Tg Eapcet 2023 14th May Evening Shift Question Paper Question Paper with Solutions | TG EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQfunctions

+1 / -0

Let $𝑓 : 𝑅 \to 𝑅$ be a function defined by

$𝑓 (𝑥) = {\begin{matrix} 𝑥^{2} - 4 𝑥 + 3, & if 𝑥 < 2 \\ 𝑥 - 3, & if 𝑥 \geq 2 \end{matrix}$

Then, the number of real numbers $𝑥$ for which $𝑓 (𝑥) = 8$ is

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Official Correct Answer:Option (B)

Step-by-Step Solution:

$Here, 𝑓 (𝑥) = {\begin{matrix} 𝑥^{2} - 4 𝑥 + 3 & , 𝑥 < 2 \\ 𝑥 - 3 & , 𝑥 \geq 2 \end{matrix}$

Case - I	$𝐢 \times 𝐦$
$\begin{matrix} 𝑓 (𝑥) = 8 \\ 𝑥 - 3 = 8 \\ 𝑥 = 11 as 𝑥 \geq 2 \end{matrix}$	$\begin{matrix} 𝑥^{2} - 4 𝑥 + 3 = 8 \\ \Rightarrow & 𝑥^{2} - 4 𝑥 - 5 = 0 \\ \Rightarrow & (𝑥 - 5) (𝑥 + 1) = 0 \\ \Rightarrow & 𝑥 = 5, - 1 \\ 𝑥 = - 1 as 𝑥 < 2 \end{matrix}$

$Number of solutions = 2$

Q 2MathematicsSection A • MCQfunctions

+1 / -0

If $𝑓 (𝑥)$ and $𝑔 (𝑥)$ are two real valued functions such that $𝑓 (𝑥) = 3 𝑥 - 2$ and $𝑔 (𝑥) = 𝑥^{2} + 2$ , then $[(𝑔 \circ 𝑓) + (𝑓 \circ 𝑔)] (𝑥) =$

$2 𝑔 (𝑥) + 2 𝑓 (𝑥)$

Incorrect

$12 𝑔 (𝑥) - 4 𝑓 (𝑥) - 22$

Incorrect

$3 𝑔 (𝑥) + 𝑓 (𝑥) - 2$

Incorrect

$2 𝑓 (𝑥) + 4 𝑔 (𝑥) - 32$

Incorrect

Q 3MathematicsSection A • MCQfunctions

+1 / -0

If $𝑓 (𝑥)$ is a real valued function defined by $𝑓 (𝑥) = \frac{𝑎 𝑥^{10} + 𝑏 𝑥^{8} + 𝑐 𝑥^{6} + 𝑑 𝑥^{4} + 𝑒 𝑥^{2} + 12 𝑥 + 15}{𝑥} (𝑥 \neq 0)$ and $𝑓 (4) = - 4$ , then $𝑓 (- 4) =$

28

Incorrect

39

Incorrect

4

Incorrect

24

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝑋_{4 \times 3}, 𝑌_{4 \times 3}$ and $𝑃_{2 \times 3}$ are the matrices, then the order of the matrix ${[𝑃 {(𝑋^{𝑇} 𝑌)}^{- 1} 𝑃^{𝑇}]}^{𝑇}$ is

$4 \times 3$

Incorrect

$3 \times 4$

Incorrect

$3 \times 3$

Incorrect

$2 \times 2$

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝐴 = [\begin{matrix} 1 & 2 \\ 3 & 5 \end{matrix}]$ and $𝛼, 𝛽 \in 𝑅$ are such that $𝛼 𝐴^{2} - 𝛽 𝐴 = 2 𝐼$ , then $𝛼^{2} + 𝛽 =$

-8

Incorrect

16

Incorrect

12

Incorrect

20

Incorrect

Q 6MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $∣ \begin{matrix} (1 + 𝛼)^{2} & (1 + 2 𝛼)^{2} & (1 + 3 𝛼)^{2} \\ (2 + 𝛼)^{2} & (2 + 2 𝛼)^{2} & (2 + 3 𝛼)^{2} \\ (3 + 𝛼)^{2} & (3 + 2 𝛼)^{2} & (3 + 3 𝛼)^{2} \end{matrix} ∣ = 𝑘$ and $𝛼 = - 2$ , then $𝑘 =$

