + 𝑒 = 0$ where $𝑏, 𝑐, 𝑑, 𝑒$ are rational numbers, then the roots of the equation $𝑏 𝑥^{2} + 𝑐 𝑥 + 𝑑 = 0$ are

real and different

Incorrect

real and equal

Incorrect

purely imaginary

Incorrect

complex conjugate

Incorrect

Q 15MathematicsSection A • MCQquadratic equations

+1 / -0

Let the transformed equation of $2 𝑥^{4} - 8 𝑥^{3} + 3 𝑥^{2} - 1 = 0$ so that the term containing the cubic power of $𝑥$ is absent be $2 𝑥^{4} + 𝑏 𝑥^{2} + 𝑐 𝑥 + 𝑑 = 0$ . Then, $𝑏 =$

-18

Incorrect

-15

Incorrect

-9

Incorrect

-16

Incorrect

Q 16MathematicsSection A • MCQpermutations and combinations

+1 / -0

$𝑎, 𝑏, 𝑐$ are three particular speakers among the 10 speakers of a meeting. The number of ways of arranging all 10 speakers on the dias in a row so that all the three speakers $𝑎, 𝑏, 𝑐$ do not sit together is

$714 (7!)$

Incorrect

$89 (8!)$

Incorrect

$719 (7!)$

Incorrect

$84 (8!)$

Incorrect

Q 17MathematicsSection A • MCQpermutations and combinations

+1 / -0

The exponent of 6 in 72 ! is

34

Incorrect

70

Incorrect

17

Incorrect

35

Incorrect

Q 18MathematicsSection A • MCQbinomial theorem

+1 / -0

If the 4 th term in the expansion of ${(\frac{𝑥}{2} - \frac{2 𝑦}{3})}^{6}$ is -20, then $𝑥 𝑦 =$

2

Incorrect

3

Incorrect

8

Incorrect

27

Incorrect

Q 19MathematicsSection A • MCQindefinite integration

+1 / -0

$\begin{matrix} If \int \frac{(𝑥 + 3)}{(𝑥 - 1)^{2} (2 𝑥 - 1)} 𝑑 𝑥 \\ = \frac{𝐴}{𝑥 - 1} + 𝐵 \log (2 𝑥 - 1) + 𝐶 \log (𝑥 - 1) + 𝑘, then 𝐴 + 𝐵 + 𝐶 = \end{matrix}$

3

Incorrect

11

Incorrect

-4

Incorrect

-11

Incorrect

Q 20MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $\frac{𝑥^{2} + 7}{(𝑥^{2} + 1) (𝑥 - 2)} = \frac{𝐴}{𝑥 - 2} + \frac{𝐵 𝑥 + 𝐶}{𝑥^{2} + 1}$ , then the determinant of the matrix $[\begin{matrix} 𝐴 & 𝐵 \\ 𝐶 & \frac{2}{5} \end{matrix}]$ is

5

Incorrect

-5

Incorrect

$94 / 25$

Incorrect

-2

Incorrect

Q 21MathematicsSection A • MCQquadratic equations

+1 / -0

If $\tan 15^{\circ}$ and $\tan 30^{\circ}$ are the roots of equation $𝑥^{2} + 𝑝 𝑥 + 𝑞 = 0$ , then $𝑝 𝑞 =$

$\frac{6 \sqrt{\sqrt 3} + 10}{\sqrt{\sqrt 3}}$

Incorrect

$\frac{10 - 6 \sqrt{\sqrt 3}}{3}$

Incorrect

$\frac{10 + 6 \sqrt{\sqrt 3}}{3}$

Incorrect

$\frac{10 - 6 \sqrt{\sqrt 3}}{\sqrt{\sqrt 3}}$

Incorrect

Q 22MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\cos 𝑥 + \cos 𝑦 = 𝑝, \sin 𝑥 + \sin 𝑦 = 𝑞$ , then $\cos (\frac{𝑥 - 𝑦}{2}) =$

$\pm \frac{\sqrt{\sqrt 𝑝^{2} + 𝑞^{2}}}{2}$

Incorrect

$\pm \frac{𝑝 𝑞}{2}$

Incorrect

$\pm (\frac{𝑝 + 𝑞}{2})$

Incorrect

$\pm \frac{\sqrt{\sqrt 𝑝^{2} + 𝑞^{2}}}{4}$

Incorrect

Q 23MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $𝐴 + 𝐵 + 𝐶 = \frac{3 𝜋}{2}$ , then $4 \sin 𝐴 \sin 𝐵 \sin 𝐶 + \cos 2 𝐴 + \cos 2 𝐵 + \cos 2 𝐶 =$

$- \sin (𝐴 + 𝐵 + 𝐶)$

Incorrect

$\cos (𝐴 + 𝐵 + 𝐶)$

Incorrect

$\sin (𝐴 + 𝐵 + 𝐶)$

Incorrect

$2 - \cos (𝐴 + 𝐵 + 𝐶)$

Incorrect

Q 24MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

$\frac{𝑒^{4 𝑥} + 𝑒^{- 4 𝑥} + 14}{4 {(𝑒^{𝑥} - 𝑒^{- 𝑥})}^{2}} =$

$\sinh^{2} 𝑥 + \coth^{2} 𝑥$

Incorrect

$\sinh^{2} 𝑥 + {sech}^{2} 𝑥$

Incorrect

$\cosh^{2} 𝑥 + {sech}^{2} 𝑥$

Incorrect

$\cosh^{2} 𝑥 + \tanh^{2} 𝑥$

Incorrect

Q 25MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\tanh 𝑥 = \frac{1}{2}$ , then $\sinh 2 𝑥 - sech 2 𝑥 =$

$\frac{29}{15}$

Incorrect

$\frac{11}{15}$

Incorrect

3

Incorrect

$\frac{- 13}{15}$

Incorrect

Q 26MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $𝐴$ is acute, $𝐶$ is obtuse, $\sin 𝐴 = \frac{3 \sqrt{\sqrt 3}}{14}, 𝑎 = 3$ and $𝑏 = 5$ , then $𝑐 =$

$16 / 7$

Incorrect

7

Incorrect

$14 / 3$

Incorrect

6

Incorrect

Q 27MathematicsSection A • MCQproperties of triangles

+1 / -0

If $Δ$ denotes the area of $△ 𝐴 𝐵 𝐶$ , then $(𝑏 \sin 𝐶 + 𝑐 \sin 𝐵) (𝑏 \cos 𝐶 + 𝑐 \cos 𝐵) =$

$𝑎 𝑏 \cos 𝐶$

Incorrect

$2 Δ$

Incorrect

$𝑏 𝑐 \cos 𝐴$

Incorrect

$4 Δ$

Incorrect

Q 28MathematicsSection A • MCQproperties of triangles

+1 / -0

Let $𝐴$ be the area of in-circle and $𝐴_{1}, 𝐴_{2}, 𝐴_{3}$ be the area of ex-circles of a triangle. If $𝐴_{1} = 4, 𝐴_{2} = 9, 𝐴_{3} = 16$ , then $𝐴 =$

81

Incorrect

$\frac{61}{169}$

Incorrect

$\frac{144}{61}$

Incorrect

$\frac{144}{169}$

Incorrect

Q 29MathematicsSection A • MCQvector algebra

+1 / -0

If $3 \hat{𝐢} - 5 \hat{𝐣} + 2 \hat{𝐤}, 7 \hat{𝐢} + 2 \hat{𝐣} - 4 \hat{𝐤}, \hat{𝐢} - 3 \hat{𝐣} + 4 \hat{𝐤}$ and $- 7 \hat{𝐢} - 17 \hat{𝐣} + 16 \hat{𝐤}$ are position vectors of the points $𝐴, 𝐵, 𝐶$ and $𝐷$ respectively, then the angle between $𝐀 𝐁$ and $𝐂 𝐃$ is

0

Incorrect

$\frac{𝜋}{4}$

Incorrect

$\frac{𝜋}{2}$

Incorrect

$𝜋$

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐴 (2 \hat{𝐢} + \hat{𝐣} - \hat{𝐤}), 𝐵 (𝜆 \hat{𝐢} + 5 \hat{𝐣} + 4 \hat{𝐤}), 𝐶 (- 4 \hat{𝐢} + 3 \hat{𝐣} + 2 \hat{𝐤})$ and $𝐷 (- \hat{𝐢} - 2 \hat{𝐣} + 3 \hat{𝐤})$ are four points in space such that $𝐀 𝐁 = 𝑥 𝐀 𝐂 + 𝑦 𝐀 𝐃$ for some real number $𝑥 \neq 0, 𝑦 \neq 0$ , then $17 (𝜆 + 9) =$

5

Incorrect

3

Incorrect

7

Incorrect

9

Incorrect

Q 31MathematicsSection A • MCQ3d geometry

+1 / -0

Let a plane $𝑃$ has the points $\hat{𝐢}, \hat{𝐣}$ and $\hat{𝐢} + \hat{𝐣} + \hat{𝐤}$ . Let $𝐿$ be the line through the point $𝐴$ and parallel to the vector $\hat{𝐢} - \hat{𝐣} + \hat{𝐤}$ . If the plane $𝑃$ and line $𝐿$ intersect at a point $𝐵 (0, 3, 2)$ and the distance from $𝐴$ to $𝐵$ is 3 units, then equations of the normal to the plane $𝑃$ through $𝐴$ are

