Tg Eapcet 2025 4th May Morning Shift Question Paper Question Paper with Solutions | TG EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝑓 (𝑥) = 𝑥^{2} + 𝑏 𝑥 + 𝑐$ and $𝑓 (1 + 𝑘) = 𝑓 (1 - 𝑘) \forall 𝑘 \in 𝑅$ , for two real numbers $𝑏$ and $𝑐$ then

$f(1)<f(0)<f(-1)$

Incorrect

$f(-1)<f(0)<f(1)$

Incorrect

$f(0)<f(-1)<f(1)$

Incorrect

$f(0)<f(1)<f(-1)$

Incorrect

Q 2MathematicsSection A • MCQfunctions

+1 / -0

The domain of the real valued function $𝑓 (𝑥) = \log_{\sqrt{\sqrt 2}} (\sqrt{\sqrt 𝑥^{2} + 𝑥} + \sqrt{\sqrt 𝑥^{2} - 𝑥})$ is

$[- 1, 1]$

Incorrect

$(- \infty, - 1] \cup [1, \infty)$

Incorrect

$(- \infty, \infty)$

Incorrect

$(0, \infty)$

Incorrect

Q 3MathematicsSection A • MCQsequences and series

+1 / -0

$𝑡_{1}, 𝑡_{2}, 𝑡_{3}, \dots, 𝑡_{𝑛}$ are positive integers, $𝑆_{𝑛} = 𝑡_{1} + 𝑡_{2} + 𝑡_{3} + \dots + 𝑡_{𝑛}$ , $𝑆_{1} = 1^{2}, 𝑆_{2} = 3^{2}, 𝑆_{3} = 6^{2}, 𝑆_{4} = 10^{2}, 𝑆_{5} = 15^{2}$ and similarly other terms are there. Following this pattern, if $𝑆_{10} = 𝑘^{2}$ then $𝑘 =$

55

Incorrect

45

Incorrect

36

Incorrect

21

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝑥 = 𝛼, 𝑦 = 𝛽, 𝑧 = 𝛾$ is the solution of the system of equations $2 𝑥 + 3 𝑦 + 𝑧 = - 1, 3 𝑥 + 𝑦 + 𝑧 = 4$ , $𝑥 - 3 𝑦 - 2 𝑧 = 1$ , then the value of $𝛽$ is

-2

Incorrect

-1

Incorrect

2

Incorrect

1

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

The positive value of ' $𝑎$ ' for which the system of linear homogeneous equations $𝑥 + 𝑎 𝑦 + 𝑧 = 0, 𝑎 𝑥 + 2 𝑦 - 𝑧 = 0$ , $2 𝑥 + 3 𝑦 + 𝑧 = 0$ has non-trivial solution is

0

Incorrect

1

Incorrect

$\frac{1 + \sqrt{\sqrt 5}}{2}$

Incorrect

$\frac{\sqrt{\sqrt 5} - 1}{2}$

Incorrect

Q 6MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴 = ⎡⎣⎢ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{matrix} ⎤⎦⎥$ then $| adj | (𝐴^{2}) ∣=$

9

Incorrect

27

Incorrect

729

Incorrect

81

Incorrect

Q 7MathematicsSection A • MCQsequences and series

+1 / -0

$𝐾 = ∣ \begin{matrix} 3 & 4 \\ 5 & 4 \end{matrix} ∣ + ∣ \begin{matrix} 1 & - 1 \\ 5 & 4 \end{matrix} ∣ + ∣ \begin{matrix} \frac{1}{3} & \frac{1}{4} \\ 5 & 4 \end{matrix} ∣ + ∣ \begin{matrix} \frac{1}{9} & - \frac{1}{16} \\ 5 & 4 \end{matrix} ∣ + \dots$ to $\infty$ , then $𝐾 =$

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Q 8MathematicsSection A • MCQcomplex numbers

+1 / -0

${(\frac{1 + 𝑖}{1 - 𝑖})}^{228} =$

$- 4 {(\frac{1 - 𝑖}{1 + 𝑖})}^{226}$

Incorrect

$4 {(\frac{1 - 𝑖}{1 + 𝑖})}^{226}$

Incorrect

${(\frac{1 - 𝑖}{1 + 𝑖})}^{228}$

Incorrect

$- {(\frac{1 - 𝑖}{1 + 𝑖})}^{228}$

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

Let $𝑧 = 𝑥 + 𝑖 𝑦$ represent a point of $𝑃 (𝑥, 𝑦)$ in the argand plane. If $𝑧$ satisfies the condition that amplitude of $\frac{𝑧 - 3}{𝑧 - 2 𝑖} = - \frac{𝜋}{2}$ then the locus of $𝑃$ is

the circle $𝑥^{2} + 𝑦^{2} - 3 𝑥 - 2 𝑦 = 0$ .

Incorrect

the arc of the circle $𝑥^{2} + 𝑦^{2} - 3 𝑥 - 2 𝑦 = 0$ intercepted by the diameter $2 𝑥 + 3 𝑦 - 6 = 0$ containing the origin and excluding the points $(3, 0)$ and $(0, 2)$ .

Incorrect

the arc of the circle $𝑥^{2} + 𝑦^{2} - 3 𝑥 - 2 𝑦 = 0$ intercepted by the diameter $2 𝑥 + 3 𝑦 - 6 = 0$ not containing the origin and excluding the points $(3, 0)$ and $(0, 2)$ .

Incorrect

the circle $𝑥^{2} + 𝑦^{2} - 3 𝑥 - 2 𝑦 = 0$ not containing the point $(0, 2)$ .

Incorrect

Q 10MathematicsSection A • MCQcomplex numbers

+1 / -0

$(1 - 𝑖 \sqrt{\sqrt 3})^{2025} =$

$2^{2025}$

Incorrect

$2^{2026}$

Incorrect

$- 2^{2025}$

Incorrect

$- 2^{2026}$

Incorrect

Q 11MathematicsSection A • MCQcomplex numbers

+1 / -0

One of the roots of the equation $(𝑥 + 1)^{4} + 81 = 0$ is

$3 (\frac{1 + 𝑖}{\sqrt{\sqrt 2}})$

Incorrect

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

Incorrect

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

Incorrect

$- (\frac{3 + 3 𝑖}{\sqrt{\sqrt 2}})$

Incorrect

Q 12MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼, 𝛽$ are the roots of the equation $𝑥^{2} + 3 𝑥 + 𝑘 = 0$ and $𝛼 + \frac{1}{𝛼}, 𝛽 + \frac{1}{𝛽}$ are the roots of the equation $4 𝑥^{2} + 𝑝 𝑥 + 18 = 0$ , then $𝑘$ satisfies the equation

$2 𝑥^{2} - 13 𝑥 + 20 = 0$

Incorrect

$𝑥^{2} - 5 𝑥 + 6 = 0$

Incorrect

$2 𝑥^{2} - 7 𝑥 + 3 = 0$

Incorrect

$𝑥^{2} - 8 𝑥 + 15 = 0$

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝑓 (𝑥)$ is a second degree polynomial such that $𝑓 (𝑥) \geq 0 \forall 𝑥 \in 𝑅, 𝑓 (- 3) = 0$ and $𝑓 (0) = 18$ , then $𝑓 (3) =$

36

Incorrect

72

Incorrect

144

Incorrect

288

Incorrect

Q 14MathematicsSection A • MCQquadratic equations

+1 / -0

If one of the roots of the equation $6 𝑥^{3} - 25 𝑥^{2} + 2 𝑥 + 8 = 0$ is an integer and $𝛼 > 0, 𝛽 < 0$ are the other two roots, then $\frac{4}{𝛼} + \frac{1}{𝛽} =$

0

Incorrect

1

Incorrect

-2

Incorrect

4

Incorrect

Q 15MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼, 𝛽, 𝛾, 𝛿$ and $𝜀$ are the roots of the equation $𝑥^{5} + 𝑥^{4} - 13 𝑥^{3} - 13 𝑥^{2} + 36 𝑥 + 36 = 0$ and $𝛼 < 𝛽 < 𝛾 < 𝛿 < 𝜀$ then $\frac{𝜀}{𝛼} + \frac{𝛿}{𝛽} + \frac{1}{𝛾} =$

0

Incorrect

1

Incorrect

-1

Incorrect

-3

Incorrect

Q 16MathematicsSection A • MCQpermutations and combinations

+1 / -0

5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is

14400

Incorrect

2880

Incorrect

576

Incorrect

625

Incorrect

Q 17MathematicsSection A • MCQpermutations and combinations

+1 / -0

All possible words (with or without meaning) the contain the word 'GENTLE' are formed using all the letters of the word 'INTELLIGENCE'. Then, the number of words in which the word 'GENTLE' appears among the first nine positions only is

1440

Incorrect

5040

Incorrect

2520

Incorrect

720

Incorrect

Q 18MathematicsSection A • MCQpermutations and combinations

+1 / -0

$^{20} 𝑃_{5} -^{19} 𝑃_{5} =$

$^{19} 𝑃_{4}$

Incorrect

$4 (^{19} 𝑃_{4})$

Incorrect

$5! (646)$

Incorrect

$6! (646)$

Incorrect

Q 19MathematicsSection A • MCQbinomial theorem

+1 / -0

If $𝐶_{0}, 𝐶_{1}, 𝐶_{2}, \dots, 𝐶_{10}$ represent the binomial coefficients in the expansion of $(1 + 𝑥)^{10}$ , then

$𝐶_{0} 𝐶_{6} + 𝐶_{1} 𝐶_{7} + 𝐶_{2} 𝐶_{8} + 𝐶_{3} 𝐶_{9} + 𝐶_{4} 𝐶_{10} =$

9690

Incorrect

4845

Incorrect

1615

Incorrect

3230

Incorrect

Q 20MathematicsSection A • MCQbinomial theorem

+1 / -0

When $| 𝑥 | < \frac{1}{2}$ the coefficient of $𝑥^{6}$ in the expansion of ${(\frac{2 - 𝑥}{1 + 2 𝑥})}^{2}$ is