0

Incorrect

-24

Incorrect

24

Incorrect

66

Incorrect

Q 7MathematicsSection A • MCQmatrices and determinants

+1 / -0

If the system of equations $𝑥 + 𝑦 + 𝑧 = 5, 𝑥 + 2 𝑦 + 2 𝑧 = 6$ and $𝑥 + 3 𝑦 + 𝜆 𝑧 = 𝜇 (𝜆, 𝜇 \in 𝑅)$ is solvable by Matrix Inversion Method, then

$𝜆 \neq 3, 𝜇 \in 𝑅$

Incorrect

$𝜆 = 3, 𝜇 = 0$

Incorrect

$𝜆 \neq 3, 𝜇 \neq 5$

Incorrect

$𝜆 = 3, 𝜇 \in 𝑅$

Incorrect

Q 8MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑥 = 𝑎 + 𝑏, 𝑦 = 𝑎 𝛼 + 𝑏 𝛽, 𝑧 = 𝑎 𝛽 + 𝑏 𝛼$ and $𝛼, 𝛽$ are the complex cube roots of unity, then $𝑥^{3} + 𝑦^{3} + 𝑧^{3} =$

$𝑎^{3} + 𝑏^{3}$

Incorrect

$3 (𝑎^{3} + 𝑏^{3})$

Incorrect

$𝑎^{3} - 𝑏^{3}$

Incorrect

$3 (𝑎^{3} - 𝑏^{3})$

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑧 = \frac{3 + 2 𝑖 \cos 𝜃}{1 - 2 𝑖 \sin 𝜃}$ is a purely imaginary number, then

$\sin^{2} 𝜃 + \cos^{2} 3 𝜃 =$

$3 / 4$

Incorrect

$7 / 4$

Incorrect

1

Incorrect

$5 / 4$

Incorrect

Q 10MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑧 = 𝑥 + 𝑖 𝑦$ is a complex number such that $𝑧 {\bar{𝑧}}^{3} + \bar{𝑧} 𝑧^{3} = 350$ and $𝑥, 𝑦$ are integers, then $| 𝑧 | =$

$\sqrt{\sqrt 41}$

Incorrect

5

Incorrect

25

Incorrect

$\sqrt{\sqrt 13}$

Incorrect

Q 11MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝛼$ and $𝛽$ are the roots of the equation $𝑥^{2} + 𝑥 + 1 = 0$ , then $(𝛼 + 𝛽)^{2} + {(𝛼^{2} + 𝛽^{2})}^{2} + {(𝛼^{3} + 𝛽^{3})}^{2} + \dots + {(𝛼^{12} + 𝛽^{12})}^{2} =$

48

Incorrect

12

Incorrect

24

Incorrect

36

Incorrect

Q 12MathematicsSection A • MCQcomplex numbers

+1 / -0

The least positive integral value of $𝑛$ such that ${[\frac{1 + \sin \frac{2 𝜋}{9} + 𝑖 \cos \frac{2 𝜋}{9}}{1 + \sin \frac{2 𝜋}{9} - 𝑖 \cos \frac{2 𝜋}{9}}]}^{𝑛} = 1$ is

9

Incorrect

18

Incorrect

36

Incorrect

72

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼, 𝛽$ are the roots of $𝑥^{2} + 𝑎 𝑥 + 2 = 0$ and $1 / 𝛼, 1 / 𝛽$ are the roots of $𝑥^{2} - 𝑏 𝑥 + 𝑐 = 0$ , then

$(𝛼 + \frac{1}{𝛽}) (𝛽 + \frac{1}{𝛼}) (𝛼 - \frac{1}{𝛼}) (𝛽 - \frac{1}{𝛽}) =$

$\frac{9}{4} (9 - 𝑎^{2})$

Incorrect

$\frac{9}{4} (9 + 𝑎^{2})$

Incorrect

$\frac{9}{4} (9 - 𝑏^{2})$

Incorrect

$\frac{9}{4} (9 + 𝑏^{2})$

Incorrect

Q 14MathematicsSection A • MCQquadratic equations

+1 / -0

The sum of all the real values of $𝑥$ satisfying the equation ${(𝑥^{2} - 7 𝑥 + 11)}^{𝑥^{2} - 6 𝑥 - 7} = 1$ is

