Ap Eapcet 2023 15th May Morning Shift Question Paper Question Paper with Solutions | AP EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQfunctions

+1 / -0

If $𝑓 (𝑥) = 𝑥^{3} - 𝑥$ and $𝑔 (𝑥) = \sin 2 𝑥$ , then $𝑓 (𝑔 (\frac{𝜋}{12})) =$

0

Incorrect

1

Incorrect

$- \frac{3}{8}$

Incorrect

2

Incorrect

Q 2MathematicsSection A • MCQfunctions

+1 / -0

For $𝑥 \in 𝑅$ if $𝑓 (𝑥) = \sqrt{\sqrt \log_{10} (\frac{3 - 𝑥}{𝑥})}$ , then the domain of $𝑓$ is

$[0, \frac{3}{2}]$

Incorrect

$(0, \frac{3}{2}]$

Incorrect

[0,1]

Incorrect

(0, 1]

Incorrect

Q 3MathematicsSection A • MCQmatrices and determinants

+1 / -0

Let $𝐴 = ⎛⎝⎜ \begin{matrix} 0 \\ - 6 \\ 8 \end{matrix} ⎞⎠⎟, 𝐵 = ⎛⎝⎜ \begin{matrix} 3 & 5 & - 7 \\ 0 & - 1 & 8 \\ 6 & - 1 & 0 \end{matrix} ⎞⎠⎟$ and $𝑋 = ⎛⎝⎜ \begin{matrix} 𝑥 \\ 𝑦 \\ 𝑧 \end{matrix} ⎞⎠⎟$ . If $𝐷 = [𝛼 𝛽 𝛾]^{𝑇}$ is the solution of $𝑋^{𝑇} 𝐵^{𝑇} = 𝐴^{𝑇}$ , then $𝐷^{𝑇} 𝐴 =$

0

Incorrect

4

Incorrect

-2

Incorrect

6

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝑆 = ⎡⎣⎢ \begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{matrix} ⎤⎦⎥$ and $𝐴 = \frac{1}{2} ⎡⎣⎢ \begin{matrix} 𝑏 + 𝑐 & 𝑐 - 𝑎 & 𝑏 - 𝑎 \\ 𝑐 - 𝑏 & 𝑐 + 𝑎 & 𝑎 - 𝑏 \\ 𝑏 - 𝑐 & 𝑎 - 𝑐 & 𝑎 + 𝑏 \end{matrix} ⎤⎦⎥$ , then $𝑆 𝐴 𝑆^{- 1} =$

$⎡⎣⎢ \begin{matrix} 𝑎 & 0 & 0 \\ 0 & 𝑏 & 0 \\ 0 & 0 & 𝑐 \end{matrix} ⎤⎦⎥$

Incorrect

$\frac{1}{2} ⎡⎣⎢ \begin{matrix} 𝑎 & 0 & 0 \\ 0 & 𝑏 & 0 \\ 0 & 0 & 𝑐 \end{matrix} ⎤⎦⎥$

Incorrect

$2 ⎡⎣⎢ \begin{matrix} 𝑎 & 0 & 0 \\ 0 & 𝑏 & 0 \\ 0 & 0 & 𝑐 \end{matrix} ⎤⎦⎥$

Incorrect

$⎡⎣⎢ \begin{matrix} 𝑎 & 𝑏 & 𝑐 \\ 𝑏 & 𝑐 & 𝑎 \\ 𝑐 & 𝑎 & 𝑏 \end{matrix} ⎤⎦⎥$

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴 = [\begin{matrix} 𝑖 & 0 \\ 0 & - 𝑖 \end{matrix}], 𝐵 = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]$ and $𝐶 = [\begin{matrix} 0 & 𝑖 \\ 𝑖 & 0 \end{matrix}]$ , then

$𝐴^{2} + 𝐵^{2} + 𝐶^{2} = 3 𝐴^{2} 𝐵^{2} 𝐶^{2}$

Incorrect

$𝐴^{2} + 𝐵^{2} + 𝐶^{2} = 3 𝐴 𝐵 𝐶$

Incorrect

$𝐴^{2} + 𝐵^{2} + 𝐶^{2} = 3 𝐼$

Incorrect

$𝐴^{2} + 𝐵^{2} + 𝐶^{2} = 2 𝐴 𝐵 𝐶$

Incorrect

Q 6MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑧_{1} = (2, - 1)$ and $𝑧_{2} = (6, 3)$ , then $amp (\frac{𝑧_{1} - 𝑧_{2}}{𝑧_{1} + 𝑧_{2}}) =$

$- \frac{3 𝜋}{4} - \tan^{- 1} (\frac{1}{4})$

Incorrect

$\frac{𝜋}{4} - \tan^{- 1} (\frac{1}{4})$

Incorrect

$\frac{3 𝜋}{4} + \tan^{- 1} (\frac{1}{4})$

Incorrect

$\frac{𝜋}{4} + \tan^{- 1} (\frac{1}{4})$

Incorrect

Q 7MathematicsSection A • MCQcomplex numbers

+1 / -0

The number of all possible solutions of the equation $𝑧^{3} + \bar{𝑧} = 0$ is

4

Incorrect

5

Incorrect

3

Incorrect

6

Incorrect

Q 8MathematicsSection A • MCQcomplex numbers

+1 / -0

${[\sqrt{\sqrt 2} (\cos 56^{\circ} 15^{'} + 𝑖 \sin 56^{\circ} 15^{'})]}^{8} =$

1

Incorrect

$𝑖$

Incorrect

16

Incorrect

$16 𝑖$

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

$(1 + 𝑖)^{2024} + (1 - 𝑖)^{2024} =$

$- 2^{1012}$

Incorrect

$2^{1013}$

Incorrect

$2^{2024} 𝑖$

Incorrect

$- 2^{1012} 𝑖$

Incorrect

Q 10MathematicsSection A • MCQquadratic equations

+1 / -0

If the values of $𝑘$ for which the euqation $𝑥^{2} + 2 (𝑘 + 2) 𝑥 + 6 𝑘 + 7 = 0$ has equal roots are $𝑘_{1}$ and $𝑘_{2}$ , then $𝑘_{2}^{1} + 𝑘_{2}^{2} =$

8

Incorrect

9

Incorrect

10

Incorrect

12

Incorrect

Q 11MathematicsSection A • MCQquadratic equations

+1 / -0

If $(3 + 2 \sqrt{\sqrt 2})^{𝑥^{2} - 4} + (3 - 2 \sqrt{\sqrt 2})^{𝑥^{2} - 4} = 6$ , then $𝑥^{4} + 𝑥^{2} + 5 =$

-30

Incorrect

-35

Incorrect

30

Incorrect

35

Incorrect

Q 12MathematicsSection A • MCQquadratic equations

+1 / -0

If the equation $𝑥^{4} + 𝑎 𝑥^{3} + 𝑏 𝑥^{2} + 𝑐 𝑥 + 𝑑 = 0$ has three equal roots, then that root is

$\frac{6 𝑐 - 𝑎 𝑏}{8 𝑏 - 3 𝑎^{2}}$

Incorrect

$\frac{𝑎 𝑏 - 6 𝑐}{8 𝑏 + 3 𝑎^{2}}$

Incorrect

$\frac{6 𝑐 - 𝑎 𝑏}{3 𝑎^{2} - 4 𝑏}$

Incorrect

$\frac{6 𝑐 - 𝑎 𝑏}{3 𝑎^{2} - 8 𝑏}$

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If -1 is a twice repeated root of the equation $𝑎 (𝑥^{3} + 𝑥^{2}) + 𝑏 𝑥 + 𝑐 = 0$ , then $𝑎 : 𝑏 : 𝑐 =$

$- 1 : 1$

Incorrect

$- 1 : 1 : 1$

Incorrect

$1 : 1 : - 1$

Incorrect

$1 : 1 : 1$

Incorrect

Q 14MathematicsSection A • MCQbinomial theorem

+1 / -0

If $𝐶_{𝑗}$ stands for $^{𝑛} 𝐶_{𝑗}$ , then

$\frac{𝐶_{1}}{𝐶_{0}} + \frac{2 \times 𝐶_{2}}{𝐶_{1}} + \frac{3 \times 𝐶_{3}}{𝐶_{2}} + \dots + \frac{𝑛 \times 𝐶_{𝑛}}{𝐶_{𝑛 - 1}} =$

$\sum_{𝑛}^{𝑘 = 1} 𝑘^{2}$

Incorrect

$\sum_{𝑛}^{𝑘 = 1} \frac{𝑘}{2}$

Incorrect

$\sum_{𝑛}^{𝑘 = 1} 2 𝑘$

Incorrect

$\sum_{𝑛}^{𝑘 = 1} 𝑘$

Incorrect

Q 15MathematicsSection A • MCQpermutations and combinations

+1 / -0

If the number of diagonals of a regular polygon of $𝑛$ sides is 104 , then $𝑛 =$

19

Incorrect

16

Incorrect

13

Incorrect

11

Incorrect

Q 16MathematicsSection A • MCQbinomial theorem

+1 / -0

If $(2 - 5 𝑥)^{\frac{- 1}{5}} = 𝑎_{0} + 𝑎_{1} 𝑥 + 𝑎_{2} 𝑥^{2} + \dots$ , then $\frac{𝑎_{1}}{𝑎_{2}} =$

$\frac{1}{3}$

Incorrect

$- \frac{2}{3}$

Incorrect

$- \frac{1}{3}$

Incorrect

$\frac{2}{3}$

Incorrect

Q 17MathematicsSection A • MCQpermutations and combinations

+1 / -0

The number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the same number, is

802

Incorrect

602

Incorrect

702

Incorrect

1106

Incorrect

Q 18MathematicsSection A • MCQpermutations and combinations

+1 / -0

A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected is

792

Incorrect

180

Incorrect

120

Incorrect

90

Incorrect

Q 19MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

$\sin 21^{\circ} \cos 9^{\circ} - \cos 84^{\circ} \cos 6^{\circ} =$

1

Incorrect

$\frac{1}{4}$

Incorrect

$\frac{1}{2}$

Incorrect

$\frac{3}{2}$

Incorrect

Q 20MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $(1+\sqrt{1+a}) \sin \alpha=(1+\sqrt{1-a}) \cos \alpha$ and $0<a<1$ , then $\sin 4 \alpha=$