1320

Incorrect

2640

Incorrect

1088

Incorrect

1980

Incorrect

Q 21MathematicsSection A • MCQfunctions

+1 / -0

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

$𝑎 = 𝑏 = 𝑐 = - 𝑑$

Incorrect

$𝑎 = 𝑏 = 2 𝑐 = - 𝑑$

Incorrect

$𝑎 = 2 𝑏 = 𝑐 = - 𝑑$

Incorrect

$𝑎 = 𝑏 = 2 𝑐 = 𝑑$

Incorrect

Q 22MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\cos 𝜃 + \sin 𝜃 = \sqrt{\sqrt 2} \cos 𝜃$ and $0 < 𝜃 < \frac{𝜋}{2}$ , then $\sec 2 𝜃 + \tan 2 𝜃 =$

$\cot 𝜃$

Incorrect

$\tan 𝜃$

Incorrect

$\cos 𝜃$

Incorrect

$\sin 𝜃$

Incorrect

Q 23MathematicsSection A • MCQtrigonometric equations

+1 / -0

If $0 \leq 𝐴, 𝐵 \leq \frac{𝜋}{4}$ and $\cot 𝐴 + \cot 𝐵 + \tan 𝐴 + \tan 𝐵 = \cot 𝐴 \cot 𝐵 - \tan 𝐴 \tan 𝐵$ , then $\sin (𝐴 + 𝐵) =$

0

Incorrect

$\frac{1}{2}$

Incorrect

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

Incorrect

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

Incorrect

Q 24MathematicsSection A • MCQapplication of derivatives

+1 / -0

If the extreme values of the function $𝑓 (𝑥) = (2 \sqrt{\sqrt 6} + 1) \cos 𝑥 + (2 \sqrt{\sqrt 2} - \sqrt{\sqrt 3}) \sin 𝑥 - 6$ are $𝑚$ and $𝑀$ then $\sqrt{\sqrt | 𝑀^{2} - 𝑚^{2} |} =$

6

Incorrect

12

Incorrect

$6 \sqrt{\sqrt 2}$

Incorrect

$12 \sqrt{\sqrt 3}$

Incorrect

Q 25MathematicsSection A • MCQtrigonometric equations

+1 / -0

Number of solutions of the equation $\tan^{2} 𝑥 + 3 \cot^{2} 𝑥 = 2 \sec^{2} 𝑥$ lying in the interval $[0, 2 𝜋]$ is

3

Incorrect

4

Incorrect

5

Incorrect

6

Incorrect

Q 26MathematicsSection A • MCQinverse trigonometric functions

+1 / -0

$\sin^{- 1} (- \cos 2) + \cos^{- 1} (\sin 3) + \tan^{- 1} (\cot 5) =$

7

Incorrect

5

Incorrect

$\frac{𝜋}{2}$

Incorrect

$𝜋$

Incorrect

Q 27MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $𝑥 = \log_{𝑒} 3$ , then $\tanh 2 𝑥 + sech 2 𝑥 =$

$\frac{4}{3}$

Incorrect

$\frac{49}{41}$

Incorrect

$\frac{4}{5}$

Incorrect

$\frac{41}{49}$

Incorrect

Q 28MathematicsSection A • MCQproperties of triangles

+1 / -0

If $𝑎 = 3, 𝑏 = 5, 𝑐 = 7$ are the sides of a $△ 𝐴 𝐵 𝐶$ , then $\cot 𝐴 + \cot 𝐵 + \cot 𝐶 =$

$\frac{15 \sqrt{\sqrt 3}}{4}$

Incorrect

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

Incorrect

$\frac{83}{15 \sqrt{\sqrt 3}}$

Incorrect

$\frac{83 \sqrt{\sqrt 3}}{15}$

Incorrect

Q 29MathematicsSection A • MCQproperties of triangles

+1 / -0

Let $𝑝_{1}, 𝑝_{2}$ and $𝑝_{3}$ be the altitudes of a $△ 𝐴 𝐵 𝐶$ drawn through the vertices $𝐴, 𝐵$ and $𝐶$ respectively. If $𝑟_{1} = 4$ , $𝑟_{2} = 6, 𝑟_{3} = 12$ are the ex-radii of $△ 𝐴 𝐵 𝐶$ , then $\frac{1}{𝑝_{2}^{1}} + \frac{1}{𝑝_{2}^{2}} + \frac{1}{𝑝_{2}^{3}} =$

$\frac{25}{72}$

Incorrect

$\frac{25}{144}$

Incorrect

$\frac{25}{288}$

Incorrect

$\frac{25}{216}$

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

$𝐴 𝐵 𝐶 𝐷$ is a tetrahedron, $\hat{𝐢} - 2 \hat{𝐣} + 3 \hat{𝐤}, - 2 \hat{𝐢} + \hat{𝐣} + 3 \hat{𝐤}$ , $3 \bar{𝑖} + 2 \bar{𝑗} - \bar{𝑘}$ are the the position vectors of the points $𝐴, 𝐵$ and $𝐶$ respectively. $- \hat{𝐢} + 2 \hat{𝐣} - 3 \hat{𝐤}$ is the position vector of the centroid of the triangular face $𝐵 𝐶 𝐷$ . If G is the centroid of the tetrahedron, then $𝐺 𝐷 =$

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

Incorrect

$\sqrt{\sqrt 23}$

Incorrect

$\frac{\sqrt{\sqrt 213}}{\sqrt{\sqrt 2}}$

Incorrect

$\sqrt{\sqrt 46}$

Incorrect

Q 31MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚 = \hat{𝐢} - 2 \hat{𝐣} + 2 \hat{𝐤}, 𝐛 = 6 \hat{𝐢} + 3 \hat{𝐣} - 2 \hat{𝐤}, 𝐜 = - 4 \hat{𝐢} + 3 \hat{𝐣} + 12 \hat{𝐤}$ are three vectors, then $\sqrt{\sqrt (| 𝐚 | + | 𝐛 | + | 𝐜 |) + | 𝐚 + 𝐛 + 𝐜 |} =$

13

Incorrect

$13 \sqrt{\sqrt 10}$

Incorrect

6

Incorrect

$10 \sqrt{\sqrt 3}$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐚$ and $𝐛$ be two vectors such that $| 𝐚 | = | 𝐛 |$ and $| 𝐚 + 2 𝐛 | = | 2 𝐚 - 𝐛 |$ . If $𝐜$ is a vector parallel to $𝐚$ , then the angle between $𝐛$ and $𝐜$ is

$0^{\circ}$

Incorrect

$30^{\circ}$

Incorrect

$60^{\circ}$

Incorrect

$90^{\circ}$

Incorrect

Q 33MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚$ and $𝐛$ are two vectors such that $| 𝐚 | = | 𝐛 | = \sqrt{\sqrt 6}$ and $𝐚 \cdot 𝐛 = - 1$ , then $| 𝐚 \times 𝐛 | \sin (𝐚, 𝐛) =$

$(| 𝐚 |^{2} - 1) (| 𝐛 |^{2} + 1)$

Incorrect

$\frac{1}{6}$

Incorrect

$(| 𝐚 |^{2} - 1) (1 + \frac{1}{| 𝐛 |^{2}})$

Incorrect

$\frac{\sqrt{\sqrt 35}}{6}$

Incorrect

Q 34MathematicsSection A • MCQvector algebra

+1 / -0

If the volume of a tetrahedron having $\hat{𝐢} + 2 \hat{𝐣} - 3 \hat{𝐤}, 2 \hat{𝐢} + \hat{𝐣} - 3 \hat{𝐤}$ and $3 \hat{𝐢} - \hat{𝐣} + 𝑝 \hat{𝐤}$ as its coterminous edges is 2 , then the values of $𝐩$ are the roots of the equation

$𝑥^{2} + 4 𝑥 - 12 = 0$

Incorrect

$𝑥^{2} + 8 𝑥 + 12 = 0$

Incorrect

$𝑥^{2} - 4 𝑥 - 12 = 0$

Incorrect

$𝑥^{2} - 8 𝑥 + 12 = 0$

Incorrect

Q 35MathematicsSection A • MCQstatistics

+1 / -0

$The coefficient of variation for the following data is$

$\begin{matrix} Class interval & 0 - 2 & 2 - 4 & 4 - 6 & 6 - 8 & 8 - 10 \\ Frequency & 2 & 3 & 5 & 3 & 2 \end{matrix}$

$\frac{8 \sqrt{\sqrt 22}}{3}$

Incorrect

$\frac{8 \sqrt{\sqrt 110}}{\sqrt{\sqrt 3}}$

Incorrect

$\frac{4 \sqrt{\sqrt 110}}{\sqrt{\sqrt 3}}$

Incorrect

$\frac{4 \sqrt{\sqrt 22}}{3}$

Incorrect

Official Correct Answer:Option (B)

Step-by-Step Solution:

Let us take assume mean $(𝐴) = 5$ and $ℎ = 2$

Classes
0-2	1	-2	2	-4	8
2-4	3	-1	3	-3	3
4-6	5	0	5	0	0
6-8	7	1	3	3	3
8-10	9	2	2	4	8
			$N = 15$	$Σ$ = 0	$Σ$

$\begin{matrix} ∵ \bar{𝑥} & = 𝐴 + \frac{Σ 𝑓_{𝑖} 𝜇_{𝑖}}{Σ 𝑓_{𝑖}} \times ℎ \\ \bar{𝑥} & = 5 + 0 = 5 \\ SD & = 𝜎 = ℎ \times \sqrt{\sqrt \frac{Σ 𝑓_{𝑖} 𝜇_{2}^{𝑖}}{𝑁} - {(\frac{Σ 𝑓_{𝑖} 𝜇_{𝑖}}{𝑁})}^{2}} \\ 𝜎 & = 2 \times \sqrt{\sqrt \frac{22}{15}} \\ CV & = \frac{𝜎}{\bar{𝑥}} \times 100 = \frac{2 \times \sqrt{\sqrt \frac{22}{15}} \times 100}{5} \\ = \frac{2 \times \sqrt{\sqrt 2} \times \sqrt{\sqrt 11}}{\sqrt{\sqrt 3} \times \sqrt{\sqrt 5} \times 5 \times \sqrt{\sqrt 5}} \times 100 \times \sqrt{\sqrt 5} \\ = \sqrt{\sqrt \frac{110}{3}} \times 8 \end{matrix}$

Q 36MathematicsSection A • MCQprobability

+1 / -0

If two smallest squares are chosen at random on a chess board, then the probability of getting these squares such that they do not have a side in common is