14

Incorrect

20

Incorrect

13

Incorrect

16

Incorrect

Q 15MathematicsSection A • MCQcomplex numbers

+1 / -0

If a polynomial $𝑃 (𝑥)$ given by

$𝑃 (𝑥) = 2 𝑥^{4} + 𝑎 𝑥^{3} + 𝑏 𝑥^{2} + 𝑐 𝑥 + 𝑑$ is such that $𝑃 (1) = 4$ ,

$𝑃 (2) = 7, 𝑃 (3) = 12$ and $𝑃 (4) = 19$ , then $𝑃 (5) =$

28

Incorrect

76

Incorrect

26

Incorrect

72

Incorrect

Q 16MathematicsSection A • MCQsequences and series

+1 / -0

If the roots of the equation $𝑘 𝑥^{3} - 18 𝑥^{2} - 36 𝑥 + 8 = 0$ are in harmonic progression, then $𝑘 =$

64

Incorrect

45

Incorrect

81

Incorrect

27

Incorrect

Q 17MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝛼, 𝛽, 𝛾$ are the roots of the equation $𝑥^{3} + 𝑥^{2} + 𝑥 + 1 = 0$ , then match the items of List I with those of List II

List - I		List - II
(i)	$\frac{1}{𝛼} + \frac{1}{𝛽} + \frac{1}{𝛾}$	(a)	-1
(ii)	$𝛼^{3} + 𝛽^{3} + 𝛾^{3}$	(b)	-4
(iii)	$𝛼^{4} + 𝛽^{4} + 𝛾^{4}$	(c)	1
(iv)	$(𝛼 - 𝛽)^{2} + (𝛽 - 𝛾)^{2} + (𝛾 - 𝛼)^{2}$	(d)	3
		(e)	0

Then, the correct match is

(i) $\to a$ , (ii) $\to a$ , (iii) $\to d$ , (iv) $\to b$

Incorrect

(i) $\to c$ , (ii) $\to a$ , (iii) $\to e$ , (iv) $\to b$

Incorrect

(i) $\to a$ , (ii) $\to c$ , (iii) $\to d$ , (iv) $\to b$

Incorrect

(i) → c, (ii) → a, (iii) → b, (iv) → e

Incorrect

Q 18MathematicsSection A • MCQpermutations and combinations

+1 / -0

The number of odd numbers greater than 600000 that can be formed by using the digits $3, 6, 7, 8, 9, 0$ without repetition is

480

Incorrect

240

Incorrect

288

Incorrect

500

Incorrect

Q 19MathematicsSection A • MCQpermutations and combinations

+1 / -0

There are three sections in a question paper, each section containing 4 questions. If a candidate has to answer only 5 questions from this paper without leaving any section, then the number of ways in which a candidate can make the choice of questions is

624

Incorrect

704

Incorrect

384

Incorrect

432

Incorrect

Q 20MathematicsSection A • MCQbinomial theorem

+1 / -0

The term independent of $𝑥$ in the expansion of $(1 - 3 𝑥 + 2 𝑥^{3}) {(\frac{3 𝑥^{2}}{2} - \frac{1}{3 𝑥})}^{9}$ is

$7 / 18$

Incorrect

$5 / 18$

Incorrect

$19 / 54$

Incorrect

$17 / 54$

Incorrect

Q 21MathematicsSection A • MCQbinomial theorem

+1 / -0

If $\sum_{20}^{𝑟 = 0}^{20 + 𝑟} 𝐶_{𝑟} = \frac{𝑝}{𝑞}^{40} 𝐶_{20}$ and GCD of $(𝑝, 𝑞) = 1$ , then $𝑝^{2} - 𝑞^{2} =$

1302

Incorrect

1220

Incorrect

1240

Incorrect

1364

Incorrect

Q 22MathematicsSection A • MCQbinomial theorem

+1 / -0

If $𝑥 = \frac{2 \cdot 5}{2! 3} + \frac{2 \cdot 5 \cdot 7}{3! 3^{2}} + \frac{2 \cdot 5 \cdot 7 \cdot 9}{4! 3^{3}} + \dots$ , then $𝑥^{2} + 8 𝑥 + 8 =$