$𝑎$

Incorrect

$2 𝑎$

Incorrect

$3 𝑎$

Incorrect

$4 𝑎$

Incorrect

Q 21MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $𝐴 = \frac{𝜋}{24}$ , then $\frac{\cos 𝐴 + \cos 3 𝐴 + \cos 5 𝐴 + \cos 7 𝐴}{\sin 𝐴 + \sin 3 𝐴 + \sin 5 𝐴 + \sin 7 𝐴} =$

$\sqrt{\sqrt 3}$

Incorrect

$2 \sqrt{\sqrt 3}$

Incorrect

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

Incorrect

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

Incorrect

Q 22MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\sec (𝜃 + 𝛼), \sec 𝜃$ and $\sec (𝜃 - 𝛼)$ are in arithmetic progression, then $\sin^{2} 𝜃 =$

$\cos 𝛼$

Incorrect

$2 \cos 𝛼$

Incorrect

$- 2 \cos 𝛼$

Incorrect

$- \cos 𝛼$

Incorrect

Q 23MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\cos 𝛼 + \cos 𝛽 = 𝑎$ and $\sin 𝛼 + \sin 𝛽 = 𝑏$ , then match the items given in List-A with those of their values in List-B

$List-A$		$List-B$
(I)	$\tan (\frac{𝛼 + 𝛽}{2}) =$	(a)	$\frac{𝑏}{𝑎}$
(II)	$\cos (𝛼 + 𝛽) =$	(b)	$\frac{2 𝑎 𝑏}{𝑎^{2} + 𝑏^{2}}$
(III)	$\sin (𝛼 + 𝛽) =$	(c)	$\frac{2 𝑎 𝑏}{𝑎^{2} - 𝑏^{2}}$
(IV)	$\tan (𝛼 + 𝛽) =$	(d)	$\frac{𝑎^{2} - 𝑏^{2}}{𝑎^{2} + 𝑏^{2}}$
		(e)	$\frac{𝑎^{2} + 𝑏^{2}}{𝑎^{2} - 𝑏^{2}}$

$(I) →(a), (II) → (e), (III) →(d), (IV) → (c)$

Incorrect

$(I) → (a), (II) → (c), (III) → (b), (IV) → (e)$

Incorrect

$(I) → (a), (II) → (d), (III) → (c), (IV) → (b)$

Incorrect

$(I) → (a), (II) → (d), (III) → (b), (IV) → (c)$

Incorrect

Q 24MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $𝛼 = \log_{𝑒} (2 + \sqrt{\sqrt 3})$ , then $\frac{\cosh 𝛼}{1 - \tanh 𝛼} + \frac{\sinh 𝛼}{1 - \coth 𝛼} =$

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

Incorrect

$7 + 4 \sqrt{\sqrt 3}$

Incorrect

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

Incorrect

$2 + \sqrt{\sqrt 3}$

Incorrect

Q 25MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $\cot \frac{𝐴}{2} : \cot \frac{𝐵}{2} : \cot \frac{𝐶}{2} = 3 : 7 : 9$ , then $𝑎 : 𝑏 : 𝑐 =$

$8 : 6 : 5$

Incorrect

$5 : 6 : 8$

Incorrect

$10 : 8 : 5$

Incorrect

$5 : 8 : 10$

Incorrect

Q 26MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $\frac{1}{𝑟_{1}}, \frac{1}{𝑟_{2}}$ and $\frac{1}{𝑟_{3}}$ are in arithmetic progression, then $𝑟_{2} : 𝑟 =$

$3 : 2$

Incorrect

$2 : 1$

Incorrect

$1 : 3$

Incorrect

$3 : 1$

Incorrect

Q 27MathematicsSection A • MCQproperties of triangles

+1 / -0

If $𝑃_{1}, 𝑃_{2}$ and $𝑃_{3}$ are the lengths of the altitudes drawn from the vertices $𝐴, 𝐵$ and $𝐶$ of $△ 𝐴 𝐵 𝐶$ respectively, then $\frac{\cos 𝐴}{𝑃_{1}} + \frac{\cos 𝐵}{𝑃_{2}} + \frac{\cos 𝐶}{𝑃_{3}} =$

$\frac{1}{𝑅}$

Incorrect

$𝑅$

Incorrect

$\frac{Δ}{𝑅}$

Incorrect

$\frac{𝑟}{𝑅}$

Incorrect

Q 28MathematicsSection A • MCQindefinite integration

+1 / -0

If $\frac{2 𝑥^{2} + 5 𝑥 + 6}{(𝑥 + 2)^{3}} = \frac{𝑎}{𝑥 + 2} + \frac{𝑏}{(𝑥 + 2)^{2}} + \frac{𝑐}{(𝑥 + 2)^{3}}$ , then $𝑎 \cdot 𝑏 + 𝑏 \cdot 𝑐 + 𝑐 \cdot 𝑎 =$

28

Incorrect

14

Incorrect

-10

Incorrect

-8

Incorrect

Q 29MathematicsSection A • MCQvector algebra

+1 / -0

a and b are two vectors such that a is not parallel to b. If $𝐩 = (𝑥 + 2 𝑦 + 3) 𝐚 + (5 𝑥 - 𝑦 + 2) 𝐛$ and $𝐪 = (2 𝑥 + 3 𝑦 + 5) 𝐚 + (𝑥 - 5 𝑦 - 2) 𝐛$ are two vectors such that $𝐩 = 2 𝐪$ , then $𝑥 - 2 𝑦 =$

3

Incorrect

2

Incorrect

-2

Incorrect

-3

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

$3 \hat{𝐢} - 2 \hat{𝐣} - \hat{𝐤}, - 2 \hat{𝐢} - \hat{𝐣} + 3 \hat{𝐤}$ and $- \hat{𝐢} + 3 \hat{𝐣} - 2 \hat{𝐤}$ are the position vectors of the vertices $𝐴, 𝐵$ and $𝐶$ of a $△ 𝐴 𝐵 𝐶$ respectively. If $𝐻$ is its orthocentre, then $𝐇 𝐀 + 𝐇 𝐁 + 𝐇 𝐂 =$

$2 𝑆 𝐴$

Incorrect

$0$

Incorrect

$2 𝐴 𝐵$

Incorrect

$\hat{𝐢} + \hat{𝐣} + \hat{𝐤}$

Incorrect

Q 31MathematicsSection A • MCQ3d geometry

+1 / -0

Let $𝜋_{1}$ be the plane determined by the vectors $\hat{𝐢} + 2 \hat{𝐣}$ and $3 \hat{𝐣} - 2 \hat{𝐤}$ . Let $𝜋_{2}$ be the plane determined by the vectors $\hat{𝐣} + 2 \hat{𝐤}$ and $3 \hat{𝐤} - 2 \hat{𝐢}$ . If $𝜃$ is the angle between $𝜋_{1}$ and $𝜋_{2}$ , then $\cos 𝜃 =$

$\frac{7}{26}$

Incorrect

$- \frac{14}{29}$

Incorrect

$- \frac{32}{5 \sqrt{\sqrt 2}}$

Incorrect

$\frac{23}{38}$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚 = 2 \hat{𝐢} + 3 \hat{𝐣}, 𝐛 = 3 \hat{𝐣} + 4 \hat{𝐤}$ and $𝐜 = 5 \hat{𝐢} + 4 \hat{𝐤}$ are three vectors, then a vector which is perpendicular to $𝐚$ and $𝐛 \times 𝐜$ is

$45 \hat{𝐢} - 30 \hat{𝐣} + 15 \hat{𝐤}$

Incorrect

$3 \hat{𝐢} - 2 \hat{𝐣} + \hat{𝐤}$

Incorrect

$- 30 \hat{𝑖} + 20 \hat{𝑗} + 4 \hat{𝑘}$

Incorrect

$- 45 \hat{𝐢} + 30 \hat{𝐣} + 4 \hat{𝐤}$

Incorrect

Q 33MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐎 𝐀 = 2 \hat{𝐢} - 3 \hat{𝐣} + \hat{𝐤}, 𝐎 𝐁 = \hat{𝐢} - 4 \hat{𝐣} - 3 \hat{𝐤}$ and $𝐎 𝐂 = - 3 \hat{𝐢} + \hat{𝐣} + 2 \hat{𝐤}$ be the position vectors of three points $𝐴, 𝐵, 𝐶$ respectively. If $𝐺$ is the centroid of $△ 𝐴 𝐵 𝐶$ , then $𝐵 𝐶^{2} + 𝐶 𝐴^{2} + 𝐴 𝐵^{2} + 9 (𝑂 𝐺)^{2} =$

162

Incorrect

156

Incorrect

144

Incorrect

132

Incorrect

Q 34MathematicsSection A • MCQstatistics

+1 / -0

The variance of 20 observations is 5. If each one of the observations is multiplied by 2 , then the variance of the resulting observations is

40

Incorrect

80

Incorrect

20

Incorrect

10

Incorrect

Q 35MathematicsSection A • MCQprobability

+1 / -0

If two subsets $𝐴$ and $𝐵$ are selected at random from a set $𝑆$ containing $𝑛$ elements, then the probability that $𝐴 \cap 𝐵 = 𝜙$ and $𝐴 \cup 𝐵 = 𝑆$ , is

$\frac{1}{2^{𝑛}}$

Incorrect

$2^{𝑛}$

Incorrect

$\frac{1}{2^{𝑛 + 1}}$

Incorrect

$\frac{1}{2^{𝑛} \times 2^{𝑛}}$

Incorrect

Q 36MathematicsSection A • MCQprobability

+1 / -0

In a game, a pair of dice is rolled 24 times. If a person whis the game by not getting 6 on both the dice in any one of the 24 rolls, then the probability that a person wins the game is

${(\frac{35}{36})}^{24}$

Incorrect

${(\frac{17}{18})}^{24}$

Incorrect

${(\frac{11}{12})}^{24}$

Incorrect

${(\frac{5}{6})}^{24}$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

Bag $𝐵_{1}$ contains 4 white and 2 black balls. Bag $𝐵_{2}$ contains 3 white and 4 black balls. A bag is chosen at random and a ball is drawn from it at random, then the probability that the ball drawn is white, is

$\frac{1}{42}$

Incorrect

$\frac{42}{32}$

Incorrect

$\frac{33}{42}$

Incorrect

$\frac{23}{42}$

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

If four dice are thrown simultaneously, then the probability that none of the dice shows the number 1 on its face, is