$\frac{1}{18}$

Incorrect

$\frac{5}{36}$

Incorrect

$\frac{17}{18}$

Incorrect

$\frac{7}{36}$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

Let $𝐴$ and $𝐵$ be two events in a random experiment . If $𝑃 (𝐴 \cap \bar{𝐵}) = 0.1, 𝑃 (\bar{𝐴} \cap 𝐵) = 0.2$ and $𝑃 (𝐵) = 0.5$ , then $𝑃 (\bar{𝐴} \cap \bar{𝐵}) =$

0.6

Incorrect

0.5

Incorrect

0.4

Incorrect

0.3

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

An urn contains 7 red, 5 white and 3 black balls. Three balls are drawn randomly one after the other without replacement. If it is known that first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is

$\frac{10}{13}$

Incorrect

$\frac{8}{13}$

Incorrect

$\frac{12}{13}$

Incorrect

$\frac{7}{13}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

The range of a discrete random variable $𝑋$ is ${1, 2, 3}$ and the probabilities of its elements are given by $𝑃 (𝑋 = 1) = 3 𝑘^{3}, 𝑃 (𝑋 = 2) = 2 𝑘^{2}$ and $𝑃 (𝑋 = 3) = 7 - 19 k$ . Then, $𝑃 (𝑋 = 3) =$

$\frac{2}{3}$

Incorrect

$\frac{2}{9}$

Incorrect

$\frac{1}{9}$

Incorrect

$\frac{4}{9}$

Incorrect

Q 40MathematicsSection A • MCQprobability

+1 / -0

Among every 8 units of a product, one is likely to be defective. If a consumer has order 5 units of that product, then the probability that atmost one unit is defective among them is

$\frac{15}{8} {(\frac{7}{8})}^{6}$

Incorrect

$\frac{57}{8^{8}}$

Incorrect

$\frac{36}{8^{5}}$

Incorrect

$\frac{3}{2} {(\frac{7}{8})}^{4}$

Incorrect

Q 41MathematicsSection A • MCQhyperbola

+1 / -0

If $𝐴 = (0, 1), 𝐵 = (1, 2), 𝐶 = (- 2, 1)$ , then the equation of the locus of a point $𝑃$ such that area of $△ 𝑃 𝐴 𝐵 =$ area of $△ 𝑃 𝐴 𝐶$ is

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

Incorrect

$𝑥^{2} + 2 𝑥 𝑦 - 3 𝑦^{2} + 2 𝑥 + 6 𝑦 - 4 = 0$

Incorrect

$𝑥^{2} - 2 𝑥 𝑦 - 3 𝑦^{2} + 2 𝑥 - 6 𝑦 + 4 = 0$

Incorrect

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

Incorrect

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

+1 / -0

$(𝑎, 𝑏)$ are the new coordinates of the point $(2, 3)$ after shifting the origin to the point $(3, 2)$ by translation of axes. If $(𝑐, 𝑑)$ are the new coordinates of the point $(𝑎, 𝑏)$ after rotating the axes through an angle $\frac{𝜋}{4}$ about the origin in the anti-clockwise direction, then $𝑑 - 𝑐 =$

0

Incorrect

1

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

$2 \sqrt{\sqrt 2}$

Incorrect

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

+1 / -0

The lines $𝑥 + 𝑦 + 4 = 0, 𝑥 - 2 𝑦 - 4 = 0$ and $3 𝑥 + 4 𝑦 - 2 = 0$

are concurrent

Incorrect

form an isosceles triangle

Incorrect

form a right-angled triangle

Incorrect

form a scalene triangle

Incorrect

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

+1 / -0

The area of the triangle formed by the line $𝐿$ with the coordinate axes is 12 sq. units. If $𝐿$ passes through the point $(12, 4)$ and the product $𝑃$ of $𝑋$ - intercept of $𝐿$ and square of the $𝑌$ -intercept of $𝐿$ is negative, then $𝑃 =$

-48

Incorrect

-24

Incorrect

-192

Incorrect

-72

Incorrect

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

+1 / -0

The area of the quadrilateral formed by the lines $𝑥 + 2 𝑦 + 3 = 0, 2 𝑥 + 4 𝑦 + 9 = 0, 𝑥 - 2 𝑦 + 3 = 0$ and $3 𝑥 - 6 𝑦 + 11 = 0$

$\frac{5}{12}$

Incorrect

$\frac{1}{4}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{7}{12}$

Incorrect

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

+1 / -0

If $(- 1, - 1)$ is the point of intersection of the pair of lines $2 𝑥^{2} + 5 𝑥 𝑦 - 3 𝑦^{2} + 2 𝑔 𝑥 + 2 𝑓 𝑦 + 𝑐 = 0$ . Then $𝑔 + 𝑓$

4 c

Incorrect

$3 𝑐$

Incorrect

2 c

Incorrect

C

Incorrect

Q 47MathematicsSection A • MCQcircle

+1 / -0

If the length of the chord $2 𝑥 + 3 𝑦 + 𝑘 = 0$ of the circle $𝑥^{2} + 𝑦^{2} - 2 𝑥 + 4 𝑦 - 11 = 0$ is $2 \sqrt{\sqrt 3}$ , then the sum of all possible values of $𝑘$ is

26

Incorrect

8

Incorrect

13

Incorrect

4

Incorrect

Q 48MathematicsSection A • MCQcircle

+1 / -0

The power of a point $(2, - 1)$ with respect to a circle $𝐶$ of radius 4 is 9 . The centre of the circle $𝐶$ lies on the lines $𝑥 + 𝑦 = 0$ and in the 2nd quadrant. If ( $𝛼, 𝛽$ ) is the centre of the circle $𝐶$ then $𝛽 - 𝛼 =$

-4

Incorrect

-10

Incorrect

4

Incorrect

10

Incorrect

Q 49MathematicsSection A • MCQcircle

+1 / -0

The angle between the tangents drawn from the point $𝑃 (𝑘, 6 𝑘)$ to the circle $𝑥^{2} + 𝑦^{2} + 6 𝑥 - 6 𝑦 + 2 = 0$ is $2 \tan^{- 1} (\frac{4}{3})$ . If the coordinates of $𝑃$ are integers, then $𝑘 =$

1

Incorrect

2

Incorrect

3

Incorrect

-2

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

The tangents drawn from a point $(2, - 1)$ touch the circle $𝑥^{2} + 𝑦^{2} + 4 𝑥 - 2 𝑦 + 1 = 0$ at the points $𝐴$ and $𝐵$ . If $𝐶$ is the centre of the circle, then the area (in sq. units) of the $△ 𝐴 𝐵 𝐶$ is

$\frac{4}{5}$

Incorrect

4

Incorrect

8

Incorrect

$\frac{8}{5}$

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

If $𝜃$ is the angle between the circles $𝑥^{2} + 𝑦^{2} - 4 𝑥 + 2 𝑦 - 4 = 0$ and $𝑥^{2} + 𝑦^{2} - 2 𝑥 + 4 𝑦 - 11 = 0$ then $\sin 𝜃 =$

$\frac{\sqrt{\sqrt 47}}{24}$

Incorrect

$\frac{23}{25}$

Incorrect

$\frac{23}{24}$

Incorrect

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

Incorrect

Q 52MathematicsSection A • MCQcircle

+1 / -0

If the line $𝑥 + 𝑦 = 2$ cuts the circle $𝑥^{2} + 𝑦^{2} + 2 𝑥 - 4 𝑦 + 4 = 0$ at two points $𝐴$ and $𝐵$ , then the radius of the circle passing through $𝐴, 𝐵$ and orthogonal to $𝑥^{2} + 𝑦^{2} - 2 𝑥 - 4 𝑦 - 4 = 0$ is

3

Incorrect

4

Incorrect

5

Incorrect

6

Incorrect

Q 53MathematicsSection A • MCQparabola

+1 / -0

A normal chord $𝑃 𝑄$ drawn at a point $𝑃$ on the parabola $𝑦^{2} = 5 𝑥$ subtends a right angle at the vertex. If $𝑃$ lies in the first quadrant, then the other end $𝑄$ of the normal chord is

$(\frac{5}{4}, \frac{5}{2})$

Incorrect

$(5, - 5)$

Incorrect

$(10, - 5 \sqrt{\sqrt 2})$

Incorrect

$(\frac{5}{2}, \frac{5 \sqrt{\sqrt 2}}{2})$

Incorrect

Q 54MathematicsSection A • MCQparabola

+1 / -0

If $𝐿 (𝑝, 𝑞), 𝑞 > 3$ is one end of the latus rectum of the parabola $(𝑦 - 2)^{2} = 3 (𝑥 - 1)$ , then the equation of the tangent at $𝐿$ to this parabola is

$2 𝑥 + 𝑦 - 7 = 0$

Incorrect

$4 𝑥 - 4 𝑦 + 7 = 0$

Incorrect

$2 𝑥 - 𝑦 - 3 = 0$

Incorrect

$2 𝑥 - 3 𝑦 + 7 = 0$

Incorrect

Q 55MathematicsSection A • MCQellipse

+1 / -0

If $𝑃$ is any point on the ellipse $\frac{𝑥^{2}}{25} + \frac{𝑦^{2}}{9} = 1$ and $𝑆, 𝑆^{'}$ are its foci, then the maximum area (in sq. units) of $△ 𝑆 𝑃 𝑆^{'} =$

15

Incorrect

12

Incorrect

6

Incorrect

25

Incorrect

Q 56MathematicsSection A • MCQellipse

+1 / -0

Let $𝑒$ be the eccentricity of the ellipse $\frac{𝑥^{2}}{𝑎^{2}} + \frac{𝑦^{2}}{𝑏^{2}} = 1$ .