108

Incorrect

54

Incorrect

100

Incorrect

144

Incorrect

Q 23MathematicsSection A • MCQbinomial theorem

+1 / -0

If the coefficient of $𝑥^{4}$ in the expansion of $\frac{𝑥}{(𝑥 - 1)^{2} (𝑥 - 2)}$ is $\frac{𝑚}{𝑛}$ and $| 𝑚 |, | 𝑛 |$ are coprimes, then $\sqrt{\sqrt | 𝑚 + 𝑛 |} =$

9

Incorrect

$\sqrt{\sqrt 33}$

Incorrect

7

Incorrect

$6 \sqrt{\sqrt 2}$

Incorrect

Q 24MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\frac{\sin^{4} 𝑥}{2} + \frac{\cos^{4} 𝑥}{3} = \frac{1}{5}$ , then $27 \sec^{6} 𝛼 + 8 {cosec}^{6} 𝛼 =$

250

Incorrect

125

Incorrect

175

Incorrect

350

Incorrect

Q 25MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\tan 𝛽 = \frac{𝑛 \sin 𝛼 \cos 𝛼}{1 - 𝑛 \cos^{2} 𝛼}$ , then $\tan (𝛼 + 𝛽) \cdot \cot 𝛼 =$

$\frac{- 1}{𝑛 - 1}$

Incorrect

$𝑛 + 1$

Incorrect

$1 - 𝑛$

Incorrect

$\frac{1}{𝑛 + 1}$

Incorrect

Q 26MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\cos 𝐴 + \cos 𝐵 + \cos 𝐶 = 0 = \sin 𝐴 + \sin 𝐵 + \sin 𝐶$ , then $\cos (𝐴 - 𝐵) + \cos (𝐵 - 𝐶) + \cos (𝐶 - 𝐴) =$

0

Incorrect

$\frac{1}{2}$

Incorrect

$\frac{3}{2}$

Incorrect

$\frac{- 3}{2}$

Incorrect

Q 27MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\sin 𝑥 \cdot \cosh 𝑦 = \cos 𝜃$ and $\cos 𝑥 \cdot \sinh 𝑦 = \sin 𝜃$ , then $\sin^{2} 𝑥 + \cosh^{2} 𝑦 =$

1

Incorrect

2

Incorrect

$3 / 2$

Incorrect

$1 / 2$

Incorrect

Q 28MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $𝑎, 𝑏, 𝑐$ are in arithmetic progression and $𝐴 = 2 𝐶$ , then $𝑏 : 𝑐 =$

$4 : 5$

Incorrect

$2 : 3$

Incorrect

$5 : 4$

Incorrect

$5 : 6$

Incorrect

Q 29MathematicsSection A • MCQproperties of triangles

+1 / -0

Assertion (A) In $△ 𝐴 𝐵 𝐶$ , if $𝑟 = 6, 𝑟_{2} = 36, 𝑅 = 15$ , then $𝑐^{2} + 𝑎^{2} = 𝑏^{2}$ .

Reason (R) In $△ 𝐴 𝐵 𝐶$ , if $𝑟 : 𝑅 : 𝑟_{2} = 1 : 2.5 : 6$ , then $𝐵 = 90^{\circ}$ . The correct option among the following is

Both (A) and (R) are true, (R) is a correct explanation of (A)

Incorrect

Both $(𝐴)$ and $(𝑅)$ are true, but $(𝑅)$ is not a correct explanation of (A)

Incorrect

(A) is true and (R) is false

Incorrect

(A) is false and (R) is true

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚, 𝐛, 𝐜$ are unit vectors such that $𝐚$ is perpendicular to both $𝐛, 𝐜$ and angle between $𝐛, 𝐜$ is $2 𝜋 / 3$ , then $| 𝑎 + 3 𝑏 - 4 𝑐 |^{2} =$

6

Incorrect

14

Incorrect

38

Incorrect

26

Incorrect

Q 31MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐚 = 2 \hat{𝐢} - \hat{𝐣} + \hat{𝐤}$ be the position vector of a point $𝐴$ . Let $𝐛 = \hat{𝐢} + 2 \hat{𝐣} - \hat{𝐤}$ and $𝐜 = \hat{𝐢} + \hat{𝐣} - 2 \hat{𝐤}$ be two vectors and $𝐫$ be a vector passing through the point $𝐴 (𝐚)$ and parallel to the vector $𝐛$ . If the projection of $𝐫$ on $𝐜$ is $\frac{9}{\sqrt{\sqrt 6}}$ , then $| 𝐫 | =$

$\sqrt{\sqrt 26}$

Incorrect

5

Incorrect

$\sqrt{\sqrt 5}$

Incorrect

$\sqrt{\sqrt 34}$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

If $𝑆$ is the circumcentre, $𝑂$ is the orthocentre and $𝐺$ is the centroid of a $△ 𝐴 𝐵 𝐶$ , then match the items of the List-I with those of the items of List-II given below.