$\frac{625}{1296}$

Incorrect

$\frac{125}{648}$

Incorrect

$\frac{1250}{1296}$

Incorrect

$\frac{625}{2592}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

The range of a random variable $𝑋$ is ${0, 1, 2}$ . If $𝑃 (𝑋 = 0) = 3 𝐶^{3}, 𝑃 (𝑋 = 1) = 4 𝐶 - 10 𝐶^{2}$ and $𝑃 (𝑋 = 2) = 5 𝐶 - 1$ , then the value of $𝐶$ is

$\frac{2}{3}$

Incorrect

$\frac{1}{3}$

Incorrect

$\frac{5}{3}$

Incorrect

$\frac{4}{3}$

Incorrect

Q 40MathematicsSection A • MCQprobability

+1 / -0

If eight coins are tossed simultaneously, then the probability of getting atleast six heads is

$\frac{37}{64}$

Incorrect

$\frac{37}{512}$

Incorrect

$\frac{37}{256}$

Incorrect

$\frac{37}{128}$

Incorrect

Q 41MathematicsSection A • MCQcircle

+1 / -0

The locus of a point which is at a distance of 2 units from the line $2 𝑥 - 3 𝑦 + 4 = 0$ and at a distance of $\sqrt{\sqrt 13}$ units from a point $(5, 0)$ , is

$8 𝑥^{2} + 12 𝑥 𝑦 + 56 𝑥 - 24 𝑦 + 84 = 0$

Incorrect

$12 𝑥 𝑦 - 5 𝑦^{2} - 56 𝑥 + 24 𝑦 + 84 = 0$

Incorrect

$8 𝑥^{2} + 12 𝑥 𝑦 + 𝑦^{2} - 56 𝑥 + 24 𝑦 + 84 = 0$

Incorrect

$8 𝑥^{2} + 12 𝑥 𝑦 - 7 𝑦^{2} - 56 𝑥 + 24 𝑦 + 84 = 0$

Incorrect

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

+1 / -0

The combined equation of the lines passing through the point $(3, 4)$ and each making an angle $45^{\circ}$ with the line $𝑥 + 𝑦 + 1 = 0$ is-

$𝑥 𝑦 - 4 𝑥 - 3 𝑦 + 12 = 0$

Incorrect

$(3 𝑥 - 2 𝑦 - 1) (𝑥 - 2 𝑦 + 2) = 0$

Incorrect

$(3 𝑥 + 2 𝑦 - 17) (𝑥 + 2 𝑦 - 11) = 0$

Incorrect

$𝑥 𝑦 - 4 𝑥 + 3 𝑦 + 12 = 0$

Incorrect

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

+1 / -0

The equal sides of an isosceles triangle are given by equations $7 𝑥 - 𝑦 + 3 = 0$ and $𝑥 + 𝑦 - 3 = 0$ . If the slope $𝑚$ of the third side is an integer, then $𝑚 =$

-3

Incorrect

3

Incorrect

4

Incorrect

-1

Incorrect

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

+1 / -0

In $△ 𝐴 𝐵 𝐶$ the coordinates of the vertex $𝐴$ are $(- 3, 1)$ . If the equation of the median through $𝐵$ is $2 𝑥 + 𝑦 - 3 = 0$ and the equation of the bisector of $∠ 𝐶$ is $7 𝑥 - 4 𝑦 - 1 = 0$ , then the equation of the side $𝐵 𝐶$ is

$7 𝑥 - 3 𝑦 = 6$

Incorrect

$18 𝑥 - 𝑦 = 49$

Incorrect

$15 𝑥 + 𝑦 = 50$

Incorrect

$4 𝑥 - 𝑦 = 7$

Incorrect

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

+1 / -0

If the lines given by $(𝑥^{2} + 𝑦^{2}) \sin^{2} 𝛼 = (𝑥 \cos 𝛼 - 𝑦 \sin 𝛼)^{2}$ are perpendicular to each other, then $\sin^{2} 𝛼 + \tan^{2} 𝛼 =$

$\frac{15}{4}$

Incorrect

0

Incorrect

$\frac{3}{2}$

Incorrect

$\frac{7}{12}$

Incorrect

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

+1 / -0

If the area of the triangle formed by the lines $𝑦 = 𝑥 + 𝑐$ and $2 𝑥^{2} + 5 𝑥 𝑦 + 3 𝑦^{2} = 0$ is $\frac{1}{20}$ sq units, then $𝑐 =$

$\pm 1$

Incorrect

$\pm \sqrt{\sqrt 2}$

Incorrect

$\pm 3$

Incorrect

$\pm \sqrt{\sqrt 3}$

Incorrect

Q 47MathematicsSection A • MCQ3d geometry

+1 / -0

If the line passing through the points $(5, 1, 𝑎)$ and $(3, 𝑏, 1)$ crosses the $𝑌 𝑍$ -plane at the point $(0, \frac{17}{2}, \frac{- 13}{2})$ , then $𝑎 + 𝑏 =$

12

Incorrect

10

Incorrect

8

Incorrect

4

Incorrect

Q 48MathematicsSection A • MCQ3d geometry

+1 / -0

$△ 𝐴 𝐵 𝐶$ is formed by $𝐴 (1, 8, 4), 𝐵 (0, - 11, 4)$ and $𝐶 (2, - 3, 1)$ . If $𝐷$ is the foot of the perpendicular drawn from $𝐴$ to $𝐵 𝐶$ , then the coordinates of $𝐷$ are

$(- 4, 5, 2)$

Incorrect

$(4, - 5, 2)$

Incorrect

$(4, - 5, - 2)$

Incorrect

$(4, 5, - 2)$

Incorrect

Q 49MathematicsSection A • MCQ3d geometry

+1 / -0

The distance between two parallel planes $𝑎 𝑥 + 𝑏 𝑦 + 𝑐 𝑧 + 𝑑_{1} = 0, 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 𝑧 + 𝑑_{2} = 0$ is given by $\frac{| 𝑑_{1} - 𝑑_{2} |}{\sqrt{\sqrt 𝑎^{2} + 𝑏^{2} + 𝑐^{2}}}$ . If the plane $2 𝑥 - 𝑦 + 2 𝑧 + 3 = 0$ has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the planes $4 𝑥 - 2 𝑦 + 4 𝑧 + 𝜆 = 0$ and $2 𝑥 - 𝑦 + 2 𝑧 + 𝜇 = 0$ respectively, then the maximum value of $𝜆 + 𝜇$ is

15

Incorrect

5

Incorrect

13

Incorrect

9

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

Let $𝑆$ be the circumcircle of the triangle formed by the line $𝑥 - 2 𝑦 - 4 = 0$ with the coordinate axes. If $𝑃 (- 2, - 4)$ is a point in the plane of the circle $𝑆$ and $𝑄$ is a point on $𝑆$ such that the distance between $𝑃$ and $𝑄$ is the least, then $𝑃 𝑄 =$

$5 - \sqrt{\sqrt 5}$

Incorrect

$5 + \sqrt{\sqrt 5}$

Incorrect

$13 + \sqrt{\sqrt 5}$

Incorrect

$13 - \sqrt{\sqrt 5}$

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

If the coordinates of point of contact of the circles $𝑥^{2} + 𝑦^{2} - 4 𝑥 + 8 𝑦 + 4 = 0$ and $𝑥^{2} + 𝑦^{2} + 2 𝑥 = 0$ is $(𝑎, 𝑏)$ , then $𝑎 + 2 𝑏 =$

-1

Incorrect

-2

Incorrect

0

Incorrect

1

Incorrect

Q 52MathematicsSection A • MCQcircle

+1 / -0

If the chord of contact of the point $𝑃 (ℎ, 𝑘)$ with respect to the circle $𝑥^{2} + 𝑦^{2} - 4 𝑥 - 4 𝑦 + 8 = 0$ meets the circle in two distinct points and it also makes an angle $45^{\circ}$ with the positive $𝑋$ -axis in the positive direction, then $(ℎ, 𝑘)$ cannot be

$(\frac{5}{2}, \frac{3}{2})$

Incorrect

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

Incorrect

$(3, 1)$

Incorrect

$(2, 2)$

Incorrect

Q 53MathematicsSection A • MCQcircle

+1 / -0

The equation of the pair of tangents drawn from the point $(1, 1)$ to the circle $𝑥^{2} + 𝑦^{2} + 2 𝑥 + 2 𝑦 + 1 = 0$ is

$3 𝑥^{2} - 8 𝑥 𝑦 + 3 𝑦^{2} - 2 𝑥 - 2 𝑦 + 6 = 0$

Incorrect

$11 𝑥^{2} - 8 𝑥 𝑦 + 11 𝑦^{2} - 4 𝑥 - 4 𝑦 - 6 = 0$

Incorrect

$3 𝑥^{2} - 8 𝑥 𝑦 + 3 𝑦^{2} + 2 𝑥 + 2 𝑦 - 2 = 0$

Incorrect

$𝑥^{2} - 4 𝑥 𝑦 + 𝑦^{2} + 𝑥 + 𝑦 = 0$

Incorrect

Q 54MathematicsSection A • MCQcircle

+1 / -0

Let the circle $𝑆 \equiv 𝑥^{2} + 𝑦^{2} + 2 𝑔 𝑥 + 2 𝑓 𝑦 + 𝑐 = 0$ cut the circles $𝑥^{2} + 𝑦^{2} - 2 𝑥 + 2 𝑦 - 2 = 0$ and $𝑥^{2} + 𝑦^{2} + 4 𝑥 - 6 𝑦 + 9 = 0$ orthogonally. If the centre of the circle $𝑆 = 0$ lies on the line $2 𝑥 + 3 𝑦 - 2 = 0$ , then $2 𝑔 + 𝑓 =$

C

Incorrect

$𝑐 + 𝑓$

Incorrect

$2 𝑔 - 𝑐$

Incorrect

$𝑐 - 𝑓$

Incorrect

Q 55MathematicsSection A • MCQparabola

+1 / -0

Let the equation of the tangent at a point $𝑃$ on the parabola $𝑥^{2} - 4 𝑥 - 4 𝑦 + 16 = 0$ be $2 𝑥 - 𝑦 - 5 = 0$ . If the equation of the normal drawn at $𝑃$ to this parabola is $𝑎 𝑥 + 𝑦 + 𝑐 = 0$ , then $𝑎 𝑐 =$