$\frac{𝑥 - 3}{1} = \frac{𝑦}{1} = \frac{𝑧 - 5}{- 1}$

Incorrect

$\frac{𝑥 + 3}{1} = \frac{𝑦 - 6}{1} = \frac{𝑧 - 1}{- 1}$

Incorrect

$\frac{𝑥 + 3}{1} = \frac{𝑦}{1} = \frac{𝑧 - 5}{- 1}$

Incorrect

$\frac{𝑥 + 3}{1} = \frac{𝑦 - 6}{- 1} = \frac{𝑧 + 1}{1}$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐚 = \hat{𝐢} + \hat{𝐣} + \hat{𝐤}$ and $𝐛$ be two vectors such that $𝐚 \cdot 𝐛 = 1$ , $\cos (𝐚 \cdot 𝐛) = \frac{1}{3}$ and the components of $𝐛$ w.r.t. $(\hat{𝐢}, \hat{𝐣}, \hat{𝐤})$ be integers. Then, the number of possible vectors that represent $𝐛$ is

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Q 33MathematicsSection A • MCQ3d geometry

+1 / -0

Let $𝜋_{'}^{1}$ be the plane passing through the point $2 \hat{𝐢} - \hat{𝐣} + \hat{𝐤}$ and perpendicular to the vector $𝑎 \hat{𝐢} + 2 \hat{𝐣} - 3 \hat{𝐤}$ and $𝜋_{2}$ be the plane passing through the point $\hat{𝐢} + 2 \hat{𝐣} - \hat{𝐤}$ and perpendicular to the vector $\hat{𝐢} - 2 \hat{𝐣} + \hat{𝐤}$ . If $𝜃$ is the angle between the planes $𝜋_{1}$ and $𝜋_{2}$ and $\cos 𝜃 = - \sqrt{\sqrt \frac{3}{7}}$ , then the integral value of $𝑎$ is

-2

Incorrect

-1

Incorrect

2

Incorrect

1

Incorrect

Q 34MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚$ and $𝐛$ are two vectors such that $𝐚 = 2 \hat{𝐢} + 2 \hat{𝐣} + 𝑝 \hat{𝐤}$ , $| 𝐛 | = 7, 𝐚 \cdot 𝐛 = 4$ and $| 𝐚 \times 𝐛 | = 5 \sqrt{\sqrt 17}$ , then $𝑝 =$

$\pm 5$

Incorrect

$\pm 6$

Incorrect

$\pm 1$

Incorrect

$\pm 3$

Incorrect

Q 35MathematicsSection A • MCQstatistics

+1 / -0

The mean deviation from the mean of the discrete data $1, 3, 4, 7, 11, 18, 29, 47, 78$ is

22

Incorrect

24

Incorrect

$\frac{176}{9}$

Incorrect

$\frac{182}{9}$

Incorrect

Q 36MathematicsSection A • MCQprobability

+1 / -0

When two dice are thrown, the probability of getting a prime number on die and a composite number on the other is

$1 / 3$

Incorrect

$1 / 4$

Incorrect

$1 / 2$

Incorrect

$1 / 6$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

Let $𝐴, 𝐵, 𝐶$ be three pairwise independent events of a random experiment. If $𝑃 (\bar{𝐵} \cup \bar{𝐶}) = \frac{1}{2}, 𝑃 (𝐴) > 0, 𝑃 (𝐵) = 𝑏$ and $𝑃 (𝐶) = 𝑐, 𝑃 ((\bar{𝐵} \cap \bar{𝐶} ∣ 𝐴) =$

$1 +$ b - c

Incorrect

$2 + 𝑏 - 𝑐$

Incorrect

$\frac{3}{2} - 𝑏 - 𝑐$

Incorrect

$2 - 𝑏 - 𝑐$

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of 4 . If $𝑝$ is the conditional probability that number 4 has appeared atleast once, then $3 𝑝 + 2 =$

$\frac{25}{12}$

Incorrect

$\frac{1}{6}$

Incorrect

$\frac{7}{3}$

Incorrect

$\frac{5}{2}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

In a random experiment of throwing 5 coins, the number of heads is defined as a random variable. The mean of the random variable is

$\frac{2}{3}$

Incorrect

$\frac{3}{2}$

Incorrect

$\frac{7}{9}$

Incorrect

$\frac{5}{2}$

Incorrect

Q 40MathematicsSection A • MCQprobability

+1 / -0

The variance of a Poisson variate $𝑋$ is 2 . Then, $𝑃 (𝑋 \geq 3) =$

$\frac{𝑒^{2} - 7}{𝑒^{2}}$

Incorrect

$\frac{𝑒^{2} - 3}{𝑒^{2}}$

Incorrect

$\frac{𝑒^{2} - 5}{𝑒^{2}}$

Incorrect

$1 - \frac{4}{𝑒^{2}}$

Incorrect

Q 41MathematicsSection A • MCQhyperbola

+1 / -0

If the perimeter of a triangle is 20 and two of its vertices are $(- 5, 0)$ and $(6, 0)$ , then the locus of the third vertex is

$40 𝑥^{2} - 81 𝑦^{2} - 40 𝑥 - 800 = 0$

Incorrect

$40 𝑥^{2} + 9 𝑦^{2} - 25 𝑥 + 800 = 0$

Incorrect

$40 𝑥^{2} - 9 𝑦^{2} = 800$

Incorrect

$5 𝑥^{2} - 3 𝑦^{2} + 3 𝑥 - 4 𝑦 + 25 = 0$

Incorrect

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

+1 / -0

The transformed equation of $3 𝑋^{2} + 4 𝑋 𝑌 + 𝑌^{2} - 8 𝑋 - 4 𝑌 - 4 = 0$ is $𝑓 (𝑋, 𝑌) = 𝑎 𝑋^{2} + 2 ℎ 𝑋 𝑌 + 𝑏 𝑌^{2} + 𝑐 = 0$ when the origin is shifted to a new point by the translation of axes. Then, $𝑓 (1, 1) =$

0

Incorrect

1

Incorrect

-1

Incorrect

-8

Incorrect

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

+1 / -0

If the line $2 𝑥 - 3 𝑦 + 4 = 0$ divides the line segment joining the points $𝐴 (- 2, 3)$ and $𝐵 (3, - 2)$ in the ratio $𝑚 : 𝑛$ , then the point which divides $𝐴 𝐵$ in the ratio $- 4 𝑚 : 3 𝑛$ is

$(- 17, 18)$

Incorrect

$(- \frac{59}{7}, \frac{66}{7})$

Incorrect

$(- 5, 6)$

Incorrect

$(- \frac{5}{7}, \frac{12}{7})$

Incorrect

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

+1 / -0

If the lines $𝐿_{1} \equiv 2 𝑥 + 𝑦 + 3 = 0, 𝐿_{2} \equiv 𝑘 𝑥 + 2 𝑦 - 3 = 0$ and $𝐿_{3} \equiv 3 𝑥 - 2 𝑦 + 1 = 0$ are concurrent then the cosine of the acute angle between the lines $𝐿_{2} = 0$ and $2 𝑥 - 5 𝑦 + 7 = 0$ is

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

Incorrect

$(\frac{15}{2 \sqrt{\sqrt 29}})$

Incorrect

$(\frac{25}{29})$

Incorrect

$(\frac{20}{29})$

Incorrect

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

+1 / -0

If $𝑄$ is the image of the point $𝑃 (1, 1)$ with respect to the straight line $𝑥 + 𝑦 + 1 = 0$ , then the length of the perpendicular drawn from $𝑄$ to the line $3 𝑥 - 4 𝑦 + 3 = 0$ is

$5 / 2$

Incorrect

2

Incorrect

1

Incorrect

$1 / 2$

Incorrect

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

+1 / -0

The centroid of the triangle formed by the lines $𝑥 - 3 𝑦 + 3 = 0, 𝑥 + 3 𝑦 + 3 = 0 𝑥 + 𝑦 - 1 = 0$ is

$(0, \frac{- 1}{3})$

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

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

+1 / -0

If the slope of one of the lines represented by $5 𝑥^{2} + \frac{40}{3} 𝑥 𝑦 + 𝑘 𝑦^{2} = 0$ is 3 , then the angle between the pair of lines is

0

Incorrect

$\frac{𝜋}{4}$

Incorrect

$\frac{𝜋}{3}$

Incorrect

$\frac{𝜋}{2}$

Incorrect

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

+1 / -0

If a line $𝐿$ is common to the pairs of lines $6 𝑥^{2} - 𝑥 𝑦 - 12 𝑦^{2} = 0$ and $15 𝑥^{2} + 14 𝑥 𝑦 - 8 𝑦^{2} = 0$ then the combined equation the other two lines is

$10 𝑥^{2} - 19 𝑥 𝑦 + 6 𝑦^{2} = 0$

Incorrect

$5 𝑥^{2} - 4 𝑥 𝑦 + 7 𝑦^{2} = 0$

Incorrect

$𝑥^{2} - 9 𝑥 𝑦 + 𝑦^{2} = 0$

Incorrect

$3 𝑥^{2} + 6 𝑥 𝑦 + 11 𝑦^{2} = 0$

Incorrect

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

+1 / -0

If $𝐿$ is a line passing through the point $(- 1, 1)$ and parallel to the common line of the pairs of lines $6 𝑥^{2} - 𝑥 𝑦 - 12 𝑦^{2} = 0$ and $15 𝑥^{2} + 14 𝑥 𝑦 - 8 𝑦^{2} = 0$ , then the equation of pair of lines joining the origin to the points of intersection of the curve $2 𝑥^{2} - 𝑥 𝑦 - 𝑦^{2} + 𝑥 - 𝑦 = 0$ and the line $𝐿$ is