	List-I		List-II
(i)		(a)	2 OS
(ii)		(b)	$2$
(iii)		(c)	O
(iv)	OG	(d)	SO
		(e)	OS

Then, the correct match is

i $\to$ c, ii $\to$ b, iii $\to$ e, iv $\to$ a

Incorrect

i $\to$ b, ii $\to$ c, iii $\to$ a, iv $\to$ d

Incorrect

i $\to$ d, ii $\to$ a, iii $\to$ c, iv $\to$ e

Incorrect

i → d, ii → c, iii → a, iv → b

Incorrect

Q 33MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐚, 𝐛, 𝐜$ be three vectors such that $𝐚 \cdot 𝐚 = 𝐛 \cdot 𝐛 = 𝐜 \cdot 𝐜 = 5$ and $| 𝐚 + 𝐛 - 𝐜 |^{2} + | 𝐛 + 𝐜 - 𝐚 |^{2} + | 𝐜 + 𝐚 - 𝐛 |^{2} = 50$ , then $𝐚 \cdot 𝐛 + 𝐛 \cdot 𝐜 + 𝐜 \cdot 𝐚 =$

$5 / 2$

Incorrect

$- 5 / 2$

Incorrect

10

Incorrect

-10

Incorrect

Q 34MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐜$ be a vector coplanar with the unit vectors $𝐚, 𝐛$ and let $𝐝$ be the unit vector perpendicular to $𝐚, 𝐛$ and $𝐜$ . If $[𝐚 𝐛 𝐝] 𝐜 - [𝐚 𝐛 𝐜] 𝐝 = \hat{𝐢} + 2 \hat{𝐣} + 2 \hat{𝐤}$ and the angle between $𝐚$ and $𝐛$ is $30^{\circ}$ , then $| 𝐜 | =$

3

Incorrect

$3 / 2$

Incorrect

6

Incorrect

1

Incorrect

Q 35MathematicsSection A • MCQstatistics

+1 / -0

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively. Later on it was found that one of the observations was taken as 50 in the place of 40 . If the wrong entry is replaced by the correct one, then the sum of the squares of all the observations is

162701

Incorrect

163501

Incorrect

162601

Incorrect

161701

Incorrect

Q 36MathematicsSection A • MCQprobability

+1 / -0

If a matrix is chosen at random from the set of all $3 \times 3$ non-zero matrices whose entries are the elements of the set ${- 1, 0, 1}$ , then the probability that the matrix is skew-symmetric is

$\frac{1}{729}$

Incorrect

$\frac{1}{757}$

Incorrect

$\frac{1}{703}$

Incorrect

$\frac{1}{742}$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

A boy throws an unbiased die. Whenever he gets 1 on the die he has a further chance to throw it once again immediately. The probability that the boy gets a score of 7 in this process is

$\frac{1}{5} (1 - \frac{1}{6^{5}})$

Incorrect

$\frac{1}{30} (1 - \frac{1}{6^{4}})$

Incorrect

$\frac{1}{30} (1 - \frac{1}{6^{5}})$

Incorrect

$\frac{1}{5} (1 - \frac{1}{6^{4}})$

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

There are 10 coins in a box out of which 8 are normal and the remaining are with heads on both sides. A coin is chosen at random from the box and tossed 6 times. If it shows heads each time, then the probability that the selected coin has head on both sides is

$\frac{16}{17}$

Incorrect

$\frac{32}{41}$

Incorrect

$\frac{8}{9}$

Incorrect

$\frac{12}{13}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

$A random variable 𝑋 has the following distribution,$

$\begin{matrix} 𝑋 = 𝑥_{𝑖} & - 2 & - 1 & 0 & 1 & 2 & 3 \\ 𝑃 (𝑋 = 𝑥_{𝑖}) & 0.1 & 𝑘 & 0.2 & 2 𝑘 & 3 𝑘 & 𝑘 \end{matrix}$