-20

Incorrect

20

Incorrect

5

Incorrect

-5

Incorrect

Q 56MathematicsSection A • MCQellipse

+1 / -0

Let

𝑥^{2} + 𝑦^{2} = 20

be the director circle of an ellipse

𝐸

whose major axis is

𝑋

-axis and minor axis is

𝑌

-axis. If the length of the latusrectum of

𝐸

is 2 . Then, the distance between its foci is

$4 \sqrt{\sqrt 5}$

Incorrect

$4 \sqrt{\sqrt 3}$

Incorrect

$4 \sqrt{\sqrt 2}$

Incorrect

3

Incorrect

Q 57MathematicsSection A • MCQhyperbola

+1 / -0

If $𝜃$ is the acute angle between the tan

from the point $(2, 3)$ to the hyperbola from the point $(2, 3)$ to the hyperbola $5 𝑥^{2} - 6 𝑦^{2} - 30 = 0$ , then $\tan 𝜃 =$

$\frac{𝜋}{4}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{4}{3}$

Incorrect

$\frac{𝜋}{2}$

Incorrect

Q 58MathematicsSection A • MCQhyperbola

+1 / -0

The difference between the focal distances of any point on the hyperbola $\frac{𝑥^{2}}{𝑎^{2}} - \frac{𝑦^{2}}{𝑏^{2}} = 1$ is 6. If $(\sqrt{\sqrt 13}, 𝑘)$ is an end point of a latusrectum of this hyperbola, then $𝑘 =$

$\pm \frac{9}{2}$

Incorrect

$\pm \frac{8}{3}$

Incorrect

$\pm 9$

Incorrect

$\pm \frac{4}{3}$

Incorrect

Q 59MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If $𝑓 (𝑥) = {\begin{matrix} 1 + 6 𝑥 - 3 𝑥^{2}, & 𝑥 \leq 1 \\ 𝑥 + \log_{2} (𝑏^{2} + 7), & 𝑥 > 1 \end{matrix}$ is continuous at all real $𝑥$ , then $𝑏 =$

$\pm 1$

Incorrect

0

Incorrect

$\pm 5$

Incorrect

$\pm 2$

Incorrect

Q 60MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

Let $𝑓 (𝑥)$ be a real valued function. If $𝑓^{'} (𝑥)$ is a constant for all $𝑥 \in 𝑅, 𝑓 (0) = 2$ and $𝑓^{'} (0) = 1$ , then

$𝑓 (x)$ is not continuous on $𝑅$

Incorrect

$𝑓 (𝑥)$ is continuous at $𝑥 = 0, 1, 2$ and 3 only

Incorrect

$𝑓 (𝑥)$ is continuous only on $[0, \infty)$

Incorrect

$𝑓 (𝑥)$ is continuous on $𝑅$

Incorrect

Q 61MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If $𝑓 : 𝑅 \to 𝑅$ defined by

$𝑓 (𝑥) = ⎧⎩⎨ \begin{matrix} \frac{\sin 𝑥 - \sin \frac{𝑋}{2}}{𝑥}, & 𝑥 < 0 \\ \frac{\sqrt{\sqrt 𝑥^{2} + 𝑥} - \sqrt{\sqrt 𝑥}}{𝑥^{3 / 2}}, & 𝑥 > 0 \end{matrix}$

is continuous on $𝑅$ , then $𝑓 (0) =$

$1 / 2$

Incorrect

$3 / 2$

Incorrect

1

Incorrect

-1

Incorrect

Q 62MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝑓 (𝑥)$ is a differentiable function, $𝑓^{'} (𝑥) \geq 5 \forall 𝑥 \in [2, 6]$ , $𝑓 (2) = 4$ and $𝑓 (3) = 15$ , then a possible value of $𝑓 (6)$

$= 24$

Incorrect

lies between 4 and 15

Incorrect

$\leq 15$

Incorrect

$= 5$

Incorrect

Q 63MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝑓 (𝑥) = \sqrt{\sqrt 𝑥 + \sin 𝑥}$ , then all the points of the set ${(𝑥, 𝑓 (𝑥)) / 𝑓^{'} (𝑥) = 0}$ lie on

a circle

Incorrect

a straight line

Incorrect

an ellipse

Incorrect

a parabola

Incorrect

Q 64MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑦 = \frac{\log 𝑥}{𝑥}$ , then the value of $𝑥^{2} \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}} + 3 𝑥 \frac{𝑑 𝑦}{𝑑 𝑥} + 𝑦$ at the point $(\sqrt[3]{\sqrt}, \sqrt{\sqrt 𝑒})$ is

0

Incorrect

1

Incorrect

$𝑒$

Incorrect

2 e

Incorrect

Q 65MathematicsSection A • MCQapplication of derivatives

+1 / -0

Let $𝑓 (𝑥)$ be a differentiable function, $𝐴 (0, 𝛼)$ and $𝐵 (8, 𝛽)$ be two points on the curve $𝑦 = 𝑓 (𝑥)$ . Given $𝑓 (0) = 2$ and $𝑓^{'} (4) = \frac{- 3}{4}$ . If the chord $𝐴 𝐵$ of the curve is parallel to the tangent drawn at the point $(4, 𝑓 (4))$ , then $𝛽 =$

-4

Incorrect

-6

Incorrect

2

Incorrect

8

Incorrect

Q 66MathematicsSection A • MCQapplication of derivatives

+1 / -0

If the tangent drawn to the curve $𝑦 = 𝑥^{3} - 𝑎 𝑥^{2} + 𝑥 + 1$ at each point $𝑥 \in 𝑅$ , is inclined at an acute angle with the positive direction of $𝑋$ -axis, then the set of all possible values of ' $𝑎$ ' is

$𝑅 - (- \sqrt{\sqrt 3}, \sqrt{\sqrt 3})$

Incorrect

$[- 3, 3]$

Incorrect

$𝑅$

Incorrect

$(- \sqrt{\sqrt 3}, \sqrt{\sqrt 3})$

Incorrect

Q 67MathematicsSection A • MCQapplication of derivatives

+1 / -0

The number of points on the curve $𝑦 = 2 𝑡^{2} + 3 𝑡 - 5$ and $𝑥 = 𝑡^{3} - 4 𝑡^{2} - 3 𝑡$ such that the normals drawn at them on the curve are parallel to $𝑋$ -axis is

1

Incorrect

4

Incorrect

3

Incorrect

2

Incorrect

Q 68MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝐴 = {9 𝑥 \geq 𝑥^{2} + 20}$ and $𝑓 : 𝐴 \to 𝑅$ is defined by $𝑓 (𝑥) = 2 𝑥^{3} - 15 𝑥^{2} + 36 𝑥 - 48$ , then the maximum value of $𝑓 (𝑥)$ is

-20

Incorrect

7

Incorrect

20

Incorrect

-16

Incorrect

Q 69MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int \frac{4 𝑒^{𝑥} + 6 𝑒^{- 𝑥}}{9 𝑒^{𝑥} - 4 𝑒^{- 𝑥}} 𝑑 𝑥 = 𝐴 𝑥 + 𝐵 \log ∣ (9 𝑒^{2 𝑥} - 4) ∣ + 𝐶$ , then $(𝐴, 𝐵) =$

$(\frac{3}{2}, \frac{35}{36})$

Incorrect

$(\frac{- 3}{2}, \frac{- 35}{36})$

Incorrect

$(\frac{- 3}{2}, \frac{35}{36})$

Incorrect

$(\frac{3}{2}, \frac{- 35}{36})$

Incorrect

Q 70MathematicsSection A • MCQindefinite integration

+1 / -0

If $𝑓 (𝑥) = \int \frac{𝑑 𝑥}{(𝑥^{2} + 2)}$ and $𝑓 (\sqrt{\sqrt 2}) = 0$ , then $𝑓 (0) =$

$\frac{𝜋}{2 \sqrt{\sqrt 2}}$

Incorrect

$\frac{- 𝜋}{2 \sqrt{\sqrt 2}}$

Incorrect

$\frac{- 𝜋}{4 \sqrt{\sqrt 2}}$

Incorrect

$\frac{𝜋}{4 \sqrt{\sqrt 2}}$

Incorrect

Q 71MathematicsSection A • MCQindefinite integration

+1 / -0

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

$𝑒^{𝑥} \sec 𝑥 + 𝐶$

Incorrect

$𝑒^{𝑥} \tan 𝑥 + 𝐶$

Incorrect

$𝑒^{𝑥} \cot 𝑥 + 𝐶$

Incorrect

$𝑒^{𝑥} cosec 𝑥 + 𝐶$

Incorrect

Q 72MathematicsSection A • MCQdefinite integration

+1 / -0

If $𝐼 = \int_{𝑎}^{- 𝑎} (𝑥^{4} - 2 𝑥^{2}) 𝑑 𝑥$ , then $𝐼$ is minimum at $𝑎 =$

2

Incorrect

$- \sqrt{\sqrt 2}$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

-2

Incorrect

Q 73MathematicsSection A • MCQdefinite integration

+1 / -0

Assertion (A) $\int_{\frac{𝜋}{3}}^{\frac{𝜋}{6}} \frac{(\sin 𝑥)^{\sqrt{\sqrt 2}} 𝑑 𝑥}{(\sin 𝑥)^{\sqrt{\sqrt 2}} + (\cos 𝑥)^{\sqrt{\sqrt 2}}} = \frac{𝜋}{12}$

Reason (R) $\int_{\frac{𝜋}{3}}^{\frac{𝜋}{6}} \frac{𝑓 (𝑥) 𝑑 𝑥}{𝑓 (𝑥) + 𝑓 (\frac{𝜋}{2} - 𝑥)} = \frac{𝜋}{12}$

$𝐴$ is true, $𝑅$ is true and $𝑅$ is the correct explanation of $𝐴$

Incorrect

$𝐴$ is true, $𝑅$ is true but $𝑅$ is not the correct explanation of $𝐴$

Incorrect

$𝐴$ is true, $𝑅$ is false

Incorrect

$𝐴$ is false, $𝑅$ is true

Incorrect

Q 74MathematicsSection A • MCQdefinite integration

+1 / -0

If $[𝑥]$ is the greatest integer not exceeding $𝑥$ , then $\int_{1.5}^{- 0.5} 𝑥^{2} [𝑥] 𝑑 𝑥 =$

$\frac{4.5}{4}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{3.5}{4}$

Incorrect

$\frac{2.375}{2}$

Incorrect

Q 75MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{50 𝜋}^{0} \sqrt{\sqrt 1 - \cos 2 𝑥} 𝑑 𝑥 =$

$- 100 \sqrt{\sqrt 2}$

Incorrect

$100 \sqrt{\sqrt 2}$

Incorrect

$50 \sqrt{\sqrt 2}$

Incorrect

$- 50 \sqrt{\sqrt 2}$

Incorrect

Q 76MathematicsSection A • MCQdefinite integration

+1 / -0

If $𝑓 (𝑥) = \frac{𝑥^{3} + 5}{\sqrt{\sqrt 12 + 𝑥}}$ and $\int_{5}^{- 5} 𝑓 (𝑥) 𝑑 𝑥 = \int_{5}^{0} (𝑓 (𝑥) + 𝑔 (𝑥)) 𝑑 𝑥$ , then $𝑔 (𝑥) =$

$\frac{5 - 𝑥^{3}}{\sqrt{\sqrt 12 - 𝑥}}$

Incorrect

$- (\frac{5 + 𝑥^{3}}{\sqrt{\sqrt 12 + 𝑥}})$

Incorrect

$\frac{- 𝑥^{3} + 5}{\sqrt{\sqrt 12 + 𝑥}}$

Incorrect

$\frac{5 + 𝑥^{3}}{\sqrt{\sqrt 12 - 𝑥}}$

Incorrect

Q 77MathematicsSection A • MCQarea under the curves

+1 / -0

The area (in sq units) bounded by the curves $𝑥^{2} = 9 𝑦$ , $(𝑥 - 6)^{2} = 9 𝑦$ and the $𝑋$ -axis is

0

Incorrect

1

Incorrect

2

Incorrect

4

Incorrect

Q 78MathematicsSection A • MCQdifferential equations

+1 / -0

The substitution $𝑥 = 𝑣 𝑦$ converts which one of the following differential equation to an equation solvable by variable separable method?