If $𝑎 = 5, 𝑏 = 4$ and the equation of the normal drawn at one end of the latus rectum that lies in the first quadrant is $𝑙 𝑥 + 𝑚 𝑦 = 27$ then $𝑙 + 𝑚 =$

$\frac{3}{𝑒}$

Incorrect

$\frac{3}{2 𝑒}$

Incorrect

$\frac{6}{𝑒}$

Incorrect

$\frac{1}{𝑒}$

Incorrect

Q 57MathematicsSection A • MCQhyperbola

+1 / -0

If the latus rectum through one of the foci of a hyperbola $\frac{𝑥^{2}}{9} - \frac{𝑦^{2}}{𝑏^{2}} = 1$ subtends a right angle at the farther vertex of the hyperbola, then $𝑏^{2} =$

4

Incorrect

16

Incorrect

25

Incorrect

27

Incorrect

Q 58MathematicsSection A • MCQ3d geometry

+1 / -0

The equation of the locus of a point whose distance from $𝑋 𝑌$ -plane is twice its distance from $𝑍$ -axis is

$2 𝑥^{2} + 2 𝑦^{2} - 𝑧^{2} = 0$

Incorrect

$2 𝑦^{2} + 2 𝑧^{2} - 𝑥^{2} = 0$

Incorrect

$4 𝑦^{2} + 4 𝑧^{2} - 𝑥^{2} = 0$

Incorrect

$4 𝑥^{2} + 4 𝑦^{2} - 𝑧^{2} = 0$

Incorrect

Q 59MathematicsSection A • MCQ3d geometry

+1 / -0

If $𝛼$ is the angle between any two diagonals of a cube and $𝛽$ is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube, then $\cos 𝛼 + \cos^{2} 𝛽 =$

$\frac{5}{9}$

Incorrect

$\frac{2}{9}$

Incorrect

1

Incorrect

$\frac{2}{3}$

Incorrect

Q 60MathematicsSection A • MCQ3d geometry

+1 / -0

If the angle between the planes $𝑎 𝑥 - 𝑦 + 3 𝑧 = 2 𝑎$ and $3 𝑥 + 𝑎 𝑦 + 𝑧 = 3 𝑎$ is $\frac{𝜋}{3}$ , then the direction ratio of the line perpendicular to the plane $(𝑎 + 2) 𝑥 + (𝑎 - 4) 𝑦 + 2 𝑎 𝑧 = 𝑎$ are

$(2, - 1, 2)$

Incorrect

$(2, 1, - 2)$

Incorrect

$(2, 1, 2)$

Incorrect

$(2, 2, - 1)$

Incorrect

Q 61MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If $lim_{𝑥 \to 0} \frac{3^{𝑥^{3}} - {(1 - 𝑥^{3})}^{\frac{2}{3}}}{𝑥^{2} \sin 𝑥} = 𝑝 + \log 𝑞$ , then $𝑝 𝑞 =$

$\frac{2}{3}$

Incorrect

2

Incorrect

3

Incorrect

-2

Incorrect

Q 62MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If $[𝑥]$ is the greatest integer function and

$𝑓 (𝑥) = {\begin{matrix} 2 [𝑥] - \frac{𝑥}{| 𝑥 |}, & 𝑥 \neq 0 \\ 1, & 𝑥 = 0 \end{matrix}$

is a real valued function, then $𝑓$ is

continuous at $𝑥 = 0$

Incorrect

continuous at $𝑥 = 1$

Incorrect

left continuous at $𝑥 = 0$

Incorrect

right continuous at $𝑥 = 1$

Incorrect

Q 63MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝑥 = 2 \sqrt{\sqrt 2} \sqrt{\sqrt \cos 2 𝜃}$ and $𝑦 = 2 \sqrt{\sqrt 2} \sqrt{\sqrt \sin 2 𝜃}, 0 < 𝜃 < \frac{𝜋}{4}$ , then the value of $\frac{𝑑 𝑦}{𝑑 𝑥}$ at $𝜃 = 22 {\frac{1}{2}}^{\circ}$ is

1

Incorrect

-1

Incorrect

0

Incorrect

$\sqrt{\sqrt 3}$

Incorrect

Q 64MathematicsSection A • MCQinverse trigonometric functions

+1 / -0

The domain of the derivative of the function $𝑓 (𝑥) = \cos^{- 1} (2 𝑥 - 5) - \sin^{- 1} (𝑥 - 2)$ is

$[2, 3]$

Incorrect

$(- \infty, 2] \cup [3, \infty)$

Incorrect

$(- \infty, 2) \cup (3, \infty)$

Incorrect

$(2, 3)$

Incorrect

Q 65MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑦 = \tan^{2} (\cos^{- 1} \sqrt{\sqrt \frac{1 + 𝑥^{2}}{2}})$ , then $\frac{𝑑 𝑦}{𝑑 𝑥} =$

$- \frac{4 𝑥}{{(1 - 𝑥^{2})}^{2}}$

Incorrect

$\frac{4 𝑥}{{(1 + 𝑥^{2})}^{2}}$

Incorrect

$- \frac{4 𝑥}{{(1 + 𝑥^{2})}^{2}}$

Incorrect

$- \frac{4 𝑥}{1 + 𝑥^{2}}$

Incorrect

Q 66MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑦 = 𝑥^{\log 𝑥} + (\log 𝑥)^{𝑥}, 𝑥 > 1$ , then ${(\frac{𝑑 𝑦}{𝑑 𝑥})}_{𝑥 = 𝑒} =$

0

Incorrect

1

Incorrect

2

Incorrect

3

Incorrect

Q 67MathematicsSection A • MCQapplication of derivatives

+1 / -0

If the curves $𝑦^{2} = 12 𝑥 - 3$ and $𝑦^{2} = 12 - 𝑘 𝑥$ cut each other orthogonally, then the length of the sub-tangent at $(1, 𝑏)$ on the curve $𝑦^{2} = 12 - 𝑘 𝑥$ is

4

Incorrect

6

Incorrect

5

Incorrect

12

Incorrect

Q 68MathematicsSection A • MCQapplication of derivatives

+1 / -0

A rod of length 41 m with an end $𝐴$ on the floor and another end $𝐵$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 fit / \min$ . When the end $𝐵$ is at the height of 9 ft from the floor, then the rate at which the area of the triangle formed by the rod with wall and floor changes at that instant is (in $ft / \min$ )

$- \frac{1519}{6}$

Incorrect

$\frac{1618}{3}$

Incorrect

$- \frac{1600}{3}$

Incorrect

$\frac{1509}{6}$

Incorrect

Q 69MathematicsSection A • MCQapplication of derivatives

+1 / -0

There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm . If the semi-vertical angle of the cone is $45^{\circ}$ , then the approximate error in its volume is (in $cu . cm$ )

1.078

Incorrect

3.08

Incorrect

1.54

Incorrect

6.16

Incorrect

Q 70MathematicsSection A • MCQapplication of derivatives

+1 / -0

The real valued function $𝑓 (𝑥) = \frac{𝑥^{2}}{2} - \log (𝑥^{2} + 𝑥 + 1)$ is

Strictly decreasing in $(1, \infty)$

Incorrect

Strictly increasing in $(1, \infty)$

Incorrect

Strictly increasing in $(- \infty, 0)$

Incorrect

Strictly decreasing in $(0, \infty)$

Incorrect

Q 71MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝑥$ and $𝑦$ are two positive real numbers such that $𝑥 𝑦 = 4$ , then the minimum value of $(\sqrt{\sqrt 𝑥} + \frac{𝑦^{2}}{2})$ is

4

Incorrect

$5 / 2$

Incorrect

$2 \sqrt{\sqrt 2}$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

Q 72MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int 𝑥^{3} \sin 3 𝑥 𝑑 𝑥 = \frac{1}{27} [𝑓 (𝑥) \cos 3 𝑥 + 𝑔 (𝑥) \sin 3 𝑥] + 𝐶$ , then $𝑓 (l) + 𝑔 (l) =$

14

Incorrect

6

Incorrect

4

Incorrect

12

Incorrect

Q 73MathematicsSection A • MCQindefinite integration

+1 / -0

If $𝐼_{1} = \int \sin^{6} 𝑥 𝑑 𝑥$ and $𝐼_{2} = \int \cos^{6} 𝑥 𝑑 𝑥$ , then $𝐼_{1} + 𝐼_{2} =$

$\frac{5 𝑥}{8} + \frac{3 \cos 4 𝑥}{32} + 𝐶$

Incorrect

$\frac{1}{32} (20 𝑥 - 3 \sin 4 𝑥) + 𝐶$

Incorrect

$\frac{1}{32} (20 𝑥 + 3 \sin 4 𝑥) + 𝐶$

Incorrect

$\frac{5 𝑥}{4} + \frac{3 \sin 4 𝑥}{16} + 𝐶$

Incorrect

Q 74MathematicsSection A • MCQindefinite integration

+1 / -0

$\int \frac{𝑥 + \cos 𝑥}{1 - \sin 𝑥} 𝑑 𝑥 =$

$𝑥 \tan (\frac{𝜋}{4} + \frac{𝑥}{2}) + 𝐶$

Incorrect

$𝑥 \tan \frac{𝑥}{2} + 𝐶$

Incorrect

$𝑥 \cot \frac{𝑥}{2} + 𝐶$

Incorrect

$𝑥 \cot (\frac{𝜋}{4} + \frac{𝑥}{2}) + 𝐶$

Incorrect

Q 75MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int \frac{1}{(𝑥 + 2) \sqrt{\sqrt 𝑥^{2} + 𝑥 + 2}} 𝑑 𝑥 =$

$- \frac{1}{2} \sinh^{- 1} (\frac{2 - 3 𝑥}{\sqrt{\sqrt 7} (𝑥 + 2)}) + 𝐶$

Incorrect

$- \frac{1}{2} \sin^{- 1} (\frac{2 + 3 𝑥}{\sqrt{\sqrt 7} (𝑥 + 2)}) + 𝐶$

Incorrect

$\frac{1}{2} \cosh^{- 1} (\frac{2 + 3 𝑥}{\sqrt{\sqrt 7} (𝑥 + 2)}) + 𝐶$

Incorrect

$- \frac{1}{2} \cos^{- 1} (\frac{2 - 3 𝑥}{\sqrt{\sqrt 7} (𝑥 + 2)}) + 𝐶$

Incorrect

Q 76MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{5}^{- 4} \frac{1}{\sqrt{\sqrt 20 + 𝑥 - 𝑥^{2}}} 𝑑 𝑥 =$

$\frac{81 𝜋}{8}$

Incorrect

$\frac{9 𝜋}{2}$

Incorrect

$𝜋$

Incorrect

$\frac{𝜋}{10}$

Incorrect

Q 77MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{\frac{𝜋}{2}}^{0} \frac{𝑑 𝑥}{\cos 𝑥 - \sqrt{\sqrt 3} \sin 𝑥} =$