Then, the variance of this distribution is

2.64

Incorrect

2.8

Incorrect

2.16

Incorrect

1.86

Incorrect

Q 40MathematicsSection A • MCQstraight lines and pair of straight lines

+1 / -0

A straight line passing through a fixed point $(- 3, 4)$ intersects the coordinate axes at $𝐴$ and $𝐵$ . If $𝑂$ is the origin and $𝑂 𝐴 𝐵 𝐶$ forms a rectangle, then the locus of $𝐶$ is

$𝑥 𝑦 + 3 𝑥 - 4 𝑦 = 0$

Incorrect

$𝑥 𝑦 - 3 𝑥 + 4 𝑦 = 0$

Incorrect

$𝑥 𝑦 - 3 𝑥 - 4 𝑦 = 0$

Incorrect

$𝑥 𝑦 + 3 𝑥 + 4 𝑦 = 0$

Incorrect

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

+1 / -0

When the origin is shifted to the point $𝑃$ by translation of axes, the equation $2 𝑥^{2} + 𝑦^{2} - 4 𝑥 + 4 𝑦 = 0$ is transformed to $2 𝑥^{2} + 𝑦^{2} - 8 𝑥 + 8 𝑦 + 18 = 0$ . Then, the transformed equation of the straight line $𝑥 + 2 𝑦 + 2 = 0$ , if the origin is shifted to the same point $𝑃$ is

$𝑥 + 2 𝑦 - 1 = 0$

Incorrect

$𝑥 + 2 𝑦 - 3 = 0$

Incorrect

$𝑥 + 2 𝑦 + 7 = 0$

Incorrect

$𝑥 + 2 𝑦 + 5 = 0$

Incorrect

Q 42MathematicsSection A • MCQcircle

+1 / -0

If the circumcenter of the triangle formed by the points $𝐴 (𝑎, 3), 𝐵 (𝑏, 5)$ and $𝐶 (𝑎, 𝑏)$ is $(1, 1)$ , then out of all the possible coordinates of $𝐶$ the sum of the absolute values of the distinct coordinates of $𝐶$ is

8

Incorrect

9

Incorrect

12

Incorrect

4

Incorrect

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

+1 / -0

If the lines $𝑥 + 𝑦 - 1 = 0, 𝑘 𝑥 + 2 𝑦 + 1 = 0$ and $4 𝑥 + 2 𝑘 𝑦 + 7 = 0$ are concurrent, then $𝑘 =$

2

Incorrect

$\frac{13}{2}$

Incorrect

$\frac{- 13}{2}$

Incorrect

-2

Incorrect

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

+1 / -0

If $𝛼, 𝛽 (𝛼 > 𝛽)$ are two values of $𝑘$ such that the equations $2 𝑥 + (3 - 2 𝑘) 𝑦 + (2 𝑘 + 1) = 0$ and $𝑘 𝑥 + (𝑘 - 1) 𝑦 - 4 = 0$ represents two perpendicular lines, then $𝛼^{2} + 2 𝛽 =$

1

Incorrect

$7 / 4$

Incorrect

7

Incorrect

10

Incorrect

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

+1 / -0

If $𝑘 = \frac{𝑎 + 𝑏}{𝑎 𝑏}$ is a non-zero constant, then the point which lies on the straight line $\frac{𝑥}{𝑎} + \frac{𝑦}{𝑏} = 1$ is

$(𝑘, 𝑘)$

Incorrect

$(𝑘, \frac{1}{𝑘})$

Incorrect

$(\frac{1}{𝑘}, 𝑘)$

Incorrect

$(\frac{1}{𝑘}, \frac{1}{𝑘})$

Incorrect

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

+1 / -0

The point of concurrence of all the chords of the curve $3 𝑥^{2} - 𝑦^{2} - 2 𝑥 + 4 𝑦 = 0$ which subtend a right angle at the origin is

$(1, 2)$

Incorrect

$(1, - 2)$

Incorrect

$(- 1, 2)$

Incorrect

$(- 1, - 2)$

Incorrect

Q 47MathematicsSection A • MCQcircle

+1 / -0

The equation of a circle passing through $(- 6, 3)$ and touching both the coordinates axes is