$(𝑦^{2} - 2 𝑥^{2} 𝑦) 𝑑 𝑥 = (𝑥^{2} - 2 𝑥 𝑦^{2}) 𝑑 𝑦$

Incorrect

$𝑥^{2} 𝑑 𝑦 - 𝑦 𝑑 𝑥 = \sqrt{\sqrt 𝑥^{2} + 𝑦^{2}} 𝑑 𝑥$

Incorrect

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

Incorrect

$(1 + 2 𝑒^{\frac{𝑥}{𝑦}}) + 2 𝑒^{\frac{𝑥}{𝑦}} (1 - \frac{𝑥}{𝑦}) \frac{𝑑 𝑦}{𝑑 𝑥} = 0$

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

If $\frac{𝑑 𝑦}{𝑑 𝑥} = 𝑓 (𝑥, 𝑦)$ is a homogeneous differential equation, then the general form of $𝑓 (𝑥, 𝑦)$ is

$𝑥^{𝑛} 𝜙 (\frac{𝑦}{𝑥}), 𝑛 \neq 1$

Incorrect

$𝑦^{𝑛} 𝜙 (\frac{𝑥}{𝑦}), 𝑛 \neq 1$

Incorrect

$𝜙 (\frac{𝑦}{𝑥})$

Incorrect

$𝐾^{𝑛} 𝑓 (𝑥, 𝑦), 𝑛 \neq 1$

Incorrect

Q 80MathematicsSection A • MCQdifferential equations

+1 / -0

The order and degree of the differential equation ${(\frac{𝑑^{3} 𝑦}{𝑑 𝑥^{3}})}^{\frac{1}{2}} - 2 {(\frac{𝑑 𝑦}{𝑑 𝑥})}^{\frac{1}{4}} + 𝑥 𝑦 = 0$ are respectively

3 and 12

Incorrect

3 and 2

Incorrect

3 and 4

Incorrect

3 and 6

Incorrect

Q 81PhysicsSection A • MCQunits and measurements

+1 / -0

Among the following the least unit for length is

parsec

Incorrect

nanometer

Incorrect

fermi

Incorrect

angstrom

Incorrect

Q 82PhysicsSection A • MCQmotion in a straight line

+1 / -0

The time of flight of a vertically projected stone is 8 s . the position of the stone after 6 s from the ground is (Acceleration due to gravity $= 10 {ms}^{- 2}$ )

20 m

Incorrect

60 m

Incorrect

75 m

Incorrect

40 m

Incorrect

Q 83PhysicsSection A • MCQmotion in a plane

+1 / -0

A stone thrown with velocity $𝑢$ at angles $𝜃$ and $(90^{\circ}$ $- 𝜃$ ) with the horizontal reaches to maximum heights $𝐻_{1}$ and $𝐻_{2}$ respectively. Its horizontal range is

$4 \sqrt{\sqrt 𝐻_{1} 𝐻_{2}}$

Incorrect

$2 H_{1} H_{2}$

Incorrect

$2 \sqrt{\sqrt H_{1} H_{2}}$

Incorrect

$4 \sqrt{\sqrt \frac{𝐻_{1}}{𝐻_{2}}}$

Incorrect

Q 84PhysicsSection A • MCQvector algebra

+1 / -0

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is

$60^{\circ}$

Incorrect

30°

Incorrect

90°

Incorrect

120°

Incorrect

Q 85PhysicsSection A • MCQlaws of motion

+1 / -0

A car of mass 1500 kg is moving with $20 {ms}^{- 1}$ velocity. If the breaks are applied, it comes to rest in 5 s, then the retarding force is

9000 N

Incorrect

6000 N

Incorrect

12000 N

Incorrect

3000 N

Incorrect

Q 86PhysicsSection A • MCQlaws of motion

+1 / -0

A body is made to move up along an inclined plane of inclination $30^{\circ}$ and the coefficient of friction is 0.5 , then its retardation is

( $𝑔$ is acceleration due to gravity)

$(\frac{2 + \sqrt{\sqrt 3}}{4}) 𝑔$

Incorrect

$(\frac{2 - \sqrt{\sqrt 3}}{4}) 𝑔$

Incorrect

$(\frac{2 - \sqrt{\sqrt 3}}{2}) 𝑔$

Incorrect

$(\frac{2 + \sqrt{\sqrt 3}}{2}) 𝑔$

Incorrect

Q 87PhysicsSection A • MCQwork power and energy

+1 / -0

A machine gun fires 300 bullets per minute each with a velocity of $500 {ms}^{- 1}$ . If the mass of each bullet is 4 g . The power of the machine gun is

3.6 kW

Incorrect

3 kW

Incorrect

5.4 kW

Incorrect

2.5 kW

Incorrect

Q 88PhysicsSection A • MCQcenter of mass

+1 / -0

A body falls freely from a height of 100 m on to the ground and rebounds to a maximum height of 36 m after collision. The coefficient of restitution between ground and the body is

0.4

Incorrect

0.36

Incorrect

0.6

Incorrect

0.5

Incorrect

Q 89PhysicsSection A • MCQrotational motion

+1 / -0

A force of $(2 \hat{𝐢} + 3 \hat{𝐣} + 4 \hat{𝐤}) N$ acts on a particle whose position vector with respect to the origin of the coordinate system is $(6 \hat{𝐢} + 𝑏 \hat{𝐣} + 12 \hat{𝐤}) m$ . If the angular momentum of the body is constant, the value of $𝑏$ is

6

Incorrect

9

Incorrect

12

Incorrect

3

Incorrect

Q 90PhysicsSection A • MCQunits and measurements

+1 / -0

The range of a projectile of weight $𝑤$ is $𝑅$ . The average torque on the projectile between the initial and final positions $𝑃$ and $𝑄$ about the point of projection is

qImage--units-and-measurement-and-dimensions-mechanics-Jeemate

$\frac{𝑤 𝑅}{2}$

Incorrect

$\frac{𝑤 𝑅}{3}$

Incorrect

$\frac{𝑤 𝑅}{4}$

Incorrect

$𝑤 𝑅$

Incorrect

Q 91PhysicsSection A • MCQelasticity

+1 / -0

Two springs $𝐴$ and $𝐵$ fixed at the top and are stretched by 8 cm and 16 cm respectively, when loads of 20 N and 10 N suspended at the lower ends. The ratio of the spring constant of the springs $𝐴$ and $𝐵$ is

$1 : 1$

Incorrect

$2 : 1$

Incorrect

$3 : 1$

Incorrect

$4 : 1$

Incorrect

Q 92PhysicsSection A • MCQsimple harmonic motion

+1 / -0

The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are $𝐴_{1}$ and $𝐴_{2}$ respectively. If the initial amplitude of the oscillator is $𝐴_{0}$ , then

$𝐴_{1} = \sqrt{\sqrt 𝐴_{0} 𝐴_{2}}$

Incorrect

$𝐴_{2} = \sqrt{\sqrt 𝐴_{0} 𝐴_{1}}$

Incorrect

$𝐴_{0} = \sqrt{\sqrt 𝐴_{1} 𝐴_{2}}$

Incorrect

$𝐴_{1} = \frac{𝐴_{0} + 𝐴_{2}}{2}$

Incorrect

Q 93PhysicsSection A • MCQgravitation

+1 / -0

The value of acceleration due to gravity at a height of $4 𝑅_{𝐸}$ from surface of earth is

( $𝑅_{𝐸}$ is radius of earth and acceleration due to gravity on the surface of the earth $= 10 {ms}^{- 2}$ )

$0.2 {ms}^{- 2}$

Incorrect

$0.3 {ms}^{- 2}$

Incorrect

$0.4 {ms}^{- 2}$

Incorrect

$3 {ms}^{- 2}$

Incorrect

Q 94PhysicsSection A • MCQelasticity

+1 / -0

The maximum possible height of a mountain on earth is approximately

(elastic limit of mountain rock $= 30 \times 10^{7} {Nm}^{- 2}$ , average density of mountain rock $= 3 \times 10^{3} {kgm}^{- 3}$ , $𝑔 = 10 {ms}^{- 2}$ )

9 km

Incorrect

10 km

Incorrect

12 km

Incorrect

8.8 km

Incorrect

Q 95PhysicsSection A • MCQfluid mechanics

+1 / -0

A person of height 1.65 m is standing upright. The additional external force required by blood vessel of length 1 cm , diameter 1 mm at feet to balance the pressure compared to similar blood vessel in head is (Density of blood $= 1.1 \times 10^{3} kg m^{- 3}, 𝑔 = 10 {ms}^{- 2}$ )

0.57 N

Incorrect

5.7 N

Incorrect

1.85 N

Incorrect

3.14 N

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

The specific heat capacity of a copper block of mass $𝑀$ is $𝑠$ . If the mass of the copper block is doubled, the specific heat capacity will be