$𝑥^{2} - 𝑥 𝑦 - 𝑦^{2} = 0$

Incorrect

$𝑥^{2} + 𝑥 𝑦 - 𝑦^{2} = 0$

Incorrect

$𝑥^{2} - 𝑦^{2} = 0$

Incorrect

$2 𝑥^{2} + 3 𝑥 𝑦 - 6 𝑦^{2} = 0$

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

From a point $𝐴 (0, 3)$ on the circle $(𝑥 + 2)^{2} + (𝑦 - 3)^{2} = 4$ , a chord $𝐴 𝐵$ is drawn and it is extended to a point $𝑄$ such that $𝐴 𝑄 = 2 𝐴 𝐵$ . Then, the locus of $𝑄$ is

$(𝑥 + 4)^{2} + (𝑦 - 3)^{2} = 16$

Incorrect

$(𝑥 + 1)^{2} + (𝑦 - 3)^{2} = 32$

Incorrect

$(𝑥 + 1)^{2} + (𝑦 - 3)^{2} = 4$

Incorrect

$(𝑥 + 1)^{2} + (𝑦 - 3)^{2} = 1$

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

If $𝑚_{1}, 𝑚_{2}$ are the slopes of the tangents drawn from a point $(1, - 3)$ to the circle $𝑥^{2} + 𝑦^{2} - 6 𝑥 + 4 𝑦 + 12 = 0$ , then $9 (𝑚_{2}^{1} + 𝑚_{2}^{2}) =$

16

Incorrect

25

Incorrect

4

Incorrect

1

Incorrect

Q 52MathematicsSection A • MCQcircle

+1 / -0

If $𝐴, 𝐵$ are the points of contact of the tangents drawn from the point $𝑃 (- 2, - 3)$ to the circle $𝑥^{2} + 𝑦^{2} - 8 𝑥 - 10 𝑦 + 5 = 0$ and the chord $𝐴 𝐵$ subtends an angle $𝜃$ at $𝑃$ , then $\tan 𝜃 =$

$\frac{3}{4}$

Incorrect

$\frac{24}{7}$

Incorrect

$\frac{7}{24}$

Incorrect

$\frac{4}{3}$

Incorrect

Q 53MathematicsSection A • MCQcircle

+1 / -0

The equation of the transverse common tangent of the circles $𝑥^{2} + 𝑦^{2} - 6 𝑥 - 8 𝑦 + 9 = 0$ and $𝑥^{2} + 𝑦^{2} + 2 𝑥 - 2 𝑦 + 1 = 0$

$4 𝑥 + 3 𝑦 - 4 = 0$

Incorrect

$3 𝑥 + 𝑦 - 1 = 0$

Incorrect

$2 𝑥 - 𝑦 + 2 = 0$

Incorrect

$𝑥 + 2 𝑦 - 3 = 0$

Incorrect

Q 54MathematicsSection A • MCQcircle

+1 / -0

If $𝜃$ is the angle between the circles

$𝑥^{2} + 𝑦^{2} - 2 𝑥 - 4 𝑦 - 4 = 0$ and $𝑥^{2} + 𝑦^{2} - 8 𝑥 - 12 𝑦 + 43 = 0$ , then $| 7 \sec 𝜃 - 18 \cos 𝜃 | =$

11

Incorrect

9

Incorrect

0

Incorrect

1

Incorrect

Q 55MathematicsSection A • MCQcircle

+1 / -0

If $(0, \frac{3}{4})$ is the radical centre of the circles $𝑆 \equiv 𝑥^{2} + 𝑦^{2} + 𝛼 𝑥 + 6 𝑦 = 0, 𝑆 \equiv 𝑥^{2} + 𝑦^{2} + 2 𝛼 𝑥 + 𝛼 𝑦 + 6 = 0$ and $𝑆^{''} \equiv 𝑥^{2} + 𝑦^{2} + 6 𝛼 𝑥 - 𝛼 𝑦 + 3 = 0$ , then the distance between the radical centre and the centre of the circle $𝑆^{'} = 0$ is

8

Incorrect

15

Incorrect

$\frac{\sqrt{\sqrt 65}}{4}$

Incorrect

$\frac{\sqrt{\sqrt 5}}{4}$

Incorrect

Q 56MathematicsSection A • MCQparabola

+1 / -0

The vertex and the focus of the parabola $2 𝑥^{2} + 5 𝑦 - 6 𝑥 + 1 = 0$ respectively, are

$(\frac{- 3}{2}, \frac{7}{10}), (\frac{- 3}{2}, \frac{53}{40})$

Incorrect

$(\frac{- 3}{2}, \frac{7}{10}), (\frac{- 3}{2}, \frac{3}{40})$

Incorrect

$(\frac{3}{2}, \frac{7}{10}), (\frac{3}{2}, \frac{53}{40})$

Incorrect

$(\frac{3}{2}, \frac{7}{10}), (\frac{3}{2}, \frac{3}{40})$

Incorrect

Q 57MathematicsSection A • MCQparabola

+1 / -0

The axis of a parabola is along the line $𝑦 = 𝑥$ and the distance of its vertex $𝐴$ from $(0, 0)$ is $\sqrt{\sqrt 2}$ and that of its focus $𝑆$ from $(0, 0)$ is $2 \sqrt{\sqrt 2}$ . If $𝐴$ and $𝑆$ lie in first quadrant, then the equation of the parabola in parametric form is

$𝑥 = (𝑡 + 1)^{2}, 𝑦 = (𝑡 - 1)^{2}$

Incorrect

$𝑥 = 𝑡^{2}, 𝑦 = 2 𝑡$

Incorrect

$𝑥 = (𝑡 - \sqrt{\sqrt 2})^{2}, 𝑦 = (𝑡 + \sqrt{\sqrt 2})^{2}$

Incorrect

$𝑥 = 𝑡^{2} + 5, 𝑦 = 𝑡^{2} - 5$

Incorrect

Q 58MathematicsSection A • MCQellipse

+1 / -0

Let $𝑆 \equiv \frac{𝑥^{2}}{𝑎^{2}} + \frac{𝑦^{2}}{𝑏^{2}} - 1 = 0, 𝑆 \equiv \frac{𝑥^{2}}{𝛼^{2}} + \frac{𝑦^{2}}{𝛽^{2}} - 1 = 0$ be two intersecting ellipses. If $𝑃 (𝑎 \cos 𝜃, 𝑏 \sin 𝜃)$ and $𝑄 (𝑎 \cos (\frac{𝜋}{2} + 𝜃), 𝑏 \sin (\frac{𝜋}{2} + 𝜃))$ are their points of intersection then $\frac{1}{2} (𝑎^{2} 𝛽^{2} + 𝑏^{2} 𝛼^{2}) =$

$𝑎^{2} 𝑏^{2}$

Incorrect

$𝛼^{2} + 𝛽^{2}$

Incorrect

$𝑎^{2} + 𝑏^{2}$

Incorrect

$𝛼^{2} 𝛽^{2}$

Incorrect

Q 59MathematicsSection A • MCQellipse

+1 / -0

$𝑃 (𝜃_{1})$ and $𝑄 (𝜃_{2})$ are two points on the ellipse $\frac{𝑥^{2}}{𝑎^{2}} + \frac{𝑦^{2}}{𝑏^{2}} = 1$ with eccentricity $𝑒$ . If $𝑃 𝑆 𝑄$ is a focal chord and $\tan (\frac{𝜃_{1}}{2}) \tan (\frac{𝜃_{2}}{2}) = - (2 \sqrt{\sqrt 2} + 3)$ , then $𝑒$ and $𝑆$ are

$\frac{1}{\sqrt{\sqrt 3}}, (\frac{𝑎}{\sqrt{\sqrt 3}}, 0)$

Incorrect

$\frac{1}{\sqrt{\sqrt 3}}, (\frac{- 𝑎}{\sqrt{\sqrt 3}}, 0)$

Incorrect

$\frac{1}{\sqrt{\sqrt 2}}, (\frac{𝑎}{\sqrt{\sqrt 2}}, 0)$

Incorrect

$\frac{1}{\sqrt{\sqrt 2}}, (\frac{- 𝑎}{\sqrt{\sqrt 2}}, 0)$

Incorrect

Q 60MathematicsSection A • MCQhyperbola

+1 / -0

Let $𝑆$ be the focus of the hyperbola $\frac{𝑥^{2}}{16} - \frac{𝑦^{2}}{9} = 1$ lying on the positive $𝑋$ - axis and $𝑃 (5, 𝑦_{1})$ be point on the hyperbola. Then $𝑆 𝑃 =$

$1 / 4$

Incorrect

$3 / 4$

Incorrect

$9 / 4$

Incorrect

$5 / 4$

Incorrect

Q 61MathematicsSection A • MCQhyperbola

+1 / -0

If $𝑃 (𝜃) = (𝑥_{1}, \frac{3 \sqrt{\sqrt 5}}{2}), 0 < 𝜃 < \frac{𝜋}{2}$ is a point on the hyperbola $\frac{𝑥^{2}}{25} - \frac{𝑦^{2}}{9} = 1$ , where $𝜃$ is the parameter in its parametric form, then $2 𝑥_{1} + 9 \sin^{2} 𝜃 =$