$𝑥^{2} + 𝑦^{2} + 20 𝑥 - 20 𝑦 + 100 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} + 10 𝑥 - 10 𝑦 + 25 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} + 6 𝑥 - 6 𝑦 + 9 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} - 30 𝑥 + 30 𝑦 + 225 = 0$

Incorrect

Q 48MathematicsSection A • MCQcircle

+1 / -0

The area (in sq units) of the triangle formed by the $𝑥$ -axis, the tangent and the normal drawn to the circle $𝑥^{2} + 𝑦^{2} = 10 𝑥$ at the point $(9, 3)$ is

$75 / 4$

Incorrect

$75 / 8$

Incorrect

75

Incorrect

25

Incorrect

Q 49MathematicsSection A • MCQcircle

+1 / -0

The number of common tangents of the circles $𝑥^{2} + 𝑦^{2} - 4 = 0$ and $𝑥^{2} + 𝑦^{2} - 6 𝑥 - 8 𝑦 - 24 = 0$ is

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

If the equation of the circle whose radius is $\sqrt{\sqrt 10}$ and which touches the circle $𝑥^{2} + 𝑦^{2} + 2 𝑥 + 8 𝑦 - 23 = 0$ externally at the point $(1, 2)$ is $𝑥^{2} + 𝑦^{2} + 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0$ , then $| 𝑎 + 𝑏 + 𝑐 | =$

5

Incorrect

13

Incorrect

33

Incorrect

23

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

If a circle ' $𝑆$ ' passing through the origin and having its centre on the line $𝑥 - 𝑦 = 0$ cuts the circle $𝑥^{2} + 𝑦^{2} - 4 𝑥 - 6 𝑦 + 10 = 0$ orthogonally, then the diameter of ' $𝑆$ ' is

$\sqrt{\sqrt 2}$

Incorrect

2

Incorrect

$2 \sqrt{\sqrt 2}$

Incorrect

4

Incorrect

Q 52MathematicsSection A • MCQcircle

+1 / -0

The equation of the circle passing through the points of intersection of the circles $𝑥^{2} + 𝑦^{2} + 6 𝑥 + 4 𝑦 - 12 = 0$ , $𝑥^{2} + 𝑦^{2} - 4 𝑥 - 6 𝑦 - 12 = 0$ and having radius $\sqrt{\sqrt 13}$ is

$𝑥^{2} + 𝑦^{2} - 2 𝑥 - 12 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} - 4 𝑥 - 6 𝑦 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} + 2 𝑦 - 12 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} + 6 𝑥 - 4 𝑦 = 0$

Incorrect

Q 53MathematicsSection A • MCQparabola

+1 / -0

If $𝐀 𝐁$ is the focal chord of the parabola $𝑦^{2} = 16 𝑥$ and $𝐴 = (1, - 4)$ , then the equation of the normal to the parabola at the point $𝐵$ is

$2 𝑥 + 𝑦 - 32 = 0$

Incorrect

$2 𝑥 + 𝑦 - 48 = 0$

Incorrect

$𝑥 - 2 𝑦 + 16 = 0$

Incorrect

$𝑥 + 2 𝑦 - 48 = 0$

Incorrect

Q 54MathematicsSection A • MCQparabola

+1 / -0

If one of the vertices of an equilateral triangle inscribed in the parabola $𝑦^{2} = 12 𝑥$ coincides with the vertex of the parabola, then the area (in sq units) of that triangle is

$192 \sqrt{\sqrt 3}$

Incorrect

$864 \sqrt{\sqrt 3}$

Incorrect

$216 \sqrt{\sqrt 3}$

Incorrect

$432 \sqrt{\sqrt 3}$

Incorrect

Q 55MathematicsSection A • MCQellipse

+1 / -0

If an ellipse with its axes as coordinate axes, $2 𝑎$ and $2 𝑏$ as the lengths of its major and minor axes respectively passes through the points $(2, 2)$ and $(3, 1)$ , then $3 𝑎^{2} + 5 𝑏^{2} =$

32

Incorrect

8

Incorrect

64

Incorrect

16

Incorrect

Q 56MathematicsSection A • MCQellipse

+1 / -0

The values of $𝑐$ such that the line $𝑦 = 4 𝑥 + 𝑐$ touches the ellipse $\frac{𝑥^{2}}{4} + \frac{𝑦^{2}}{1} = 1$ is