$2 𝑠$

Incorrect

$\frac{𝑠}{2}$

Incorrect

$𝑠$

Incorrect

$\sqrt{\sqrt \frac{3}{2}} 𝑠$

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

2 moles of a monatomic gas requires heat energy $𝑄$ to be heated from $30^{\circ} C$ to $40^{\circ} C$ at constant volume. The heat energy required to raise the temperature of 4 moles of a diatomic gas from $28^{\circ} C$ to $33^{\circ} C$ at constant volume is

$2 𝑄$

Incorrect

$\frac{7 𝑄}{2}$

Incorrect

$\frac{4 𝑄}{3}$

Incorrect

$\frac{5 𝑄}{3}$

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A block of steel of mass 2 kg slides down a rough inclined plane of inclination of $\sin^{- 1} (\frac{3}{5})$ at a constant speed. The temperature of the block as it slides through 80 cm , assuming that the mechanical energy lost is used to increase the temperature of the block is nearly (Specific heat capacity of steel $= 420 {Jkg}^{- 1} K^{- 1}$ and Acceleration due to gravity $= 10 {ms}^{- 2}$ )

${0.0190}^{\circ} C$

Incorrect

${0.0114}^{\circ} C$

Incorrect

${0.0152}^{\circ} C$

Incorrect

${0.0952}^{\circ} C$

Incorrect

Q 99PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Isothermal bulk modulus of a gas at a pressure $𝑝$ is ( $𝛾$ -ratio of specific heat capacities of the gas)

$𝛾$

Incorrect

$𝛾 𝑝$

Incorrect

$𝑝$

Incorrect

$\frac{𝛾}{𝑝}$

Incorrect

Q 100PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A vessel of volume 10 litres is filled with $H_{2}$ gas. The total average translational kinetic energy of its molecules is $4.5 \times 10^{5} J$ . The pressure of hydrogen in the vessel is

$3 \times 10^{6} {Nm}^{- 2}$

Incorrect

$30 \times 10^{6} {Nm}^{- 2}$

Incorrect

$30 \times 10^{4} {Nm}^{- 2}$

Incorrect

$3 \times 10^{4} {Nm}^{- 2}$

Incorrect

Q 101PhysicsSection A • MCQwaves

+1 / -0

Small amplitude progressive wave in a stretched string has a speed of $100 {cms}^{- 1}$ and frequency 100 Hz . The phase difference between two points 2.75 cm apart on the string in radians, is

0

Incorrect

$11 \frac{𝜋}{2}$

Incorrect

$\frac{𝜋}{4}$

Incorrect

$\frac{3 𝜋}{8}$

Incorrect

Q 102PhysicsSection A • MCQwave optics

+1 / -0

$Blue colour of the sky is due to$

reflection of light

Incorrect

refraction of light

Incorrect

diffraction of light

Incorrect

scattering of light

Incorrect

Q 103PhysicsSection A • MCQwave optics

+1 / -0

The property of light which cannot be explained by Huygen's construction of wavefront is

Refraction

Incorrect

Reflection

Incorrect

Diffraction

Incorrect

Origin of spectra

Incorrect

Q 104PhysicsSection A • MCQelectrostatics

+1 / -0

The electric field ( E in ${NC}^{- 1}$ ) in a region is given by $E = 3 \hat{i} + 5 \hat{j}$ . The net electric flux through a square area of side 2 m parallel to $𝑦 𝑧$ -plane is

$3 {NC}^{- 1} m^{2}$

Incorrect

$6 {NC}^{- 1} m^{2}$

Incorrect

$12 {NC}^{- 1} m^{2}$

Incorrect

$24 {NC}^{- 1} m^{2}$

Incorrect

Q 105PhysicsSection A • MCQelectrostatics

+1 / -0

Two thin conducting concentric shells of radii $𝑅$ and $2 𝑅$ are shown in the figure. The outer shell carries a charge $+ 𝑄$ and the inner shell is neutral. Then the correct statement/s is

(a) When the switch is closed, the potential on the inner shell becomes zero

(b) With the switch closed, the charge on the inner sphere is $- \frac{𝑄}{2}$

qImage--electrostatics-electromagnetism-Jeemate

(a) and (b) are correct

Incorrect

(a) is correct,(b) is wrong

Incorrect

(a) is wrong,(b) is correct

Incorrect

(a) and (b) are wrong

Incorrect

Q 106PhysicsSection A • MCQcapacitor

+1 / -0

Two square shaped metal plates of side 1 m , kept 0.01 m apart in air from a parallel plate capacitor. It is connected to a battery of 500 V . The plates of the capacitor are then immersed in an insulating oil by lowering the plates vertically with a speed of $0.001 {ms}^{- 1}$ . If the dielectric constant of the oil is 11 , the current drawn from the battery during this process is

$4.425 \times 10^{- 6} A$

Incorrect

$4.425 \times 10^{- 5} A$

Incorrect

$4.425 \times 10^{- 9} A$

Incorrect

$4.425 \times 10^{- 2} A$

Incorrect

Q 107PhysicsSection A • MCQcurrent electricity

+1 / -0

When a resistance $𝑅_{1}$ is connected across a cell, the current is $𝐼_{1}$ and if the resistance $𝑅_{1}$ is replaced by $𝑅_{2}$ , the current is $𝐼_{2}$ . Then the internal resistance of the cell is

$\frac{𝐼_{1} 𝑅_{1} + 𝐼_{2} 𝑅_{2}}{𝐼_{1} + 𝐼_{2}}$

Incorrect

$\frac{𝐼_{1} 𝑅_{2} + 𝐼_{2} 𝑅_{1}}{𝐼_{1} + 𝐼_{2}}$

Incorrect

$\frac{𝐼_{1} 𝑅_{2} - 𝐼_{2} 𝑅_{1}}{𝐼_{1} - 𝐼_{2}}$

Incorrect

$\frac{𝐼_{2} 𝑅_{2} - 𝐼_{1} 𝑅_{1}}{𝐼_{1} - 𝐼_{2}}$

Incorrect

Q 108PhysicsSection A • MCQcurrent electricity

+1 / -0

Charge passing through a conductor of cross-section $0.3 m^{2}$ is given by $𝑞 = (3 𝑡^{2} + 5 𝑡 + 2) C$ where $𝑡$ is in seconds. The drift velocity at $𝑡 = 2 s$ is (Concentration of electrons in the conductor $= 2 \times 10^{25} m^{- 3}$ )

$0.77 \times 10^{- 5} {ms}^{- 1}$

Incorrect

$0.93 \times 10^{- 5} {ms}^{- 1}$

Incorrect

$1.77 \times 10^{- 5} {ms}^{- 1}$

Incorrect

$2.08 \times 10^{- 5} {ms}^{- 1}$

Incorrect

Q 109PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A magnetic field intensity at the centre of a circular wire of radius 0.1 m carrying a current 0.2 A is

$2 𝜋 \times 10^{- 5} T$

Incorrect

$𝜋 \times 10^{- 7} T$

Incorrect

$10^{- 7} T$

Incorrect

$4 𝜋 \times 10^{- 7} T$

Incorrect

Q 110PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A wire is first bent in the form of a circular coil of 5 turns and the same wire is then bent in the form of another circular coil of 10 turns. If same current is passed in both the coils, then the ratio of the magnetic fields at their centres is

$1 : 8$

Incorrect

$1 : 1$

Incorrect

$1 : 2$

Incorrect

$1 : 4$

Incorrect

Q 111PhysicsSection A • MCQmagnetism and matter

+1 / -0

A solenoid has a core of a material with relative permeability 400 . The windings of the solenoid are insulated from the core and carry of 4 A . If the number of turns is 500 per metre, then the magnetising field is

$2 𝜋 \times 10^{3} {Am}^{- 1}$

Incorrect

$1 \times 10^{3} {Am}^{- 1}$

Incorrect

$4 \times 10^{3} {Am}^{- 1}$

Incorrect

$2 \times 10^{3} {Am}^{- 1}$

Incorrect

Q 112PhysicsSection A • MCQelectromagnetic induction

+1 / -0

In an AC generator, if coils of $𝑁$ turns and area $𝐴$ is rotated at $𝑣$ revolutions per second in a uniform magnetic field $𝐵$ , then the motional emf produced is equal to (At $𝑡 = 0 s$ , the coil is perpendicular to the field)

$𝑁 𝐵 𝐴 (2 𝜋 𝑣) \sin (2 𝜋 𝑣 𝑡)$

Incorrect

$𝑁 𝐵 𝐴^{2} (2 𝜋 𝑣) \sin (2 𝜋 𝑣 𝑡)$

Incorrect

$𝑁^{2} 𝐵^{2} 𝐴^{2} (2 𝜋 𝑣) \sin (2 𝜋 𝑣 𝑡)$

Incorrect

$𝑁 𝐵 𝐴 (4 𝜋 𝑣) \sin (2 𝜋 𝑣 𝑡)$

Incorrect

Q 113PhysicsSection A • MCQalternating current

+1 / -0

The frequency of AC at which $16 𝜇 F$ capacitor and $\frac{10}{𝜋^{2}} mH$ inductor will have same reactance is

1 kHz

Incorrect

1.25 kHz

Incorrect

1.5 kHz

Incorrect

2 kHz

Incorrect

Q 114PhysicsSection A • MCQelectromagnetic waves

+1 / -0

The average power output of a point source of an electromagnetic radiation is 1080 W . The maximum value of the rms value of the electric field at a distance of 3 m from the source is

$20 {Vm}^{- 1}$

Incorrect

$40 {Vm}^{- 1}$

Incorrect

$60 {Vm}^{- 1}$

Incorrect

$90 {Vm}^{- 1}$

Incorrect

Q 115PhysicsSection A • MCQdual nature of radiation

+1 / -0

The velocity of a particle $𝐴$ is 3 times the velocity of proton. If the ratio of the de- Broglie wavelengths of the particle $𝐴$ and the proton is $3 : 2$ , the mass of the particle $𝐴$ is

( $𝑚_{𝑝} =$ mass of proton)

$\frac{2}{9} 𝑚_{𝑝}$

Incorrect

$\frac{2}{3} 𝑚_{𝑝}$

Incorrect

$\frac{2}{5} 𝑚_{𝑝}$

Incorrect

$\frac{2}{7} 𝑚_{𝑝}$

Incorrect

Q 116PhysicsSection A • MCQatoms and nuclei

+1 / -0

The transition of an electron in hydrogen atom that emits a photon whose wavelength lies in the ultraviolet region of the electromgnetic spectrum is

$5 \to 4$

Incorrect

$4 \to 3$

Incorrect

$3 \to 2$

Incorrect

$2 \to 1$

Incorrect

Q 117PhysicsSection A • MCQatoms and nuclei

+1 / -0

The relation between the mean-life time $𝜏$ and the half-life time $𝑇_{1 / 2}$ of a radioactive substance is

$𝑇_{1 / 2} = 𝜏 \log_{𝑒} 2$

Incorrect

$𝑇_{1 / 2} = 𝜏 \log_{10} 2$

Incorrect

$𝑇_{1 / 2} = 𝜏$

Incorrect

$𝑇_{1 / 2} = 2 𝜏 \log_{𝑒} 2$

Incorrect

Q 118PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

A $𝑝 - 𝑛$ junction diode is reverse biased with a voltage of 8 V . If the resistance of the diode is $4 \times 10^{7} Ω$ , then the reverse saturation current is

$32 𝜇 A$

Incorrect

$2 𝜇 A$

Incorrect

$0.2 𝜇 A$

Incorrect

$0.5 𝜇 A$

Incorrect

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

$In a 𝑝 - 𝑛 - 𝑝 transistor$

emitter is heavily doped and collector is moderately doped.