0

Incorrect

$\frac{1}{2} \log (2 - \sqrt{\sqrt 3})$

Incorrect

$\frac{1}{2} \log (2 + \sqrt{\sqrt 3})$

Incorrect

$\frac{1}{2} \log (2 \sqrt{\sqrt 3} - 3)$

Incorrect

Q 78MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{\frac{𝜋}{2}}^{0} \sqrt{\sqrt \tan 𝑥 𝑑 𝑥} =$

$\frac{𝜋}{\sqrt{\sqrt 2}}$

Incorrect

$\frac{𝜋}{2}$

Incorrect

$\sqrt{\sqrt 2} 𝜋$

Incorrect

$2 𝜋$

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

If $𝑦 = 𝑓 (𝑥)$ is the solution of the differential equation $(1 + \cos^{2} 𝑥) 𝑓^{'} (𝑥) - 4 \sin 2 𝑥 - 𝑓 (𝑥) \sin 2 𝑥 = 0$ when $𝑓 (0) = 0$ , then $𝑓 (\frac{𝜋}{3}) =$

3

Incorrect

$\frac{12}{5}$

Incorrect

$\frac{3}{5}$

Incorrect

4

Incorrect

Q 80MathematicsSection A • MCQdifferential equations

+1 / -0

The differential equation corresponding to the family of ellipses $\frac{𝑥^{2}}{𝑎^{2}} + \frac{𝑦^{2}}{4} = 1$ , where ' $𝑎$ ' is an arbitrary constant is

$𝑥 𝑦 \frac{𝑑 𝑦}{𝑑 𝑥} = 4 - 𝑦^{2}$

Incorrect

$𝑥 𝑦 \frac{𝑑 𝑦}{𝑑 𝑥} = 4 - 𝑥^{2}$

Incorrect

$𝑥 𝑦 \frac{𝑑 𝑦}{𝑑 𝑥} = 𝑥^{2} - 4$

Incorrect

$𝑥 𝑦 \frac{𝑑 𝑦}{𝑑 𝑥} = 𝑦^{2} - 4$

Incorrect

Q 81PhysicsSection A • MCQwave optics

+1 / -0

Match the "Technology" given in List-I with the "Principle of physics" given in List-II.

$\begin{matrix} List-I (Technology) & List-II (Principle of physics) \\ (A) & Steam engine & I & \begin{matrix} Magnetic confinement of \\ plasma \end{matrix} \\ (B) & Electron microscope & II & Laws of thermodynamics \\ (C) & Non-reflecting coatings & III & Wave nature of electrons \\ (D) & Tokamak & IV & Interference of light \end{matrix}$

A-I, B-II, C-III, D-IV

Incorrect

A-II, B-III, C-IV, D-I

Incorrect

A-II, B-IV, C-III, D-I

Incorrect

A-II, B-I, C-III, D-IV

Incorrect

Q 82PhysicsSection A • MCQunits and measurements

+1 / -0

In an experiment, the coefficient of viscosity (in

mPa . s)

of a liquid was determined as

2.62, 2.68, 2.58

,

2.57, 2.54

and 2.55 . The mean absolute error in the determination of the coefficient of viscosity of the liquid is

0.08 mPa s

Incorrect

0.12 mPa s

Incorrect

0.06 mPa s

Incorrect

0.04 mPa s

Incorrect

Q 83PhysicsSection A • MCQmotion in a straight line

+1 / -0

The relation between the displacement ' $𝑥$ ' (in metre) and the time ' $𝑡$ ' (in second) of a particle is $𝑡 = 2 𝑥^{2} + 3 𝑥$ . If the displacement of the particle is 25 cm from the origin $(𝑥 = 0)$ , then the acceleration of the particle is

$+ \frac{1}{16} {ms}^{- 2}$

Incorrect

$- \frac{1}{16} {ms}^{- 2}$

Incorrect

$+ \frac{1}{8} {ms}^{- 2}$

Incorrect

$- \frac{1}{8} {ms}^{- 2}$

Incorrect

Q 84PhysicsSection A • MCQmotion in a plane

+1 / -0

A body projected at certain angle $(\neq 90^{\circ})$ from the ground crosses a point in its path at a time of 2.3 s and from there it reaches the ground after a time of 5.7 s . The maximum heigh reached by the body is (Acceleration due to gravity $= 10 {ms}^{- 2}$ )

80 m

Incorrect

120 m

Incorrect

40 m

Incorrect

160 m

Incorrect

Q 85PhysicsSection A • MCQcircular motion

+1 / -0

A circular path of radius 75 m is banked at an angle of $\tan^{- 1} (0.2)$ . If the coefficient of static friction between the tyres of the car and the circular path is 0.1 , then the maximum permissible speed of the car to avoid slipping is

$10 {ms}^{- 1}$

Incorrect

$20 {ms}^{- 1}$

Incorrect

$15 {ms}^{- 1}$

Incorrect

$30 {ms}^{- 1}$

Incorrect

Q 86PhysicsSection A • MCQlaws of motion

+1 / -0

A horizontal force of 10 N is applied on a block of mass 1.5 kg which is initially at rest on a rough horizontal surface. The work done by the applied force in a time of 6 s from the beginning of the motion is (Acceleration due to gravity $= 10 {ms}^{- 2}$ ; the coefficient of kinetic friction between the block and the surface is 0.2)

588 J

Incorrect

360 J

Incorrect

840 J

Incorrect

420 J

Incorrect

Q 87PhysicsSection A • MCQcenter of mass

+1 / -0

A ball is allowed to fall freely from a height of 42 m form the ground. If the coefficient of restitution between the ball and the ground is 0.4 , then the total distance travelled by the ball before it comes to rest is

84 m

Incorrect

87 m

Incorrect

72 m

Incorrect

58 m

Incorrect

Q 88PhysicsSection A • MCQrotational motion

+1 / -0

A thin uniform wire of mass ' $𝑚$ ' and linear density ' $𝜌$ ' is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is ' $𝑚$ '

$\frac{3 𝑚^{3}}{8 𝜋^{2} 𝜌^{2}}$

Incorrect

$\frac{8 𝑚^{3}}{3 𝜋^{2} 𝜌^{2}}$

Incorrect

$\frac{8 𝜋^{2} 𝑚^{3}}{3 𝜌^{2}}$

Incorrect

$\frac{3 𝜋^{2} 𝑚^{3}}{8 𝜌^{2}}$

Incorrect

Q 89PhysicsSection A • MCQrotational motion

+1 / -0

A solid sphere and a thin uniform circular disc of same radius are rolling down an inclined plane without slipping. If the acceleration of the sphere is $3 {ms}^{- 2}$ , then the acceleration of the disc is

$4 {ms}^{- 2}$

Incorrect

$2.8 {ms}^{- 2}$

Incorrect

$3 {ms}^{- 2}$

Incorrect

$3.2 {ms}^{- 2}$

Incorrect

Q 90PhysicsSection A • MCQsimple harmonic motion

+1 / -0

If the amplitudes of a damped harmonic oscillator at times $𝑡 = 0, 𝑡_{1}$ and $𝑡_{2}$ are $𝐴_{0}, 𝐴_{1}$ and $𝐴_{2}$ respectively, then the amplitude of the oscillator at a time of $(𝑡_{1} + 𝑡_{2})$ is

$\frac{𝐴_{0} + 𝐴_{1} + 𝐴_{2}}{3}$

Incorrect

$\frac{𝐴_{2} 𝐴_{0}}{𝐴_{1}}$

Incorrect

$\frac{𝐴_{1} 𝐴_{0}}{𝐴_{2}}$

Incorrect

$\frac{𝐴_{1} 𝐴_{2}}{𝐴_{0}}$

Incorrect

Q 91PhysicsSection A • MCQgravitation

+1 / -0

A meteor of mass ' $𝑚$ ' having a speed ' $𝑉$ ' at infinity reaches the surface of the Earth with a speed of ( $𝑣_{𝑐}$ is escape speed from the Earth's surface)

$\sqrt{\sqrt 2} 𝑣_{𝑒}$

Incorrect

$𝑣_{𝑒}$

Incorrect

$2 \sqrt{\sqrt 𝑣^{2} + 𝑣_{2}^{𝑒}}$

Incorrect

$\sqrt{\sqrt 𝑣^{2} + 𝑣_{2}^{0}}$

Incorrect

Q 92PhysicsSection A • MCQelasticity

+1 / -0

The work to be done to produce a strain of $10^{- 3}$ in a steel wire of mass 2.96 kg and density $7.4 g {cm}^{- 3}$ is

(Young's modulus of steel $= 2 \times 10^{11} {Nm}^{- 2}$ )

0.04 kJ

Incorrect

0.04 J

Incorrect

100 kJ

Incorrect

400 J

Incorrect

Q 93PhysicsSection A • MCQfluid mechanics

+1 / -0

A wooden block of outer volume 1 litre and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then, the volume of the cavity is

250 mL

Incorrect

500 mL

Incorrect

333.3 mL

Incorrect

666.6 mL

Incorrect

Q 94PhysicsSection A • MCQheat and thermodynamics

+1 / -0

When ' $𝑛$ ' identical mercury drops combine to form a single big drop

surface area increases and heat is released.

Incorrect

surface area decreases and heat is released.

Incorrect

surface area increases and heat is absorbed.

Incorrect

surface area decreases and heat is absorbed.