8

Incorrect

10

Incorrect

20

Incorrect

34

Incorrect

Q 62MathematicsSection A • MCQ3d geometry

+1 / -0

If the points $𝐴 (1, 3, 5), 𝐵 (2, 4, 6), 𝐶 (4, 5, 𝑘)$ form a right angled triangle then the number of possible values of $𝑘$ is

2

Incorrect

3

Incorrect

0

Incorrect

1

Incorrect

Q 63MathematicsSection A • MCQ3d geometry

+1 / -0

Let $𝐴 = (3, 4, 0), 𝐵 = (4, 4, 4), 𝐶 = (- 6, 2, 3)$ and $𝐷 = (1, 1, 2)$ . If $𝜃$ is the acute angle between the lines $𝐴 𝐵$ and $𝐶 𝐷$ , then $\cos 𝜃 =$

$\frac{4}{17 \sqrt{\sqrt 3}}$

Incorrect

$\frac{3}{17 \sqrt{\sqrt 3}}$

Incorrect

$\frac{12}{17 \sqrt{\sqrt 3}}$

Incorrect

$\frac{11}{17 \sqrt{\sqrt 3}}$

Incorrect

Q 64MathematicsSection A • MCQ3d geometry

+1 / -0

A plane containing two lines whose direction ratios are $(- 1, 2, 1)$ and $(1, 3, 2)$ passes through the point $(2, 1, 𝑘)$ . If this plane also passes through the point $(3, - 1, 4)$ , then $𝑘 =$

5

Incorrect

3

Incorrect

6

Incorrect

-3

Incorrect

Q 65MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

Let $𝐴 = (𝑎_{𝑖 𝑗})$ be an $𝑛 \times 𝑛$ matrix defined by $𝑎_{𝑖 𝑗} = {\begin{matrix} 𝑘^{𝑖}, & \forall 𝑖 = 𝑗 \\ 0, & otherwise \end{matrix}$ . If $𝑚 =$ trace of $𝐴$ and $lim_{𝑘 \to 1} \frac{𝑛 - 𝑚}{1 - 𝑘} = 171$ , then the value of $𝑛$ is

18

Incorrect

23

Incorrect

35

Incorrect

42

Incorrect

Q 66MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

$lim_{𝑥 \to \infty} 𝑥^{3} [\sqrt{\sqrt 𝑥^{2} + \sqrt{\sqrt 𝑥^{4} + 1}} - \sqrt{\sqrt 2 𝑥}] =$

0

Incorrect

1

Incorrect

$1 / 4 \sqrt{\sqrt 2}$

Incorrect

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

Incorrect

Q 67MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

Let $𝑓 (𝑥) = ⎧⎩⎨⎪⎪ \begin{matrix} 3 - 𝑥 & if & 𝑥 < - 3 \\ 6 & if & - 3 \leq 𝑥 \leq 3 . Let 𝛼 be the number \\ 3 + 𝑥 & if & 𝑥 > 3 \end{matrix}$ of points of discontinuity of $𝑓$ and $𝛽$ be the number of points where $𝑓$ is not differentiable. Then, $𝛼 + 𝛽 =$

6

Incorrect

3

Incorrect

2

Incorrect

0

Incorrect

Q 68MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑎 𝑓 (𝑥) + 𝑏 𝑓 (\frac{1}{𝑥}) = 𝑥 + 1$ , and $\frac{𝑑}{𝑑 𝑥} (𝑥^{2} 𝑓 (𝑥)) = 2 𝑥^{2} + 2 𝑥 + \frac{1}{3}$ , then $𝑎 - 𝑏$

2

Incorrect

3

Incorrect

0

Incorrect

1

Incorrect

Q 69MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑓 (𝑥) = \sin (\cosh (\frac{𝑥^{2} + 1}{𝑥^{2} + 2}))$ , then $𝑓^{'} (1) =$

$\frac{2}{9} \sinh (\frac{2}{3}) \cos (\cosh (\frac{2}{3}))$

Incorrect

$\sinh (\frac{2}{3}) \cos (\cosh (\frac{2}{3}))$

Incorrect

$\frac{2}{9} \cos (\cosh (\frac{2}{3}))$

Incorrect

$\frac{2}{9} \cosh (\frac{2}{3}) \cos (\sinh (\frac{2}{3}))$

Incorrect

Q 70MathematicsSection A • MCQapplication of derivatives

+1 / -0

If an error of $0.02 sq . cm$ is found in the surface area of a sphere when its radius is measured as 10 cm , then the approximate error that occurs in the volume of the sphere, in cubic centimeters, is

0.2

Incorrect

0.01

Incorrect

0.3

Incorrect

0.1

Incorrect

Q 71MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝜃$ is the angle between the curves $𝑦^{2} = 4 𝑥$ and $𝑥^{2} + 𝑦^{2} = 5$ , then $| \tan 𝜃 | =$

5

Incorrect

4

Incorrect

3

Incorrect

2

Incorrect

Q 72MathematicsSection A • MCQapplication of derivatives

+1 / -0

The local maximum value of the function $𝑓 (𝑥) = - (𝑥 - 2)^{3} (𝑥 + 2)^{2}$ is

0

Incorrect

$\frac{12^{3} \cdot 8^{2}}{5^{5}}$

Incorrect

125

Incorrect

$\frac{2^{9} \cdot 3^{2}}{5^{6}}$

Incorrect

Q 73MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int \frac{1 + \cos 8 𝑥}{\tan 2 𝑥 - \cot 2 𝑥} 𝑑 𝑥 = 𝑓 (𝑥) \cdot \cos (𝑔 (𝑥)) + 𝑐$ , then $𝑓 (\frac{1}{4}) + 𝑔 (\frac{1}{4}) =$

2

Incorrect

$\frac{17}{8}$

Incorrect

$\frac{15}{8}$

Incorrect

$\frac{33}{16}$

Incorrect

Q 74MathematicsSection A • MCQindefinite integration

+1 / -0

Let $𝑥 \neq \frac{- 3}{5}, \frac{2}{5}$ , if $𝑓 (\frac{2 𝑥 + 1}{5 𝑥 + 3}) = 𝑥 + 2$ , then $\int 𝑓 (𝑥) 𝑑 𝑥 =$

$\frac{7}{5} 𝑥 - \frac{1}{5} \log | 5 𝑥 + 3 | + 𝑐$

Incorrect

$\frac{7}{5} 𝑥 - \frac{1}{25} \log | 5 𝑥 + 3 | + 𝑐$

Incorrect

$\frac{7}{5} 𝑥 - \frac{1}{25} \log | 5 𝑥 - 2 | + 𝑐$

Incorrect

$\frac{7}{5} 𝑥 - \frac{1}{5} \log | 5 𝑥 - 2 | + 𝑐$

Incorrect

Q 75MathematicsSection A • MCQindefinite integration

+1 / -0

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

$\int \frac{\cos (\log (\frac{2 𝑥 + 3}{3 - 2 𝑥}))}{(3 - 2 𝑥)^{2}} 𝑑 𝑥 = \frac{𝑓 (𝑥)}{24} [\cos (𝑔 (𝑥)) + \sin (𝑔 (𝑥))] + 𝑐$

then $𝑔 (1) =$

5

Incorrect

$\log 𝑓 (2)$

Incorrect

$\log 𝑓 (1)$

Incorrect

0

Incorrect

Q 76MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{2}^{1} 𝑥 \sqrt{\sqrt 4 - 𝑥^{2}} 𝑑 𝑥 =$

$\sqrt{\sqrt 3}$

Incorrect

2

Incorrect

$1 / \sqrt{\sqrt 3}$

Incorrect

$1 / 2$

Incorrect

Q 77MathematicsSection A • MCQdefinite integration

+1 / -0

If $[𝑥]$ denotes the greatest integer function of $𝑥$ and

$\int_{3 / 2}^{- 3 / 2} [2 𝑥 - 3] 𝑑 𝑥 = 𝑘, then ∣ 𝑘 + \frac{1}{2} ∣ =$

7

Incorrect

8

Incorrect

10

Incorrect

12

Incorrect

Q 78MathematicsSection A • MCQdifferential equations

+1 / -0

The differential equation corresponding to the family of curves given by $𝑎 𝑥^{2} + 𝑏 𝑦^{2} = 1$ , where $𝑎$ and $𝑏$ are arbitrary constants is

$𝑥 \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}} = \frac{𝑑 𝑦}{𝑑 𝑥}$

Incorrect

$𝑥 𝑦 \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}} + 𝑥 {(\frac{𝑑 𝑦}{𝑑 𝑥})}^{2} - 𝑦 \frac{𝑑 𝑦}{𝑑 𝑥} = 0$

Incorrect

$𝑥 𝑦 \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}} + 𝑦 {(\frac{𝑑 𝑦}{𝑑 𝑥})}^{2} - 𝑥 \frac{𝑑 𝑦}{𝑑 𝑥} = 0$

Incorrect

$𝑥 𝑦 \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}} - 𝑥 {(\frac{𝑑 𝑦}{𝑑 𝑥})}^{2} + 𝑦 \frac{𝑑 𝑦}{𝑑 𝑥} = 0$

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

For the differential equation

$\sqrt{\sqrt \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}}} = \sqrt[3]{\sqrt}$

Order is 2 and degree is 3

Incorrect

Order is 3 and degree is 3

Incorrect

Order is 3 and degree is 2

Incorrect

Order is 2 and degree is not defined

Incorrect

Q 80MathematicsSection A • MCQdifferential equations

+1 / -0

The general solution of the differential equation $\frac{𝑑 𝑦}{𝑑 𝑥} = \frac{𝑥 𝑦 + 𝑥 - 2 𝑦 - 2}{𝑥 𝑦 - 2 𝑥 + 𝑦 - 2}$ is

$𝑥 + 𝑦 + 3 \log ∣ \frac{𝑥 + 1}{𝑦 + 1} ∣ = 𝑐$

Incorrect

$𝑥 + 𝑦 + 3 \log ∣ \frac{𝑦 + 1}{𝑥 + 1} ∣ = 𝑐$

Incorrect

$𝑥 - 𝑦 + 3 \log ∣ \frac{𝑥 + 1}{𝑦 + 1} ∣ = 𝑐$

Incorrect

$𝑥 - 𝑦 + 3 \log ∣ \frac{𝑦 + 1}{𝑥 + 1} ∣ = 𝑐$

Incorrect

Q 81PhysicsSection A • MCQatoms and nuclei

+1 / -0

Which of the following interaction is responsible for beta decay?