Incorrect

emitter is moderately doped and collector is heavily doped.

Incorrect

both emitter and collector are heavily doped.

Incorrect

both emitter and collector are moderately doped.

Incorrect

Q 120PhysicsSection A • MCQcommunication systems

+1 / -0

A carrier wave of peak voltage 15 V is used to transmit a message signal. If the modulation index is $60 %$ , then the peak of voltage of the modulating signal is

3 V

Incorrect

6 V

Incorrect

9 V

Incorrect

12 V

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

Vijaywada FM radio station broadcasts at frequency of 103.4 MHz . The wavelength of the corresponding radio wave (in m ) is

2.90

Incorrect

29.0

Incorrect

9.20

Incorrect

92.0

Incorrect

Q 122ChemistrySection A • MCQatomic structure

+1 / -0

The minimum number of quantum numbers required to specify an orbital in an atom is

1

Incorrect

4

Incorrect

2

Incorrect

3

Incorrect

Q 123ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Consider the following two statements.

Statement I Among $Mg, Al, {Mg}^{2 +}, {Al}^{3 +}$ the one having smallest size is ${Al}^{3 +}$ .

Statement II Eu is having exceptionally high atomic radii among lanthanide elements.

The correct answer is

both statement I and II are correct.

Incorrect

both statements I and II are not correct.

Incorrect

statement I is correct but statement II is not correct.

Incorrect

statement I is not correct but statement II is correct.

Incorrect

Q 124ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Identify the pair of elements with the highest and lowest electronegativity respectively

K and Rb

Incorrect

I and F

Incorrect

F and Fr

Incorrect

Fr and Li

Incorrect

Q 125ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

If the bond order in $𝐶_{2}$ is ' $𝑥^{'}$ then the bond order in $𝐵_{2}$ and $O_{2}$ , respectively are

$\frac{1}{2} 𝑥, 2 𝑥$

Incorrect

$𝑥, 𝑥$

Incorrect

$\frac{1}{2} 𝑥, 𝑥$

Incorrect

$𝑥, 2 𝑥$

Incorrect

Q 126ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

Identify incorrectly matched set from the following.

Molecules with incomplete octet- ${BeH}_{2}, {BCl}_{3}$ .

Incorrect

Polar molecules- ${BF}_{3}, {CCl}_{4}$ .

Incorrect

Molecules with expanded octet- ${PCl}_{5}, {SF}_{6}$ .

Incorrect

Odd electron molecules- $NO, {NO}_{2}$ .

Incorrect

Q 127ChemistrySection A • MCQstates of matter

+1 / -0

An ideal gas $(𝑋)$ present in a vessel of volume $𝑉 L$ exerted a pressure of 16.4 atm at 200 K . What is its concentration in $mol L^{- 1}$ ?

(Given, $𝑅 = 0.082 L atm {mol}^{- 1} K^{- 1}$ )

0.50

Incorrect

0.25

Incorrect

1.00

Incorrect

1.50

Incorrect

Q 128ChemistrySection A • MCQstates of matter

+1 / -0

A 100 L cylinder containing $H_{2}$ exerted a pressure of 4 atm at 300 K . It was accidentally opened and some $H_{2}$ was escaped. When it was closed, it exerted a pressure of 3 atm at 300 K . The number of moles of $H_{2}$ remaining in the cylinder is equal to

(Assume, $H_{2}$ as an ideal gas; $𝑅 =$ gas constant)

$\frac{1}{2 𝑅}$

Incorrect

$𝑅$

Incorrect

$\frac{1}{𝑅}$

Incorrect

$2 𝑅$

Incorrect

Q 129ChemistrySection A • MCQredox reactions

+1 / -0

Observe the following reaction,

${Cl}_{2} (𝑔) + 2 {OH}^{-} (𝑎 𝑞) ⟶ {ClO}^{-} (𝑎 𝑞) + {Cl}^{-} (𝑎 𝑞) + H_{2} O (𝑙)$

Identify the correct statements about this reaction,

[I.] ${Cl}_{2} (𝑔)$ is oxidised to ${ClO}^{-} (𝑎 𝑞)$ .

[II.] ${Cl}_{2} (𝑔)$ is oxidised to ${Cl}^{-} (𝑎 𝑞)$ .

[III.] ${Cl}_{2} (𝑔)$ is reduced to ${ClO}^{-} (𝑎 𝑞)$ .

[IV.] ${Cl}_{2} (𝑔)$ is reduced to ${Cl}^{-} (𝑎 𝑞)$ .

The correct answer is

I, IV only

Incorrect

I, III only

Incorrect

I, II, IV only

Incorrect

II, III only

Incorrect

Q 130ChemistrySection A • MCQthermodynamics

+1 / -0

If the standard enthalpy change $(Δ_{𝑟} 𝐻^{-})$ for a certain reaction at 298 K and constant pressure $- 1860 kJ {mol}^{- 1}$ , the standard entropy change $(Δ_{sys} Ω^{\circ})$ of the same reaction is $- 550 J K^{- 1} {mol}^{- 1}$ . Which one of the following statements is correct?

$(Δ_{sys} S^{\circ}) + Δ_{surr} S^{\circ} = - 7692 J {mol}^{- 1} K^{- 1}$ , the reaction is spontaneous.

Incorrect

$(Δ_{sys} S^{\circ}) + Δ_{surr} S^{\circ} = - 5692 J {mol}^{- 1} K^{- 1}$ , the reaction is non-spontaneous.

Incorrect

$(Δ_{sys} S^{\circ}) + Δ_{surr} S^{\circ} = + 5692 J {mol}^{- 1} K^{- 1}$ , the reaction is spontaneous.

Incorrect

$(Δ_{sys} S^{\circ}) + Δ_{surr} S^{\circ} = + 7692 J {mol}^{- 1} K^{- 1}$ , the reaction is non-spontaneous.

Incorrect

Q 131ChemistrySection A • MCQthermodynamics

+1 / -0

If the standard enthalpy change $(Δ_{𝑟} 𝐻^{\circ})$ for reaction $H_{2} (g) + {Br}_{2} (𝑙) ⟶ 2 HBr (g)$ is -72.8 kJ , the standard enthalpy of formation $(Δ_{𝑓} 𝐻^{\circ})$ of $HBr (𝑔)$ (in $kJ {mol}^{- 1}$ ) is

-36.4

Incorrect

+36.4

Incorrect

-18.2

Incorrect

+18.2

Incorrect

Q 132ChemistrySection A • MCQchemical equilibrium

+1 / -0

At $𝑇 (K)$ , the equilibrium constant for $𝐴 (𝑔) ⇌ 𝐵 (𝑔)$ is $10^{- 2}$ . If rate of forward reaction is $0.025 mol L^{- 1} s^{- 1}$ . The rate of backward reaction (in $mol L^{- 1} s^{- 1}$ ) is

$4 \times 10^{1}$

Incorrect

$2.5 \times 10^{- 4}$

Incorrect

$2.5 \times 10^{- 2}$

Incorrect

$5 \times 10^{- 2}$

Incorrect

Q 133ChemistrySection A • MCQchemical equilibrium

+1 / -0

One mole $H_{2} O (𝑔)$ and one mole $CO (𝑔)$ are taken in 1 L flask and heated to 725 K . At equilibrium, $40 %$ (by mass) of water reacted with $CO (𝑔)$ as follows

$H_{2} O (𝑔) + CO (𝑔) ⇌ H_{2} (𝑔) + {CO}_{2} (𝑔)$

Its $𝐾_{𝑐}$ value is

0.444

Incorrect

2.220

Incorrect

0.222

Incorrect

4.440

Incorrect

Official Correct Answer:Option (A)

Step-by-Step Solution:

$\begin{matrix} 𝑉 & = 1 L \\ 𝑇 & = 725 K \end{matrix}$

The equilibrium reaction is

$H_{2} O (𝑔) + CO (𝑔) ⇌ H_{2} (𝑔) + {CO}_{2} (𝑔)$

		CO
Initial moles	1	1	0	0
Change	-0.4	-0.4	0.4	0.4
Moles at equilibrium	0.6	0.6	0.4	0.4

The expression for the equilibrium constant is $𝐾_{𝐶} = \frac{0.4 \times 0.4}{0.6 \times 0.6} = \frac{4}{9} = 0.444$

Q 134ChemistrySection A • MCQhydrogen

+1 / -0

The $O - H$ bond length in $H_{2} O$ in gas phase is

95.7 pm

Incorrect

90.2 pm

Incorrect

104.5 pm

Incorrect

115.5 pm

Incorrect

Q 135ChemistrySection A • MCQs block elements

+1 / -0

Which of the following alloys are correctly matched with their uses?

$Li / Mg$ Armour plates

$Cu / Be$ High strength springs

$Mg / Al$ Aircraft construction

(i), (ii) only

Incorrect

(ii), (iii) only

Incorrect

(i), (iii) only

Incorrect

(i), (ii), (iii)

Incorrect

Q 136ChemistrySection A • MCQp block elements

+1 / -0

$Match the following.$

List I (Group 13 elements)		List II (Metallic radius pm)
A.	Al	I.	135
B.	Ga	II.	143
C.	In	III.	170
D.	Tl	IV.	167

The correct answer is

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Official Correct Answer:Option (B)

Step-by-Step Solution:

The correct match is A-II, B-I, C-IV, D-III.