Incorrect

Q 95PhysicsSection A • MCQheat and thermodynamics

+1 / -0

The temperature of a body shown by a faulty Celsius thermometer is $49^{\circ} C$ and by a correct Fahrenheit thermometer is $122^{\circ} F$ . The correction to be applied to the faulty thermometer is

$- 12^{\circ} C$

Incorrect

$+ 1^{\circ} C$

Incorrect

$+ 12^{\circ} C$

Incorrect

$- 1^{\circ} C$

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 \overset{o}{A}$ , the intensity of radiation emitted by it is

(Stefan-Boltzmann's constant $= 5.67 \times 10^{- 8} {Wm}^{- 2} K^{- 4}$ and Wein's constant $= 2.9 \times 10^{- 3} mK$ )

$5.67 \times 10^{8} {Wm}^{- 2}$

Incorrect

$5.67 {Wm}^{- 2}$

Incorrect

$5670 {Wm}^{- 2}$

Incorrect

$2.9 {Wm}^{- 2}$

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

The ratio of the work done, change in internal energy and heat absorbed when a diatomic gas expands at constant pressure is

$2 : 3 : 5$

Incorrect

$7 : 5 : 2$

Incorrect

$5 : 3 : 2$

Incorrect

$2 : 5 : 7$

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

If the temperature of a gas is increased from $127^{\circ} C$ to $527^{\circ} C$ , then the rms speed of the gas molecules

increases by 4 times

Incorrect

becomes $\sqrt{\sqrt 2}$ times

Incorrect

becomes half

Incorrect

decreases by $\sqrt{\sqrt 2}$ times

Incorrect

Q 99PhysicsSection A • MCQwaves

+1 / -0

An air column in a tube of length 50 cm , closed at one end is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at 42 cm from the open end is

$90^{\circ}$

Incorrect

$18^{\circ}$

Incorrect

$0^{\circ}$

Incorrect

$270^{\circ}$

Incorrect

Q 100PhysicsSection A • MCQwaves

+1 / -0

A metal rod of length 125 cm is clamped at its midpoint. If the speed of the sound in the metal is $5000 {ms}^{- 1}$ , then the fundamental frequency of the longitudinal vibrations of the rod is

2 kHz

Incorrect

20 kHz

Incorrect

0.2 kHz

Incorrect

200 kHz

Incorrect

Q 101PhysicsSection A • MCQray optics

+1 / -0

If the distances of the object and its real image from the principal focus of a concave mirror are 16 cm and 9 cm respectively, then the focal length of the mirror is

30 cm

Incorrect

12 cm

Incorrect

18 cm

Incorrect

24 cm

Incorrect

Q 102PhysicsSection A • MCQray optics

+1 / -0

If the angle of minimum deviation produced by an equilateral prism is equal to the angle of the prism, then the refractive index of the material of the prism is nearly

1.515

Incorrect

1.414

Incorrect

1.732

Incorrect

1.625

Incorrect

Q 103PhysicsSection A • MCQwave optics

+1 / -0

When two light waves of equal intensity superimpose, the maximum intensity obtained is $𝐼$ . If the intensity of one of the waves is quadrupled, then the maximum intensity obtained is

$\frac{41}{9}$

Incorrect

$\frac{9 /}{4}$

Incorrect

$\frac{21}{3}$

Incorrect

$\frac{31}{2}$

Incorrect

Q 104PhysicsSection A • MCQelectrostatics

+1 / -0

The electric field due to an infinitely long thin straight wire with uniform linear charge density of $2.5 \times 10^{- 7} {cm}^{- 1}$ at a radial distance of $𝑥$ from the wire is $7.5 \times 10^{4} {NC}^{- 1}$ . Then, $𝑥 =$

2 cm

Incorrect

3 cm

Incorrect

4 cm

Incorrect

6 cm

Incorrect

Q 105PhysicsSection A • MCQcapacitor

+1 / -0

A parallel plate capacitor of capacitance $10 𝜇 F$ is charged by a 220 V supply. The capacitor is then disconnected from the supply and is connected to another uncharged parallel plate capacitor of capacitance $12 𝜇 F$ . The loss of electrostatic energy in this process is

132 mJ

Incorrect

220 mJ

Incorrect

66 mJ

Incorrect

110 mJ

Incorrect

Q 106PhysicsSection A • MCQcurrent electricity

+1 / -0

The lengths of two wires made of the same material are in the ratio $2 : 3$ and their radii are in the ratio $1 : 2$ . If the two wires are connected in parallel to a battery, then the ratio of the drift velocities of free electrons in the two wires is

$2 : 1$

Incorrect

$3 : 1$

Incorrect

$3 : 2$

Incorrect

$3 : 4$

Incorrect

Official Correct Answer:Option (C)

Step-by-Step Solution:

Same material: This implies that the resistivity ( $𝜌$ ) and the number density of free electrons ( $𝑛$ ) are the same for both wires. Also, the charge of an electron ( $𝑒$ ) is a constant.
Lengths ratio: $𝐿_{1} : 𝐿_{2} = 2 : 3$ , which means $𝐿_{1} / 𝐿_{2} = 2 / 3$ .
Radii ratio: $𝑟_{1} : 𝑟_{2} = 1 : 2$ .
Connected in parallel to a battery: This means the potential difference (voltage $𝑉$ ) across both wires is the same, i.e., $𝑉_{1} = 𝑉_{2} = 𝑉$ .

We need to find the ratio of the drift velocities ( $𝑣_{𝑑 1} : 𝑣_{𝑑 2}$ ).

The relationship between current ( $𝐼$ ), number density of free electrons ( $𝑛$ ), cross-sectional area ( $𝐴$ ), charge of an electron ( $𝑒$ ), and drift velocity ( $𝑣_{𝑑}$ ) is given by:

$𝐼 = 𝑛 𝐴 𝑒 𝑣_{𝑑}$

From this, the drift velocity can be expressed as:

$𝑣_{𝑑} = \frac{𝐼}{𝑛 𝐴 𝑒}$ (Equation 1)

According to Ohm's Law, the current in a wire is related to the potential difference ( $𝑉$ ) and resistance ( $𝑅$ ):

$𝐼 = \frac{𝑉}{𝑅}$ (Equation 2)

The resistance of a wire is given by:

$𝑅 = \frac{𝜌 𝐿}{𝐴}$ (Equation 3)

where $𝜌$ is the resistivity, $𝐿$ is the length, and $𝐴$ is the cross-sectional area.

Now, substitute Equation 3 into Equation 2:

$𝐼 = \frac{𝑉}{𝜌 𝐿 / 𝐴} = \frac{𝑉 𝐴}{𝜌 𝐿}$ (Equation 4)

Finally, substitute Equation 4 into Equation 1 for $𝐼$ :

$𝑣_{𝑑} = \frac{𝑉 𝐴 / (𝜌 𝐿)}{𝑛 𝐴 𝑒}$

Notice that the cross-sectional area ( $𝐴$ ) appears in both the numerator and the denominator, so it cancels out:

$𝑣_{𝑑} = \frac{𝑉}{𝑛 𝑒 𝜌 𝐿}$

This derived formula shows that the drift velocity ( $𝑣_{𝑑}$ ) depends on the applied voltage ( $𝑉$ ), the number density of free electrons ( $𝑛$ ), the electron charge ( $𝑒$ ), the resistivity ( $𝜌$ ), and the length of the wire ( $𝐿$ ).

Since the wires are made of the same material, $𝑛$ and $𝜌$ are constant. The charge of an electron $𝑒$ is also a constant. When connected in parallel, the voltage $𝑉$ across both wires is the same.

Therefore, for these two wires, $𝑉$ , $𝑛$ , $𝑒$ , and $𝜌$ are all constant. This means the drift velocity is inversely proportional to the length of the wire:

$𝑣_{𝑑} \propto \frac{1}{𝐿}$

So, the ratio of the drift velocities will be:

$\frac{𝑣_{𝑑 1}}{𝑣_{𝑑 2}} = \frac{1 / 𝐿_{1}}{1 / 𝐿_{2}} = \frac{𝐿_{2}}{𝐿_{1}}$

We are given the ratio of lengths $𝐿_{1} : 𝐿_{2} = 2 : 3$ .

This means $\frac{𝐿_{1}}{𝐿_{2}} = \frac{2}{3}$ .

Therefore, $\frac{𝐿_{2}}{𝐿_{1}} = \frac{3}{2}$ .

Substituting this into the ratio of drift velocities:

$\frac{𝑣_{𝑑 1}}{𝑣_{𝑑 2}} = \frac{3}{2}$

The ratio of the drift velocities is $3 : 2$ .

Note that the information about the radii ratio was not needed for this calculation, as the cross-sectional area cancels out in the final expression for drift velocity when the voltage across the wire is constant.

The final answer is $3:2$ .

Q 107PhysicsSection A • MCQcurrent electricity

+1 / -0

In a potentiometer experiment for the determination of the internal resistance of a cell, when an external resistance of $𝑅$ is connected parallel to the cell, the balancing length decreases by $10 %$ . The internal resistance of the cell is

$\frac{𝑅}{9}$

Incorrect

$\frac{𝑅}{7}$

Incorrect

$\frac{𝑅}{5}$

Incorrect

$\frac{𝑅}{11}$

Incorrect

Q 108PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

The number of turns of two circular coils $𝐴$ and $𝐵$ are 300 and 200 respectively. The magnetic moments of the two coils $𝐴$ and $𝐵$ are in the ratio $1 : 2$ . If the two coils carry equal currents, then the ratio of radii of coils $𝐴$ and $𝐵$ is

$2 : \sqrt{\sqrt 3}$

Incorrect

$2 : 3$

Incorrect

$1 : 2$

Incorrect

$1 : \sqrt{\sqrt 3}$

Incorrect

Q 109PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

Two long straight parallel wires carry currents of 8 A and 10 A in opposite directions. If the distance of separation between the wires is 9 cm , then the net magnetic field at a point between the two wires, which is at a perpendicular distance of 4 cm from the wire carrying 8 A current is

zero

Incorrect

$4 \times 10^{- 5} T$

Incorrect

$8 \times 10^{- 5} T$

Incorrect

$12 \times 10^{- 5} T$

Incorrect

Q 110PhysicsSection A • MCQmagnetism and matter

+1 / -0

A short bar magnet of magnetic moment $2.5 {Am}^{2}$ is kept in a uniform magnetic field of $4 \times 10^{- 5} T$ . The work done in moving the magnet from its most stable position to most unstable position is

$40 \times 10^{- 5} J$

Incorrect

$25 \times 10^{- 5} J$

Incorrect

$10 \times 10^{- 5} J$

Incorrect

$20 \times 10^{- 5} J$

Incorrect

Q 111PhysicsSection A • MCQelectromagnetic induction

+1 / -0

The radius of a coil of $𝑁$ turns is $𝑅$ . If the plane of the coil is placed parallel to a uniform magnetic field $𝐵$ , then the flux linked with the coil is

$𝜋 𝐵 𝑁 𝑅^{2}$

Incorrect

$2 𝜋 𝐵 𝑁 𝑅^{2}$

Incorrect

$\frac{𝜋 𝐵 𝑁 𝑅^{2}}{2}$

Incorrect

zero

Incorrect

Q 112PhysicsSection A • MCQalternating current

+1 / -0

The inductance $𝐿$ , capacitance $𝐶$ and resistance $𝑅$ are the values of the components connected in series to an AC source of angular frequency $𝜔$ . The inductive and capacitive reactances are $𝑋_{𝐿}$ and $𝑋_{𝐶}$ respectively. If the circuit is purely resistive, then