Gravitational

Incorrect

Weak

Incorrect

Electromagnetic

Incorrect

Strong

Incorrect

Q 82PhysicsSection A • MCQunits and measurements

+1 / -0

In a $𝑅$ - $𝐶$ circuit, where $𝑅$ is resistance and $𝐶$ is capacitance, which of the following has the dimension of time?

$𝑅 / 𝐶$

Incorrect

$𝐶 / 𝑅$

Incorrect

$\sqrt{\sqrt 𝑅 𝐶}$

Incorrect

$𝑅 𝐶$

Incorrect

Q 83PhysicsSection A • MCQmotion in a straight line

+1 / -0

A particle starts from rest. Its acceleration (a) versus time $(𝑡)$ graph is as shown in the figure. The maximum speed of the particle will be

qImage--motion-in-a-straight-line-mechanics-Jeemate

$150 m / s$

Incorrect

$75 m / s$

Incorrect

$37.5 m / s$

Incorrect

$45 m / s$

Incorrect

Q 84PhysicsSection A • MCQmotion in a straight line

+1 / -0

Assertion (A) The zero velocity of a particle at any instant always implies zero acceleration at that instant.

Reason (R) A body is momentarily at rest when it reverses its direction of motion. 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 85PhysicsSection A • MCQmotion in a straight line

+1 / -0

A river has a steady speed of $𝑣$ . A man swims upstream at a distance of $𝑑$ and swims back to the starting point in total time $𝑡$ . The man can swim at a speed of $2 𝑣$ in still water. If the time taken by the man in still water is $𝑡_{0}$ to complete the same length of swim, then $\frac{𝑡}{𝑡_{0}}$ is

$\frac{1}{2}$

Incorrect

$\frac{3}{2}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{4}{3}$

Incorrect

Q 86PhysicsSection A • MCQmotion in a plane

+1 / -0

A projectile is given an initial velocity of $(3 \hat{𝐢} + 4 \hat{𝐣}) m / s$ where $\hat{𝐢}$ is along the ground and $\hat{𝐣}$ is along the vertical. Assuming $𝑔 = 10 m / s^{2}$ , if the equation of its trajectory can be written as $\frac{1}{9} [𝛽 𝑥 + 𝛾 𝑥^{2}]$ . Then the value of $𝛾$ is

-8

Incorrect

-5

Incorrect

-6

Incorrect

-12

Incorrect

Q 87PhysicsSection A • MCQlaws of motion

+1 / -0

A block is placed on a parabolic shape ramp given by equation, $𝑦 = \frac{𝑥^{2}}{20}$ . If the coefficient of static friction $(𝜇_{𝑠})$ is 0.5 , then what is the maximum height above the ground at which the block can be placed without slipping?

2.5 m

Incorrect

1.25 m

Incorrect

0.5 m

Incorrect

0.25 m

Incorrect

Q 88PhysicsSection A • MCQmotion in a plane

+1 / -0

A small object slides down with initial velocity equal to zero from the top of a smooth hill of height $𝐻$ . The other end of the hill is horizontal and is at height $𝐻 / 2$ as shown in the figure. The horizontal distance covered by the object from the end of the hill to the ground is

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

2 H

Incorrect

H

Incorrect

$\frac{𝐻}{2}$

Incorrect

$\frac{3 𝐻}{2}$

Incorrect

Q 89PhysicsSection A • MCQcenter of mass

+1 / -0

A moving particle collides with a stationary particle of mass $\frac{1}{𝑛}$ times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is

$\frac{4 𝑛^{2}}{(1 + 𝑛)^{2}}$

Incorrect

$\frac{4 𝑛}{(1 + 𝑛)^{2}}$

Incorrect

$\frac{4 𝑛}{1 + 𝑛^{2}}$

Incorrect

$4 𝑛^{2}$

Incorrect

Q 90PhysicsSection A • MCQrotational motion

+1 / -0

A solid cylinder of mass $𝑚$ and radius $𝑅$ rolls down on an inclined plane of height 30 m without slipping. The speed of its centre of mass, when the cylinder reaches the bottom is

[use $𝑔 = 10 m / s^{2}$ ]

$10 m / s$

Incorrect

$20 m / s$

Incorrect

$30 m / s$

Incorrect

$40 m / s$

Incorrect

Q 91PhysicsSection A • MCQsimple harmonic motion

+1 / -0

A simple pendulum consists of a small sphere of mass $𝑚$ suspended by a thread of length $𝑙$ . The sphere carries a positive charge $𝑞$ . The pendulum is allowed to do small oscillations in uniform electric field $𝐸$ with direction vertically upwards. The time period of oscillation is

$2 𝜋 \sqrt{\sqrt \frac{1}{𝑔}}$

Incorrect

$2 𝜋 \sqrt{\sqrt \frac{𝑚 𝑙}{𝑞 𝐸}}$

Incorrect

$2 𝜋 \sqrt{\sqrt \frac{1}{𝑔 + \frac{𝑞}{𝑚} 𝐸}}$

Incorrect

$2 𝜋 \sqrt{\sqrt \frac{1}{𝑔 - \frac{𝑞}{𝑚} 𝐸}}$

Incorrect

Q 92PhysicsSection A • MCQgravitation

+1 / -0

A rocket is fired vertically with a speed of $4 km / s$ from the earth's surface. How far from the earth does the rocket go before returning to the earth?

(Take, radius of earth $= 6.4 \times 10^{6} m$ and $𝑔 = 10 m / s^{2}$ )

500.24 km

Incorrect

914.28 km

Incorrect

1230.24 km

Incorrect

1750.28 km

Incorrect

Q 93PhysicsSection A • MCQelasticity

+1 / -0

A swimming pool has a depth of 22 m and area $700 m^{2}$ . Calculate fractional change $Δ 𝑣 / 𝑣$ of water at the bottom of the swimming pool, given that the bulk modulus of water is $2.2 \times 10^{9} {Nm}^{- 2}, 𝑔 = 10 m / s^{2}$ , and density of water is $1000 kg / m^{3}$

$22 \times 10^{- 4}$

Incorrect

$0.7 \times 10^{- 4}$

Incorrect

$0.31 \times 10^{- 4}$

Incorrect

$10^{- 4}$

Incorrect

Q 94PhysicsSection A • MCQfluid mechanics

+1 / -0

A hollow spherical body of outer and inner radii of 4 cm and 2 cm respectively, floats half submerged in a liquid of density $2.0 g / {cm}^{3}$ . The density of the material of the sphere is

$1.02 g / {cm}^{2}$

Incorrect

$1.14 g / {cm}^{2}$

Incorrect

$1.18 g / {cm}^{2}$

Incorrect

$124 g / {cm}^{2}$

Incorrect

Q 95PhysicsSection A • MCQfluid mechanics

+1 / -0

What is the terminal velocity of a rain drop of radius 0.02 mm ?

[Note that the coefficient of viscosity of air is $1.8 \times 10^{- 5} N / m^{2}$ , density of water is $1000 kg / m^{3}$ . Use, $𝑔 = 10 m / s^{2}$ and density of air can be neglected in comparision with density of water]

$4.9 cm / s$

Incorrect

$9.8 cm / s$

Incorrect

$0.49 cm / s$

Incorrect

$49 cm / s$

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A hole of diameter 5 cm is drilled in a metal sheet at $30^{\circ} C$ . The linear expansion of metal is $2 \times 10^{- 5} K^{- 1}$ . The diameter of the hole when the temperature is raised to $230^{\circ} C$ , is equal to

5.01 cm

Incorrect

5.02 cm

Incorrect

5.03 cm

Incorrect

5.04 cm

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A metal cube absorbs 2100.0 J of heat when its temperature is raised by $2^{\circ} C$ . If the specific heat of the metal is $900 J {kg}^{- 1} K^{- 1}$ , then the mass of the cube is

1.116 kg

Incorrect

2.33 kg

Incorrect

1.66 kg

Incorrect

1.33 kg

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

The net work done by an ideal gas going through the cycle as shown in the $𝑝 - 𝑉$ diagram below is

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

0

Incorrect

$𝑝_{1} 𝑉_{1}$

Incorrect

$\frac{3}{2} 𝑝_{1} 𝑉_{1}$

Incorrect

$\frac{1}{2} 𝑝_{1} 𝑉_{1}$

Incorrect

Q 99PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A diatomic gas $(𝐶_{𝑝} = \frac{7}{2} 𝑅)$ does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is

600 J

Incorrect

800 J

Incorrect

900 J

Incorrect

700 J

Incorrect

Q 100PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Statement I Gas thermometers are less sensitive than liquid thermometers.