List I (Group 13 elements)		List II (Metallic radius pm)
A.	Al	II.	143
B.	Ga	I.	135
C.	In	IV.	167
D.	Tl	III.	170

Q 137ChemistrySection A • MCQp block elements

+1 / -0

Choose the acidic oxide from the following.

CO

Incorrect

GeO

Incorrect

SnO

Incorrect

PbO

Incorrect

Q 138ChemistrySection A • MCQhydrocarbons

+1 / -0

In the Kolbe electrolysis of sodium propanoate, the products $𝑋$ and $𝑌$ are formed at respected electrodes. What are $𝑋$ and $𝑌$ ?

$𝑋 = {CH}_{3} - {CH}_{2} - {CH}_{2} - {CH}_{3}$ at cathode; $𝑌 = H_{2}$ at anode

Incorrect

$𝑋 = {CH}_{3} - {CH}_{2} - {CH}_{3}$ at cathode; $𝑌 = H_{2}$ at anode

Incorrect

$𝑋 = {CH}_{3} - {CH}_{2} - {CH}_{2} - {CH}_{3}$ at anode; $𝑌 = H_{2}$ at cathode

Incorrect

$𝑋 = {CH}_{3} - {CH}_{3}$ at anode; $𝑌 = H_{2}$ at cathode

Incorrect

Q 139ChemistrySection A • MCQhydrocarbons

+1 / -0

$Which of the following molecule is not aromatic?$

Incorrect

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

qImage--hydrocarbons-organic-chemistry-Jeemate

Incorrect

Q 140ChemistrySection A • MCQsolid state

+1 / -0

An example for network solid is

${SiO}_{2}$

Incorrect

MgO

Incorrect

${CaF}_{2}$

Incorrect

ZnS

Incorrect

Q 141ChemistrySection A • MCQsome basic concepts of chemistry

+1 / -0

20 mL of 0.1 M HCl is added to the 30 mL of 0.1 M NaOH . To this solution extra 50 mL of water was added. What is the molarity of the final solution formed?

0.1 M

Incorrect

0.01 M

Incorrect

0.5 M

Incorrect

0.05 M

Incorrect

Q 142ChemistrySection A • MCQsolutions

+1 / -0

The molarity of one molal glucose solution having density of $1.2 g / mL$ is

0.101 M

Incorrect

1.01 M

Incorrect

2.01 M

Incorrect

0.001 M

Incorrect

Q 143ChemistrySection A • MCQelectrochemistry

+1 / -0

The conductivity of a solution containing 2.08 g of anhydrous barium chloride in 200 mL solution is $6 \times 10^{- 3} {ohm}^{- 1} {cm}^{- 1}$ . The molar conductivity of the solution (in ${ohm}^{- 1} {cm}^{2} {mol}^{- 1}$ ) is $\underline{𝑥} \times 10^{2}$ . The value of $\underline{𝑥}$ is (Atomic mass of $Ba = 137, Cl = 35.5$ )

1.2

Incorrect

2.4

Incorrect

3.6

Incorrect

3.0

Incorrect

Q 144ChemistrySection A • MCQchemical kinetics

+1 / -0

For the reaction $𝐴 + 𝐵 \to 𝐶$ , the following data were obtained

Expt.	Initial concentration		Initial rate
Expt.	[A] M	[B] M	$(𝑀 min^{- 1})$
1.	0.1	0.1	$1.0 \times 10^{- 4}$
2.	0.1	0.3	$9.0 \times 10^{- 4}$
3.	0.3	0.3	$2.7 \times 10^{- 4}$

The order of reaction with respect to $𝐴$ and $𝐵$ are respectively

$1, 2$

Incorrect

$2, 1$

Incorrect

$1.5, 1.5$

Incorrect

$0, 3$

Incorrect

Q 145ChemistrySection A • MCQsurface chemistry

+1 / -0

The correct statements about zeolites are

They are good shape selective catalysts.

They contain Al-O-Si framework.

They are not found in nature.

They are used as catalysts for cracking hydrocarbons, in petrochemical industry.

I and II only

Incorrect

II and III only

Incorrect

III and IV only

Incorrect

I, II and IV only

Incorrect

Q 146ChemistrySection A • MCQsurface chemistry

+1 / -0

Which of the following is not the application of adsorption?

Use of ${SiO}_{2}$ gel for removing the moisture.

Incorrect

Use of coconut charcoal to separate inert gases.

Incorrect

Use of ${Al}_{2} O_{3}$ to separate the components of organic mixture in chromatography.

Incorrect

Use of ${CaCl}_{2}$ for removing the moisture.

Incorrect

Q 147ChemistrySection A • MCQmetallurgy

+1 / -0

How many of the following can be purified by using zone refining method?

Ni, B, Ti, In, Ge, Mn, Ag, Si, Ga

4

Incorrect

5

Incorrect

6

Incorrect

7

Incorrect

Q 148ChemistrySection A • MCQp block elements

+1 / -0

For ozone molecule consider the following.

It is a linear molecule with bond angle $180^{\circ}$ .

It is an angular molecule with bond angle $117^{\circ}$ .

The bond lengths of both $O - O$ bonds are same.

With respect to oxygen it is thermodynamically more stable.

The correct options are

(B), (C) only

Incorrect

(A), (B) only

Incorrect

(B), (D) only

Incorrect

(A), (D) only

Incorrect

Q 149ChemistrySection A • MCQd and f block elements

+1 / -0

From the list given below, the number of lanthanides which exhibit +4 state in their oxides is Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy

5

Incorrect

4

Incorrect

6

Incorrect

2

Incorrect

Q 150ChemistrySection A • MCQd and f block elements

+1 / -0

Given below are two statements.

Assertion (A) All Cu (II) halides are known except the iodide.

Reason (R) ${Cu}^{2 +}$ oxidises $I^{-}$ to $I_{2}$ .

Both (A) and (R) are correct and (R) is the correct explanation of (A).

Incorrect

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

Incorrect

(A) is correct but (R) is not correct.

Incorrect

(A) is not correct but (R) is correct.

Incorrect

Q 151ChemistrySection A • MCQpolymers

+1 / -0

$Monomers of nylon 2-nylon 6 are$

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 152ChemistrySection A • MCQbiomolecules

+1 / -0

Given below are two statements

Assertion (A) Hydrolysis of DNA does not form equal number of $𝐴$ and $𝑇, 𝐺$ and $𝐶$ .

Reason (R) In DNA, adenine forms hydrogen bonds with thymine and cytosine forms hydrogen bonds with guanine.

The correct answer is

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

Incorrect

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

Incorrect

$𝐴$ is correct but $𝑅$ is incorrect

Incorrect

$𝐴$ is incorrect but $𝑅$ is correct

Incorrect

Q 153ChemistrySection A • MCQbiomolecules

+1 / -0

$The structure of Gly-Ala is$

qImage--biomolecules-organic-chemistry-Jeemate

Incorrect

qImage--biomolecules-organic-chemistry-Jeemate

Incorrect

qImage--biomolecules-organic-chemistry-Jeemate

Incorrect

qImage--biomolecules-organic-chemistry-Jeemate

Incorrect

Q 154ChemistrySection A • MCQchemistry in everyday life

+1 / -0

$The group present in prontosil is$

$- N = N -$

Incorrect

$- As = As -$

Incorrect

qImage--chemistry-in-everyday-life-organic-chemistry-Jeemate

Incorrect

qImage--chemistry-in-everyday-life-organic-chemistry-Jeemate

Incorrect

Q 155ChemistrySection A • MCQisomerism

+1 / -0

The optically inactive compound from the following is

2-bromopropanal

Incorrect

3-bromopropanal

Incorrect

3-bromo 2-iodopropanal

Incorrect

2-bromo 3-iodopropanal

Incorrect

Q 156ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

$\begin{matrix} Which is the correct option for the following reaction? \\ 2 {CH}_{3} {CH}_{2} Br \overset{2 Na / Dry ether}{\to\leftarrow} ? \end{matrix}$

Wurtz reaction : ${CH}_{3} {CH}_{2} {CH}_{2} {CH}_{3}$

Incorrect

Wurtz-Fittig reaction : ${CH}_{3} {CH}_{2} {CH}_{2} {CH}_{3}$

Incorrect

Wurtz reaction : ${CH}_{3} {CH}_{2} {CH}_{2} {CH}_{2} {CH}_{3}$

Incorrect

Wurtz-Fittig reaction : ${CH}_{3} {CH}_{2} {CH}_{2} {CH}_{2} {CH}_{3}$

Incorrect

Q 157ChemistrySection A • MCQaldehyde and ketone

+1 / -0

The number of products obtained in the following reaction is

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

1

Incorrect

3

Incorrect

2

Incorrect

4

Incorrect

Q 158ChemistrySection A • MCQaldehyde and ketone

+1 / -0

What are ' $𝑋$ ' and ' $𝑌$ ' respectively in the following reaction?

$C_{6} H_{5} CHO + C_{6} H_{5} {COCH}_{3} {\to\leftarrow}_{293 K}^{{OH}^{-}} \underset{Major}{𝑋} \overset{{NaBH}_{4}}{\to\leftarrow} 𝑌$

$C_{6} H_{5} COCH = C ({CH}_{3}) C_{6} H_{5}, C_{6} H_{5} {CH}_{2} {CH}_{2} {COC}_{6} H_{5}$

Incorrect

$C_{6} H_{5} COCH = C ({CH}_{3}) C_{6} H_{5}, C_{6} H_{5} = CHCH (OH) C_{6} H_{5}$

Incorrect

$C_{6} H_{5} CH = {CHCOC}_{6} H_{5}, C_{6} H_{5} CH = CHCH (OH) C_{6} H_{5}$

Incorrect

$C_{6} H_{5} CH = {CHCOC}_{6} H_{5}, C_{6} H_{5} {CH}_{2} {CH}_{2} {COC}_{6} H_{5}$

Incorrect

Q 159ChemistrySection A • MCQcarboxylic acids and its derivatives

+1 / -0

Which of the following is used in perfumery?

Esters of benzoic acid

Incorrect

Ethanoic acid

Incorrect

Methanoic acid

Incorrect

Sodium benzoate

Incorrect

Q 160ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

Arrange the following in increasing order of their boiling points.

[I.] N-ethylethanamine

[II.] Butanamine

[III.] N,N-dimethyl ethanamine

III $>$ II $>$ I

Incorrect

III $>$ I $>$ II

Incorrect

II $>$ III $>$ I

Incorrect

II $>$ I $>$ III

Incorrect

AP EAPCET 2023 15th May Morning Shift Question Paper with Solutions