$𝐿 = 𝐶$

Incorrect

$𝑋_{𝐿} = 𝑋_{𝐶}$

Incorrect

$𝜔 𝐿 = 𝜔 𝐶$

Incorrect

$𝑅 = 𝐿 = 𝐶$

Incorrect

Q 113PhysicsSection A • MCQcapacitor

+1 / -0

If the rate of change of electric field across the plates of a parallel plate capacitor is $𝐸$ and the displacement current is $𝐼$ , then the area of one plate of the capacitor is ( $𝜀_{0}$ is permittivity of free space)

$\frac{1}{2 𝜀_{0} 𝐸}$

Incorrect

$\frac{2 𝐼}{𝜀_{0} 𝐸}$

Incorrect

$𝜀_{0} 𝐸$

Incorrect

$\frac{1}{𝜀_{0} 𝐸}$

Incorrect

Q 114PhysicsSection A • MCQdual nature of radiation

+1 / -0

The work done to accelerate an electron from rest so that it can have a de-Broglie wavelength of $6600 \overset{o}{A}$ is nearly

(Planck's constant $= 6.6 \times 10^{- 34} Js$ and mass of electron $= 9 \times 10^{- 31} kg$ )

$5.56 \times 10^{- 25} eV$

Incorrect

1.88 eV

Incorrect

$5.56 \times 10^{- 25} J$

Incorrect

1.88 J

Incorrect

Q 115PhysicsSection A • MCQatoms and nuclei

+1 / -0

If the total energy of an electron in an orbit is positive, then

electron will revolve in a circular orbit.

Incorrect

electron will revolve in an elliptical orbit.

Incorrect

electron will not follow a closed orbit.

Incorrect

electron will fall into the nucleus.

Incorrect

Q 116PhysicsSection A • MCQatoms and nuclei

+1 / -0

If $87.5 %$ of atoms of a radioactive element decay in 6 days, then the fraction of atoms of the element that decay in 8 days is

$1 / 8$

Incorrect

$\frac{7}{8}$

Incorrect

$1 / 16$

Incorrect

$15 / 16$

Incorrect

Q 117PhysicsSection A • MCQatoms and nuclei

+1 / -0

If the ratio of the mass numbers of two nuclei is $27 : 125$ , then the ratio of their surface areas is

$3 : 5$

Incorrect

$9 : 25$

Incorrect

$27 : 125$

Incorrect

$1 : 1$

Incorrect

Q 118PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

At absolute zero temperature, a semiconductor behaves like

semiconductor

Incorrect

superconductor

Incorrect

conductor

Incorrect

insulator

Incorrect

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

Three logic gates are connected as shown in the figure. If the inputs are $𝐴 = 1, 𝐵 = 0$ and $𝐶 = 1$ , then the values of $𝑦_{1}, 𝑦_{2}$ and $𝑦_{3}$ respectively are

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

1, 0, 0

Incorrect

$0, 1, 0$

Incorrect

$1, 1, 0$

Incorrect

1, 0, 1

Incorrect

Q 120PhysicsSection A • MCQcommunication systems

+1 / -0

The radio horizon of a transmitting antenna of height 39.2 m is (Radius of the Earth $= 6400 km$ )

44.8 km

Incorrect

19.6 km

Incorrect

22.4 km

Incorrect

78.4 km

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

The radius of second orbit of hydrogen atom is same as that of orbit ( $𝑛$ ) of an ion ( $𝑥$ ), $𝑛$ and $𝑥$ are respectively.

$4, {Be}^{2 +}$

Incorrect

$3, {Li}^{2 +}$

Incorrect

$4, {Be}^{3 +}$

Incorrect

$2, {He}^{+}$

Incorrect

Q 122ChemistrySection A • MCQatomic structure

+1 / -0

An electromagnetic radiation of wavelength 331.5 nm is made to strike the surface of a metal. Electrons are emitted with a kinetic energy of $12 \times 10^{5} J {mol}^{- 1}$ . The work function (in eV ) of the metal is $(ℎ = 6.63 \times 10^{- 34} Js, 𝑁_{𝐴} = 6 \times 10^{23} {mol}^{- 1})$

1.5

Incorrect

3.0

Incorrect

3.5

Incorrect

2.5

Incorrect

Q 123ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Match the following

\begin{matrix} List-I (Element) & List-II (Block) \\ (A) & Cd & I & 𝑓 -block \\ (B) & Eu & II & 𝑠 -block \\ (C) & Se & III & 𝑑 -block \\ (D) & Ba & IV & 𝑝 -block \end{matrix}

The correct answer is

A-IV, B-III, C-II, D-I

Incorrect

A-II, B-IV, C-I, D-III

Incorrect

A-III, B-IV, C-II, D-I

Incorrect

A-III, B-I, C-IV, D-II

Incorrect

Q 124ChemistrySection A • MCQperiodic classification of elements

+1 / -0

In long form of periodic table an element ' $𝐸$ ' has atomic number 78 . The period and group number of the element are $𝑥$ and $𝑦$ respectively. $(𝑥 + 𝑦)$ is equal to

18

Incorrect

15

Incorrect

17

Incorrect

16

Incorrect

Q 125ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

In which of the following options, the molecules are correctly arranged in the increasing order of their bond angles?

${NH}_{3} < O_{3} < H_{2} O < {SO}_{2}$

Incorrect

$H_{2} O < O_{3} < {NH}_{3} < {SO}_{2}$

Incorrect

$H_{2} O < {NH}_{3} < {SO}_{2} < O_{3}$

Incorrect

$H_{2} O < {NH}_{3} < O_{3} < {SO}_{2}$

Incorrect

Q 126ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

In which of the following the compounds are correctly arranged in the decreasing order of boiling points?

$HF > H_{2} O > {NH}_{3} > {PH}_{3}$

Incorrect

$H_{2} O > HF > {NH}_{3} > {PH}_{3}$

Incorrect

$H_{2} O > HF > {PH}_{3} > {NH}_{3}$

Incorrect

$HF > {NH}_{3} > H_{2} O > {PH}_{3}$

Incorrect

Q 127ChemistrySection A • MCQstates of matter

+1 / -0

The force $(𝐹)$ required to maintain the flow of layers of a liquid is equal to

( $𝐴 =$ area of contact of layers

$𝑑 𝑧 =$ distance between the layers

$𝑑 𝑢 =$ change in velocity

$𝜂 =$ coefficient of viscosity)

$𝜂 \frac{𝑑 𝑢}{𝑑 𝑧} \cdot \frac{1}{𝐴}$

Incorrect

$𝜂 \frac{𝑑 𝑧}{𝑑 𝑢} \cdot 𝐴$

Incorrect

$𝜂 A \frac{𝑑 𝑢}{𝑑 𝑧}$

Incorrect

$𝜂 \frac{𝑑 𝑧}{𝐴} \cdot \frac{1}{𝑑 𝑢}$

Incorrect

Q 128ChemistrySection A • MCQredox reactions

+1 / -0

$\begin{matrix} Consider the following redox reaction in basic medium. \\ \begin{matrix} 𝑥 Cr (OH)_{3} + 𝑦 {({IO}_{3})}^{-} & + z (OH)^{-} \to 𝑎 {({CrO}_{4})}^{2 -} + 𝑏 (I)^{-} + c (H_{2} O) \end{matrix} \end{matrix}$

The incorrect option about it is

$𝑥 + 𝑦 = 3$

Incorrect

$𝑎 + 𝑏 = 7$

Incorrect

$𝑧 = 4$

Incorrect

$𝑏 = 1$

Incorrect

Q 129ChemistrySection A • MCQthermodynamics

+1 / -0

The entropy and enthalpy changes for the reaction $CO (g) + H_{2} O (g) ⇌ {CO}_{2} (g) + H_{2} (g)$ at 300 K and 1 atm are respectively $- 42.4 {JK}^{- 1}$ and -41.2 kJ . The temperature at which the reaction will go in the reverse direction is

761.8 K

Incorrect

671.8 K

Incorrect

961.8 K

Incorrect

971.8 K

Incorrect

Q 130ChemistrySection A • MCQionic equilibrium

+1 / -0

The volume of water required to dissolve $0.1 g {PbCl}_{2}$ to get a saturated solution (in mL ) is (Given $𝐾_{𝑠 𝑝} ({PbCl}_{2}) = 3.2 \times 10^{- 8}$ ; Atomic mass of $Pb = 207 u$ )

150

Incorrect

100

Incorrect

120

Incorrect

180

Incorrect

Q 131ChemistrySection A • MCQsolutions

+1 / -0

1 mL of " $𝑥$ volume" $H_{2} O_{2}$ solution on heating gives 20 mL of oxygen gas at STP. The $(𝑤 / 𝑣) %$ corresponding to " $𝑥$ volume" of $H_{2} O_{2}$ is

3.03

Incorrect

6.06

Incorrect

9.09

Incorrect

30.3

Incorrect

Q 132ChemistrySection A • MCQs block elements

+1 / -0

Identify the correct statement from the following

I. LiF is less soluble in water than NaF

II. Both LiCl and ${MgCl}_{2}$ are insoluble in ethanol

III. Both Li and Mg form nitrides

IV. ${Na}_{2} {CO}_{3}$ gives ${CO}_{2}$ on heating

I and IV

Incorrect

I and III

Incorrect

I and II

Incorrect

II and III

Incorrect

Q 133ChemistrySection A • MCQs block elements

+1 / -0

The major ingredient $(51 %)$ in Portland cement is

${Ca}_{2} {SiO}_{4}$

Incorrect

${Ca}_{3} {SiO}_{5}$

Incorrect

${Ca}_{3} {Al}_{3} O_{6}$

Incorrect

${CaSO}_{4} \cdot 2 H_{2} O$

Incorrect

Q 134ChemistrySection A • MCQp block elements

+1 / -0

Boron trifluoride on reaction with lithium aluminium hydride in ether gives ${LiF}^{\circ} {AlF}_{3}$ and $𝑋 . 𝑋$ on reaction with ${NH}_{3}$ gives $𝑌$ . $𝑌$ on further heating gives a compound $𝑍$ . The number of $𝜎$ -bonds and $𝜋$ -bonds in $𝑍$ are $𝑥$ and $𝑦$ respectively. $(𝑥 + 𝑦)$ is equal to

15

Incorrect

12

Incorrect

14

Incorrect

18

Incorrect

Q 135ChemistrySection A • MCQpolymers

+1 / -0

Consider the following sequence of reaction

$2 {CH}_{3} Cl + Si {\to\leftarrow}_{573 K}^{Cu} 𝑋 \overset{H_{2} O}{\to\leftarrow} 𝑌 \overset{Polymerisation}{\to\leftarrow} 𝑍$

The repeating structural unit in Z is

qImage--polymers-organic-chemistry-Jeemate

Incorrect

qImage--polymers-organic-chemistry-Jeemate

Incorrect

qImage--polymers-organic-chemistry-Jeemate

Incorrect

qImage--polymers-organic-chemistry-Jeemate

Incorrect

Q 136ChemistrySection A • MCQenvironmental chemistry

+1 / -0

Which of the following is not the common component of photochemical smog?