Statement II The ratio of universal gas constant and avogadro's number is called Boltzmann's constant.

Statement III The density of a given mass of a gas at constant pressure is inversely proportional to its absolute temperature.

The correct option among the following is

Statements I, II, III are true

Incorrect

Statements I, II are true, but statement III is false

Incorrect

Statements II, III are true, but statement I is false.

Incorrect

Statements I, II, III are false.

Incorrect

Q 101PhysicsSection A • MCQwaves

+1 / -0

The distance between two successive minima of a transverse wave is 2.7 m . Five crests of the wave pass a given point along the direction of travel every 15.0 s . The speed of the wave is

$0.9 m / s$

Incorrect

$1.2 m / s$

Incorrect

$0.5 m / s$

Incorrect

$2.4 m / s$

Incorrect

Q 102PhysicsSection A • MCQray optics

+1 / -0

A convex lens focusses an object 20 cm from it on a screen placed 5 cm away from it. A glass plate (refractive index $= 7 / 5$ ) of thickness 1.4 cm is inserted between the lens and the screen. What is the distance of the object from the lens, so that its image is again focused on the screen?

22.5 cm

Incorrect

30.7 cm

Incorrect

25.0 cm

Incorrect

28.4 cm

Incorrect

Q 103PhysicsSection A • MCQwave optics

+1 / -0

The angular width of a fringe in a double slit experiment is found to be ${0.2}^{\circ}$ on a screen 1 m away the wavelength of light used is 600 nm . The change in angular width of the fringe, if the entire measurement system is immersed in water is [use refractive index of water as $4 / 3$ ]

${0.05}^{\circ}$

Incorrect

${0.10}^{\circ}$

Incorrect

${0.15}^{\circ}$

Incorrect

${0.20}^{\circ}$

Incorrect

Q 104PhysicsSection A • MCQelectrostatics

+1 / -0

A large metal plate has a surface charge density of $8.85 \times 10^{- 6} C / m^{2}$ . An electron having initial kinetic energy of $8 \times 10^{- 17} J$ is moving towards the centre of the plate. If the electron stops just before reaching the plate, then the initial distance between the electron and the plate is

[take $𝜀_{0} = 8.85 \times 10^{- 12} C^{2} / N - m^{2}$ ]

0.5 mm

Incorrect

0.1 mm

Incorrect

0.2 cm

Incorrect

0.02 cm

Incorrect

Q 105PhysicsSection A • MCQcapacitor

+1 / -0

The equivalent capacitance between points $𝐴$ and $𝐵$ is

qImage--capacitor-electromagnetism-Jeemate

$5 / 6 C$

Incorrect

$11 / 5 C$

Incorrect

6 C

Incorrect

$5 / 11 C$

Incorrect

Q 106PhysicsSection A • MCQcurrent electricity

+1 / -0

A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by $6 %$ . The percentage increase in its length is

$2 %$

Incorrect

$4 %$

Incorrect

$3 %$

Incorrect

$12 %$

Incorrect

Q 107PhysicsSection A • MCQcurrent electricity

+1 / -0

Find the current in the three resistors as shown in the following figure?

qImage--current-electricity-electromagnetism-Jeemate

$𝑖_{1} = 0, 𝑖_{2} = \frac{4 𝑉}{𝑅}, 𝑖_{3} = \frac{2 𝑉}{𝑅}$

Incorrect

$𝑖_{1} = 0, 𝑖_{2} = 0, 𝑖_{3} = 0$

Incorrect

$𝑖_{1} = 0, 𝑖_{2} = \frac{2 𝑉}{𝑅}, 𝑖_{3} = \frac{4 𝑉}{𝑅}$

Incorrect

$𝑖_{1} = 0, 𝑖_{2} = \frac{2 𝑉}{𝑅}, 𝑖_{3} = \frac{2 𝑉}{𝑅}$

Incorrect

Q 108PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A horizontal wire carries 160 A current below which another wire of linear density $10 g / m$ carrying a current is kept at 4 cm distance. If the wire kept below hangs in air, what is the current in this wire, when the direction of current in both the wires is same? $(𝑔 = 10 m / s^{2}$ and $𝜇_{0} = 4 𝜋 \times 10^{- 7})$

125 A

Incorrect

140 A

Incorrect

110 A

Incorrect

100 A

Incorrect

Q 109PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A long solenoid has 70 turns / cm and carries current $𝐼$ . An electron moves within the solenoid in a circle of radius 2.5 cm perpendicular to the solenoid axis. If the speed of the electron is $4.4 \times 10^{6} m / s$ , then the current $𝐼$ in the solenoid is

(take $𝜇_{0} = 4 𝜋 \times 10^{- 7}$ Si unit, mass electron $= 9 \times 10^{- 31}$

kg , charge of electron $1.6 \times 10^{- 19} C$ )

98.5 mA

Incorrect

112.5 mA

Incorrect

125 mA

Incorrect

175.0 mA

Incorrect

Q 110PhysicsSection A • MCQmagnetism and matter

+1 / -0

Assertion (A) The magnetic field lines are continuous and form closed loops. Reason (R) Magnetic monopole does not exist. 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 111PhysicsSection A • MCQelectromagnetic induction

+1 / -0

A flat circular coil has 100 turns of wire of radius 10 cm . A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of $0.1 T / s$ . The induced emf in the coil is

$𝜋 V$

Incorrect

$10 𝜋 V$

Incorrect

$\frac{𝜋}{10} V$

Incorrect

$2 𝜋 V$

Incorrect

Q 112PhysicsSection A • MCQalternating current

+1 / -0

A $2 𝜇 F$ capacitor is charged to 50 V by a battery. The battery is removed after capacitor if fully charged. At time $𝑡 = 0$ , a 10 mH coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is

$2000 A / s$

Incorrect

$5000 A / s$

Incorrect

$2500 A / s$

Incorrect

$10000 A / s$

Incorrect

Q 113PhysicsSection A • MCQelectromagnetic waves

+1 / -0

An electromagnetic wave has its electric and magnetic fields given by

$𝐄 (𝑡) = 𝐄_{𝑚} \sin (𝑘 𝑥 - 𝜔 𝑡); 𝐁 (𝑡) = 𝐁_{𝑚} \sin (𝑘 𝑥 - 𝜔 𝑡)$

If the direction of $𝐄_{𝑚}$ and $𝐁_{𝑚}$ are in the direction of $(\hat{𝐢} + \hat{𝐣})$ and $(\hat{𝐢} - \hat{𝐣})$ respectively, the unit vector that gives the direction of propagation of the wave is

$- \hat{𝑘}$

Incorrect

$\hat{k}$

Incorrect

$\hat{i}$

Incorrect

$- \hat{𝐢}$

Incorrect

Q 114PhysicsSection A • MCQdual nature of radiation

+1 / -0

The value of planck's constant, if the slope of the graph of stopping potential versus frequency of incident light is $4 \times 10^{- 15} V$ -s is (given charge of an electron $= 1.6 \times 10^{- 19} C$ )

$6.0 \times 10^{- 34} J - s$

Incorrect

$62 \times 10^{- 34} J - s$

Incorrect

$6.4 \times 10^{- 34} J - s$

Incorrect

$6.6 \times 10^{- 34} J - s$

Incorrect

Q 115PhysicsSection A • MCQelectromagnetic waves

+1 / -0

A beam of white light is incident normally on a plane surface absorbing 70\% of the light and reflecting the rest. If the incident beam carries 10 W of power, the force exerted by it on the surface is

$3.3 \times 10^{- 8} N$

Incorrect

$4.33 \times 10^{- 8} N$

Incorrect

$2.3 \times 10^{- 8} N$

Incorrect

$3.53 \times 10^{- 8} N$

Incorrect

Q 116PhysicsSection A • MCQatoms and nuclei

+1 / -0

If the series limit frequency of Balmer series is $𝑣_{𝐵}$ , then the series limit frequency of the Brackett series is

$\frac{4 𝑣_{𝐵}}{25}$

Incorrect

$\frac{𝑉_{𝐵}}{9}$

Incorrect

$\frac{𝑉_{𝐵}}{4}$

Incorrect

$\frac{9 𝑣_{𝐵}}{4}$

Incorrect

Q 117PhysicsSection A • MCQatoms and nuclei

+1 / -0

Consider a nucleus $_{60}^{30} X$ . Its approximate density is (take, $1 amu = 1.6 \times 10^{- 27} kg, 𝑅_{0} = 1.2 \times 10^{- 15} m$ )

$12 \times 10^{18} kg / m^{3}$

Incorrect

$18.5 \times 10^{19} kg / m^{3}$

Incorrect

$3.3 \times 10^{16} kg / m^{3}$

Incorrect

$22 \times 10^{17} kg / m^{3}$

Incorrect

Q 118PhysicsSection A • MCQcurrent electricity

+1 / -0

The resistivity of a material is found to be $10^{8} Ω - m$ , then the material would be