Ozone

Incorrect

Formaldehyde

Incorrect

Acrolein

Incorrect

Sulphur dioxide

Incorrect

Q 137ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

Identify the compound $(𝑍)$ in the following reaction sequence

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

propanal

Incorrect

propanone

Incorrect

propanoic acid

Incorrect

propanamide

Incorrect

Q 138ChemistrySection A • MCQiupac nomenclature

+1 / -0

$The correct IUPAC name of the following compound is$

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

5-amino-4-hydroxy-1-bromo-1-cyanopentan-4-ol

Incorrect

1-amino-6-bromo-3-hydroxy-4-oxopentanenitrile

Incorrect

6-amino-2-bromo-5-hydroxy-3-oxohexanenitrile

Incorrect

6-amino-2-bromo-5-hydroxy-3-oxopentanenitrile

Incorrect

Q 139ChemistrySection A • MCQgeneral organic chemistry

+1 / -0

Which purification method is generally used for a high boiling organic liquid compound which decompose below its boiling point?

Distillation

Incorrect

Distillation under reduced pressure

Incorrect

Steam distillation

Incorrect

Fractional distillation

Incorrect

Q 140ChemistrySection A • MCQhydrocarbons

+1 / -0

$Match the following$

qImage--hydrocarbons-organic-chemistry-Jeemate

The correct answer is

A-II, B-IV, C-I, D-III

Incorrect

A-II, B-V, C-I, D-III

Incorrect

A-III, B-IV, C-II, D-I

Incorrect

A-II, B-III, C-IV, D-I

Incorrect

Q 141ChemistrySection A • MCQsolid state

+1 / -0

Sodium metal crystallises in a body centred cubic lattice with edge length of $𝑥 \overset{o}{A}$ . If the radius of sodium atom is $1.86 \overset{o}{A}$ the value of $𝑥$ is

4.29

Incorrect

3.29

Incorrect

2.39

Incorrect

3.93

\overset{o}{A}

Incorrect

Q 142ChemistrySection A • MCQsolutions

+1 / -0

In a mixture of liquids $𝐴$ and $𝐵$ , if the mole fractions of component $𝐴$ in vapour phase and liquid mixture are $𝑥_{1}$ and $𝑥_{2}$ respectively, then the total vapour pressure of liquid mixture is

(Where $𝑝_{0}^{A}$ and $𝑝_{0}^{B}$ are the vapour pressure of pure $𝐴$ and $𝐵$ )

$\frac{𝑃_{0}^{𝐵} 𝑋_{1}}{𝑋_{2}}$

Incorrect

$\frac{𝑝_{0}^{3} 𝑥_{2}}{𝑥_{1}}$

Incorrect

$\frac{𝑝_{0}^{A} x_{2}}{𝑥_{1}}$

Incorrect

$\frac{𝑝_{0}^{𝐴} 𝑥_{1}}{𝑥_{2}}$

Incorrect

Q 143ChemistrySection A • MCQelectrochemistry

+1 / -0

A current of 0.5 ampere is passed through molten ${AlCl}_{3}$ for 96.5 seconds. The mass of aluminium deposited at cathode is $𝑥 mg$ and volume of chlorine liberated (at STP) at anode is $𝑦 mL . 𝑥$ and $𝑦$ are respectively.

$18.0, 22.4$

Incorrect

$13.5, 16.8$

Incorrect

$9.0, 11.2$

Incorrect

$4.5, 5.6$

Incorrect

Q 144ChemistrySection A • MCQchemical kinetics

+1 / -0

$𝑅 \to 𝑃$ is a first order reaction. For this reaction a graph of $\ln [𝑅]$ (on $𝑦$ -axis) and time (on x -axis) gave a straight line with negative slope. The intercept on $𝑦$ -axis is equal to ( $𝑘 =$ rate constant)

$\ln [𝑅]_{0}$

Incorrect

$[𝑅]_{0}$

Incorrect

$𝑘 \times 2.303$

Incorrect

$\frac{𝑘}{2.303}$

Incorrect

Q 145ChemistrySection A • MCQsurface chemistry

+1 / -0

The correct statements about the properties of colloidal solutions are

A. Tyndall effect is used to distinguish between a colloidal solution and a true solution.

B. Zeta potential is related to movement of colloidal particles.

C. Brownian motion in colloidal solution is faster if the viscosity of the solution is very high.

D. Brownian motion stabilises the sols.

A and B

Incorrect

B and C

Incorrect

A and D

Incorrect

B and D

Incorrect

Q 146ChemistrySection A • MCQmetallurgy

+1 / -0

The ore of which metal is concentrated by leaching?

Zn

Incorrect

Cu

Incorrect

Al

Incorrect

Fe

Incorrect

Q 147ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

Arrange the following molecules in the correct order of their bond angles

$S_{8}$	$𝑃_{4}$	$S_{6}$	$O_{3}$
A	B	C	D

$𝐴 < 𝐶 < 𝐷 < 𝐵$

Incorrect

$𝐵 < 𝐴 < 𝐶 < 𝐷$

Incorrect

$𝐶 < 𝐵 < 𝐴 < 𝐷$

Incorrect

$𝐵 < 𝐶 < 𝐴 < 𝐷$

Incorrect

Q 148ChemistrySection A • MCQredox reactions

+1 / -0

What are the products formed when ammonium dichromate is thermally decomposed?

${NO}_{2}, {Cr}_{2} O_{3}, H_{2}$

Incorrect

$N_{2} O, {Cr}_{2} O_{3}, H_{2} O$

Incorrect

$N_{2}, {CrO}_{3}, H_{2} O$

Incorrect

$N_{2}, {Cr}_{2} O_{3}, H_{2} O$

Incorrect

Q 149ChemistrySection A • MCQp block elements

+1 / -0

Sulphur dioxide on reaction with chlorine in the presence of charcoal gives compound $(𝐴)$ . This on reaction with white phosphorus gives ${SO}_{2}$ and compound $(𝐵)$ . The correct statement about ' $𝐵$ ' is

the shape of ' $𝐵$ ' is pyramidal.

Incorrect

' $𝐵$ ' on hydrolysis gives phosphorus acid.

Incorrect

' $𝐵$ ' in solid state exists as an ionic solid.

Incorrect

In ' $𝐵$ ' all bonds are equivalent.

Incorrect

Q 150ChemistrySection A • MCQd and f block elements

+1 / -0

In which of the following transition metal ion (aquated) is not correctly matched with its colour?

${Fe}^{2 +}$ -Green

Incorrect

${Cu}^{2 +}$ - Blue

Incorrect

${Fe}^{3 +} -$ Pink

Incorrect

$V^{3 +}$ -Green

Incorrect

Q 151ChemistrySection A • MCQcoordination compounds

+1 / -0

Which one of the following complex ions is diamagnetic in nature?

${[{CoF}_{6}]}^{3 -}$

Incorrect

${[Co (Ox)_{3}]}^{3 -}$

Incorrect

${[Mn (CN)_{6}]}^{3 -}$

Incorrect

${[Fe (CN)_{6}]}^{3 -}$

Incorrect

Q 152ChemistrySection A • MCQpolymers

+1 / -0

Polymer $𝑋$ is an example of polyester and $𝑌$ is an example of polyamide $𝑋$ and $𝑌$ are respectively

novolac, terylene

Incorrect

dacron, nylon 6,6

Incorrect

nylon 6 , terylene

Incorrect

teflon, terylene

Incorrect

Q 153ChemistrySection A • MCQbiomolecules

+1 / -0

The general structure of alpha amino acid can be represented as

qImage--biomolecules-organic-chemistry-Jeemate

Which amino acid is not correctly matched with $𝑅$ given?

$𝑅 = - {CH}_{2} - C_{6} H_{4} - OH (p) -$ (Tyrosine)

Incorrect

$𝑅 = - {CH}_{2} - SH - ($ Cysteine)

Incorrect

$𝑅 = - {CH}_{2} - {CH}_{2} - S - {CH}_{3}$ -(Serine)

Incorrect

qImage--biomolecules-organic-chemistry-Jeemate

Incorrect

Q 154ChemistrySection A • MCQchemistry in everyday life

+1 / -0

Consider the following.

Assertion (A) Aspirin is useful in the prevention of heart attacks.

Reason (R) Aspirin acts as anti-blood clotting agent The correct answer is

Both $𝐴$ and $𝑅$ are correct and $𝑅$ is the correct explanation of $𝐴$ .

Incorrect

A is correct and R is not correct.

Incorrect

Both A and R are correct and R is not the correct explanation of A.

Incorrect

A is incorrect and R is correct.

Incorrect

Q 155ChemistrySection A • MCQhydrocarbons

+1 / -0

Chlorobenzene when subjected to fittig reaction gives a compound ' $𝑋$ '. The sum of $𝜎$ and $𝜋$ - bonds in $𝑋$ is

30

Incorrect

28

Incorrect

18

Incorrect

29

Incorrect

Q 156ChemistrySection A • MCQhydrocarbons

+1 / -0

Cumene on oxidation in air gives a compound, $𝑋$ . This on reaction with dilute acid gives $𝑌$ and $𝑍 . 𝑌$ reacts with sodium metal and not $𝑍$ . What is $𝑍$ ?

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

Q 157ChemistrySection A • MCQaldehyde and ketone

+1 / -0

The reaction of benzene with CO and HCl in the presence of anhydrous ${AlCl}_{3}$ gives a compound $𝑋 \cdot 𝑋$ can also be obtained from which of the following reaction?

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