Only insulator

Incorrect

Only metal

Incorrect

Only semiconductor

Incorrect

Only Superconductor

Incorrect

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

The behaviour of the circuit is like $____$ gate

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

OR

Incorrect

NOR

Incorrect

NAND

Incorrect

AND

Incorrect

Q 120PhysicsSection A • MCQcommunication systems

+1 / -0

A message signal of frequency 15 kHz is used to modulate a carrier of frequency $𝑣_{𝑐}$ . If the side bands produced are 1515 kHz and 1485 kHz , then $𝑣_{𝑐}$ is

2.0 MHz

Incorrect

1.5 MHz

Incorrect

2.5 MHz

Incorrect

3.0 MHz

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

The total number of spectral lines observed when electron returns from the 6th shell to the 2nd shell in hydrogen atom is

15

Incorrect

10

Incorrect

8

Incorrect

2

Incorrect

Q 122ChemistrySection A • MCQatomic structure

+1 / -0

The orbital angular momentum of an electron in $𝑑$ -orbital is equal to

0

Incorrect

$2 \sqrt{\sqrt 3} ℏ$

Incorrect

$6 ℏ$

Incorrect

$\sqrt{\sqrt 6} ℏ$

Incorrect

Q 123ChemistrySection A • MCQperiodic classification of elements

+1 / -0

The correct order of decreasing acidic nature of oxides is

${Li}_{2} O > BeO > {CO}_{2} > B_{2} O_{3} > N_{2} O_{3}$

Incorrect

${CO}_{2} > N_{2} O_{3} > B_{2} O_{3} > {Li}_{2} O > BeO$

Incorrect

${CO}_{2} > BeO > {Li}_{2} O > B_{2} O_{3} > N_{2} O_{3}$

Incorrect

$N_{2} O_{3} > {CO}_{2} > B_{2} O_{3} > BeO > {Li}_{2} O$

Incorrect

Q 124ChemistrySection A • MCQthermodynamics

+1 / -0

The change in enthalpy $[Δ 𝐻]$ in $kJ {mol}^{- 1}$ for the reaction, $Mg + 2 F ⟶ {MgF}_{2}$ is

Given, electron affinity of $F = 328 kJ {mol}^{- 1}$ ,

IE $_{1}$ of $Mg = 737 {kJmol}^{- 1}, {IE}_{2}$ of $Mg = 1451 {kJmol}^{- 1}$

3064

Incorrect

876

Incorrect

1860

Incorrect

1532

Incorrect

Q 125ChemistrySection A • MCQstates of matter

+1 / -0

Dipole-induced dipole interactions are present between which of the following pairs?

$H_{2} O$ and $C_{2} H_{5} OH$

Incorrect

${Cl}_{2}$ and ${CCl}_{4}$

Incorrect

${NH}_{3}$ and $H_{2}$

Incorrect

${SiF}_{4}$ and ${BF}_{3}$

Incorrect

Q 126ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

According to the Lewis formula of $O_{3}$ , the correct option is

qImage--chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Incorrect

qImage--chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Incorrect

qImage--chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Incorrect

qImage--chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Incorrect

Q 127ChemistrySection A • MCQstates of matter

+1 / -0

A gaseous mixture of 2 moles of $𝐴, 3$ moles of $𝐵$ , 5 moles of $𝐶$ and 10 moles of $𝐷$ is contained is contained in a vessel. Assuming that gases are ideal and partial pressure of $𝐶$ is 1.5 atm , the total pressure is

15 atm

Incorrect

10 atm

Incorrect

3 atm

Incorrect

6 atm

Incorrect

Q 128ChemistrySection A • MCQchemical kinetics

+1 / -0

The rate constant of a reaction is increased by 4 times after addition of catalyst to the reaction mixture at the same temperature of $27^{\circ} C$ . The change in the activation energy of this reaction is (Take $\ln (1 / 4) = - 1386, 𝑅 = 8.314$ )

$- 15 kJ / mol$

Incorrect

$- 1.5 kJ / mol$

Incorrect

$- 3.45 kJ / mol$

Incorrect

$- 34.5 kJ / mol$

Incorrect

Q 129ChemistrySection A • MCQsurface chemistry

+1 / -0

A cube of edge length 1 cm is divided into smaller cubes of uniform size of length 1 nm . Assuming that, no voids are present, the ratio of total surface area of all the cubes of 1 nm edge length to the surface area of the initial cube is

$10^{9}$

Incorrect

$10^{7}$

Incorrect

$10^{6}$

Incorrect

$10^{5}$

Incorrect

Q 130ChemistrySection A • MCQsome basic concepts of chemistry

+1 / -0

Calculate the number of moles of NaOH required to completely neutralise 100 g of $118 %$ oleum.

2.4

Incorrect

1.2

Incorrect

4.8

Incorrect

8.4

Incorrect

Q 131ChemistrySection A • MCQthermodynamics

+1 / -0

A certain mass of a gas was brought from state $𝐴$ to $𝐵$ by following three different paths, namely 1,2 and 3 , respectively. Which of the following relations is correct for the work done?

qImage--thermodynamics-physical-chemistry-Jeemate

$W_{1} = W_{2} = W_{3}$

Incorrect

$𝑊_{1} < 𝑊_{2} < 𝑊_{3}$

Incorrect

$𝑊_{1} > 𝑊_{2} > 𝑊_{3}$

Incorrect

$𝑊_{1} = 𝑊_{3} < 𝑊_{2}$

Incorrect

Q 132ChemistrySection A • MCQchemical equilibrium

+1 / -0

For the formation of ammonia gas from its constituent elements, the $𝐾_{𝑝} / 𝐾_{𝐶}$ is

$𝑅 𝑇$

Incorrect

$\frac{1}{(𝑅 𝑇)^{2}}$

Incorrect

$\frac{1}{\sqrt{\sqrt 𝑅 𝑇}}$

Incorrect

1

Incorrect

Q 133ChemistrySection A • MCQionic equilibrium

+1 / -0

$Match the following.$

List I		List II
A	Aqueous solution of ${AlCl}_{3}$	I	Basic
B	Aqueous solution ${CH}_{3} COONa$	II	Acidic
C	Aqueous solution of KCl	III	Highly conductive
D	${Al}_{2} O_{3}$	IV	Strongly basic
		V	Amphoteric

$The correct match is$

A	B	C	D
II	I	III	V

Incorrect

A	B	C	D
I	III	IV	V

Incorrect

A	B	C	D
III	II	I	V

Incorrect

A	B	C	D
IV	V	II	I

Incorrect

Q 134ChemistrySection A • MCQhydrogen

+1 / -0

The most effective water softening method is

lime - soda process

Incorrect

permutit process

Incorrect

ion - exchange process

Incorrect

boiling followed by filtration

Incorrect

Q 135ChemistrySection A • MCQs block elements

+1 / -0

Potassium superoxide on hydrolysis gives

$K^{+} + {OH}^{-} + O_{2}$

Incorrect

$K^{+} + K_{2} O + O_{2} + {OH}^{-}$

Incorrect

$K^{+} + H_{2} O_{2} + O_{2} + {OH}^{-}$

Incorrect

$K^{+} + H_{2} O_{2} + {OH}^{-}$

Incorrect

Q 136ChemistrySection A • MCQp block elements

+1 / -0

When aluminium chloride is dissolved in water, it gives

${[Al (OH)_{6}]}^{3 -} + 3 HCl$

Incorrect

${Al}_{2} O_{3} + 6 HCl$

Incorrect

${[Al {(H_{2} O)}_{6}]}^{3 +} + 3 {Cl}^{-}$

Incorrect

${Al}^{3 +} + 3 {Cl}^{-}$

Incorrect

Q 137ChemistrySection A • MCQthermodynamics

+1 / -0

Among the following given substances, the one with zero $Δ_{𝑓} 𝐻^{\circ}$ is

diamond

Incorrect

graphite

Incorrect

fullerene

Incorrect

bituminous coal

Incorrect

Q 138ChemistrySection A • MCQisomerism

+1 / -0

Identify the chiral molecule among the following.

Isopropyl alcohol

Incorrect

2-pentanol

Incorrect

1-bromo-3-butene

Incorrect

Isobutyl alcohol

Incorrect

Q 139ChemistrySection A • MCQhydrocarbons

+1 / -0

The most suitable solvent for Wurtz reaction is

dry acetonitrile

Incorrect

dry dichloromethane

Incorrect

dry ethanol

Incorrect

dry ether

Incorrect

Q 140ChemistrySection A • MCQaldehyde and ketone

+1 / -0

Propyne was subjected to a reaction with ${HgSO}_{4} /$ dil. $H_{2} {SO}_{4}$ , which resulted in a product $𝑃$ . The product $𝑃$ was heated with $Ba (OH)_{2}$ to give the product $𝑄$ . The molecular formula of the product $𝑄$ is

$C_{3} H_{6} O$

Incorrect

$C_{3} H_{8} OH$

Incorrect

$C_{6} H_{12} O_{2}$

Incorrect

$C_{6} H_{10} O$

Incorrect

Q 141ChemistrySection A • MCQsolid state

+1 / -0

The correct option for axial distances and axial angles for hexagonal crystal system is

$𝑎 \neq 𝑏 \neq 𝑐, 𝛼 \neq 𝛽 \neq 𝛾 = 90^{\circ}$

Incorrect

$𝑎 = 𝑏 \neq 𝑐, 𝛼 = 𝛽 = 𝛾 = 90^{\circ}$

Incorrect

$𝑎 = 𝑏 \neq 𝑐, 𝛼 = 𝛽 = 90^{\circ}, 𝛾 = 120^{\circ}$

Incorrect

$𝑎 \neq 𝑏 \neq 𝑐, 𝛼 = 𝛽 = 𝛾 = 90^{\circ}$

Incorrect

Q 142ChemistrySection A • MCQsolutions

+1 / -0

Which of the following is/are "not correct" for ${CH}_{3} OH + {CH}_{3} COOH$ mixture solution?

1. $Δ 𝐻_{mix} < 0$
2. Does not obey Raoult's law.
3. $Δ 𝐻_{mix} > 0$
4. An example of ideal solution.

4 only

Incorrect

1,3 only

Incorrect

1, 2, 3 only

Incorrect

3, 4 only

Incorrect

Q 143ChemistrySection A • MCQsolutions

+1 / -0

Henry's law is valid for

(A) ammonia gas dissolution in water

(B) $O_{2}$ gas dissolution in unsaturated blood

(C) $O_{2}$ dissolution in water

(D) ${CO}_{2}$ dissolution in water

A and B

Incorrect

B and C

Incorrect

C and D

Incorrect

B and D

Incorrect

Q 144ChemistrySection A • MCQelectrochemistry

+1 / -0

On passing a current of 1.2 A through a solution of salt of copper for $40 \min, 0.96 g$ of copper was deposited. The equivalent weight of copper in g is

21.2

Incorrect

31.75

Incorrect

63.5

Incorrect

15.9

Incorrect

Q 145ChemistrySection A • MCQchemical kinetics

+1 / -0

Half-life periods for a reaction at initial concentrations of 0.1 M and 0.01 M are 5 and 50 minutes, respectively. The order of reaction is

3

Incorrect

2

Incorrect

1

Incorrect

0

Incorrect

Q 146ChemistrySection A • MCQsurface chemistry

+1 / -0

Catalysts in the following reactions are

(I) ${CH}_{3} {COOCH}_{3} (𝑙) + H_{2} O (𝑙) ⟶ {CH}_{3} COOH (𝑎 𝑞) + {CH}_{3} OH (𝑙)$

(II) $2 {SO}_{2} (g) ⟶ 2 {SO}_{3} (g)$

(III) $2 {SO}_{2} (g) + O_{2} (g) ⟶ 2 {SO}_{3} (g)$

(IV) $N_{2} (g) + 3 H_{2} (g) ⟶ 2 {NH}_{3} (g)$

$HCl (s), Pt (s), NO (g)$ and $Fe (s)$

Incorrect

$HCl (s), NO (g), Pt (s)$ and $Fe (s)$

Incorrect

$HCl (s, Ni (s), NO (g)$ and $Fe (s)$

Incorrect

$HCl (Ω, Pt (s), N_{2} O (g)$ and $Fe (s)$

Incorrect

Q 147ChemistrySection A • MCQp block elements

+1 / -0

The total number of paramagnetic gaseous products formed in all the following reactions $[𝐴 + 𝐵 + 𝐶]$ are

(A) ${NH}_{4} {NO}_{3} \overset{Δ}{\to\leftarrow}$ Products

(B) ${NaNO}_{2} + H_{2} {SO}_{4} ⟶$ Products

(C) $Pb {({NO}_{3})}_{2} \overset{673 K}{\to\leftarrow}$ Products

0

Incorrect

1

Incorrect

2

Incorrect

3

Incorrect

Q 148ChemistrySection A • MCQp block elements

+1 / -0

The main products $𝑃$ and $𝑄$ of the following unbalanced disproportionation reaction ${Se}_{2} {Cl}_{2} ⟶ 𝑃 + 𝑄$ are

${SeCl}_{2} {SeCl}_{3}$

Incorrect

${SeCl}_{4} {SeCl}_{2}$

Incorrect

${SeCl}_{4} Se$

Incorrect

${SeCl}_{4} {Se}_{2}$

Incorrect

Official Correct Answer:Option (C)

Step-by-Step Solution:

$2 {Se}_{2} {Cl}_{2} ⟶ {SeCl}_{4} + 3 Se$

In a disproportionation reaction, the element is oxidised and reduced simultaneously.

Campound Element	$Oxidation state of Se$
${{Se}_{2} Cl}_{2}$	+1
(P) ${SeCl}_{4}$	+4
(Q) $Se$	0

Q 149ChemistrySection A • MCQp block elements

+1 / -0

The correct order of acidity of $HClO, HBrO$ and HIO is

$HIO > HBrO > HClO$

Incorrect

$HBrO > HIO > HClO$

Incorrect

$HClO > HBrO > HIO$

Incorrect

$HIO > HClO > HBrO$

Incorrect

Q 150ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

The linear molecule among the following is

${SnCl}_{2}$

Incorrect

${PbCl}_{2}$

Incorrect

${SO}_{2}$

Incorrect

${XeF}_{2}$

Incorrect

Official Correct Answer:Option (D)

Step-by-Step Solution:

$Molecule$	Shape
${SnCl}_{2}$	Bent or angular
${PbCl}_{2}$	Bent or V shape
${SO}_{2}$	Trigonal planar
${XeF}_{2}$	Linear

qImage--chemical-bonding-and-molecular-structure-inorganic-chemistry-Jeemate

Q 151ChemistrySection A • MCQd and f block elements

+1 / -0

Assertion (A) In general, transition metals have high melting points.

Reason (R) More number of electrons from ' $(𝑛 - 1) 𝑑^{'}$ and ' $𝑛 𝑠$ ' are involved in interatomic metallic bonding.

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 152ChemistrySection A • MCQcoordination compounds

+1 / -0

Among the given complexes the possess " ${CO}^{''}$ as a bridged ligands are

I. $[{Co}_{2} (CO)_{8}]$

II. $[{Fe}_{3} (CO)_{12}]$

III. $[{Mn}_{2} (CO)_{10}]$

IV. $[{Fe}_{2} (CO)_{9}]$

I, II and III

Incorrect

II, III and IV

Incorrect

I, II and IV

Incorrect

I, III and IV

Incorrect

Q 153ChemistrySection A • MCQbiomolecules

+1 / -0

The amount of sucrose needed to produce 1 mole of glucose using acid hydrolysis is

360 g

Incorrect

180 g

Incorrect

342 g

Incorrect

171 g

Incorrect

Q 154ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

The order of reactivity of the following compounds towards dilute aqueous KOH in

S_{N} 1

reaction is I.

{CH}_{3} {CH}_{2} {CH}_{2} {CH}_{2} Br

II.

H_{3} {CCH}_{2} {CHBrCH}_{3}

III.

({CH}_{3}) {CHCH}_{2} Br

IV.

{({CH}_{3})}_{3} CBr

I $<$ IV $<$ III $<$ II

Incorrect

IV $<$ II $<$ III $<$ I

Incorrect

III $<$ II $<$ I $<$ IV

Incorrect

I $<$ III $<$ II $<$ IV

Incorrect

Q 155ChemistrySection A • MCQalcohols phenols and ethers

+1 / -0

$𝐴, 𝐵, 𝐶, 𝐷 in the following reactions are$

qImage--alcohol-phenols-and-ethers-organic-chemistry-Jeemate

Incorrect

qImage--alcohol-phenols-and-ethers-organic-chemistry-Jeemate

Incorrect

qImage--alcohol-phenols-and-ethers-organic-chemistry-Jeemate

Incorrect

qImage--alcohol-phenols-and-ethers-organic-chemistry-Jeemate

Incorrect

Q 156ChemistrySection A • MCQalcohols phenols and ethers

+1 / -0

Which of the following statements are correct for phenol?

(A) In general, phenol is more acidic than alcohol.

(B) Phenol is used in the production of melamine plastic.

(C) Phenol gives violet colour with neutral ferric chloride solution.

(D) Phenol when heated with acetyl chloride gives phenetole.

C and D

Incorrect

A and D

Incorrect

B and C

Incorrect

A and C

Incorrect

Q 157ChemistrySection A • MCQaldehyde and ketone

+1 / -0

$The major product in the following reactions is$

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 158ChemistrySection A • MCQaldehyde and ketone

+1 / -0

$The major product of the following reaction is$

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 159ChemistrySection A • MCQcarboxylic acids and its derivatives

+1 / -0

$𝑛$ - propanol on treatment with concentrated HBr gives $𝑃$ . The product $𝑃$ on reaction with KCN gave the product $𝑄$ . The product $𝑄$ on heating with aqueous acidic solution, furnished the product $𝑅$ . The product ' $𝑅$ ' is

propanoic acid

Incorrect

propanamide

Incorrect

butanoic acid

Incorrect

butanamide

Incorrect

Q 160ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

The major product of the following synthetic sequence 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

List-I	List-II	Explanation
(A) Aqueous solution of ${AlCl}_{3}$	(II) Acidic	Salt of strong acid and weak base. $(Al (OH)_{3} + HCl)$
(B) Aqueous solution of ${CH}_{3} COONa$	(I) Basic	Salt of weak acid and strong base. ( ${CH}_{3} COOH + NaOH$ )
(C) Aqueous solution of KCl	(III) Highly conductive	Salt of strong acid and strong base. ( $KOH + HCl$ )
(D) Aqueous solution of ${Al}_{2} O_{3}$	(V) Amphoteric	Reacts both with acids and bases.

TG EAPCET 2022 18th July Evening Shift Question Paper with Solutions