$\pm 13$

Incorrect

$\pm 7$

Incorrect

$\pm \sqrt{\sqrt 65}$

Incorrect

$\pm \sqrt{\sqrt 74}$

Incorrect

Q 57MathematicsSection A • MCQhyperbola

+1 / -0

If the line $2 𝑥 + \sqrt{\sqrt 6} 𝑦 = 2$ touches the hyperbola $𝑥^{2} - 2 𝑦^{2} = 4$ , then the coordinates of the point of contact are

$(\frac{1}{2}, \frac{1}{\sqrt{\sqrt 6}})$

Incorrect

$(4, - \sqrt{\sqrt 6})$

Incorrect

$(4, \sqrt{\sqrt 6})$

Incorrect

$(- 2, \sqrt{\sqrt 6})$

Incorrect

Q 58MathematicsSection A • MCQ3d geometry

+1 / -0

If the circumcenter of the triangle formed by the points $(1, 2, 3), (3, - 1, 5)$ and $(4, 0, - 3)$ is $(𝛼, 𝛽, 𝛾)$ , then $| 𝛼 | + | 𝛽 | =$

$| 𝛾 |$

Incorrect

$3 | 𝛾 |$

Incorrect

$4 | 𝛾 |$

Incorrect

$2 | 𝛾 |$

Incorrect

Q 59MathematicsSection A • MCQ3d geometry

+1 / -0

If $𝜃$ is the acute angle between the two lines whose direction cosines are connected by the relations $𝑙 + 𝑚 + 𝑛 = 0$ and $2 𝑙 𝑚 + 2 𝑛 𝑙 - 𝑚 𝑛 = 0$ , then $\cos 𝜃 =$

$1 / 2$

Incorrect

$\sqrt{\sqrt 3} / 2$

Incorrect

$5 / 6$

Incorrect

$3 / 5$

Incorrect

Q 60MathematicsSection A • MCQ3d geometry

+1 / -0

If the foot of the perpendicular drawn from the point $(1, 0, - 2)$ to the plane $𝜋$ is $(2, 0, - 1)$ and the equation of the plane $𝜋$ is $𝑎 𝑥 + 𝑏 𝑦 + 𝑐 𝑧 = 2$ , then $𝑎^{2} + 𝑏^{2} + 𝑐^{2} =$

2

Incorrect

8

Incorrect

4

Incorrect

9

Incorrect

Q 61MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

$\begin{matrix} lim_{𝑥 \to 0} \frac{2 \tan 𝑥 + \cos 𝑥 - 1 + 𝑥}{\sqrt{\sqrt 4 \sin^{2} 𝑥 + 2 \tan 𝑥 + 1}} = \\ - \sqrt{\sqrt 3 \tan^{2} 𝑥 + \sin 𝑥 + 1} \end{matrix}$

1

Incorrect

3

Incorrect

6

Incorrect

$2 / 3$

Incorrect

Q 62MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If a function $𝑓$ is defined by $𝑓 (𝑥) = \frac{\cot^{3} 𝑥 - \tan 𝑥}{\cos (𝑥 + 𝜋 / 4)}, (𝑥 \neq 𝜋 / 4)$ , then $lim_{𝑥 \to 𝜋 / 4} 𝑓 (𝑥) =$

4

Incorrect

8

Incorrect

$8 / 3$

Incorrect

16

Incorrect

Q 63MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑓 (𝑥) = \sqrt{\sqrt 𝑥} (𝑥 \geq 0)$ and $𝑔 (𝑥) = 1 + 𝑥^{2}$ , then $(𝑓 \circ 𝑔)^{'} (1) =$

1

Incorrect

$1 / 2$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

$1 / \sqrt{\sqrt 2}$

Incorrect

Q 64MathematicsSection A • MCQdifferentiation

+1 / -0

Match the values of $\frac{𝑑 𝑦}{𝑑 𝑥}$ at $𝑥 = \frac{𝜋}{3}$ for the following system of curves in parametric form given in List-I with those of the items in List-II

List-I			List-II
(i)	$x = a (θ - \sin θ), y = a (1 - \cos θ)$	(a)	$4 \sqrt{3}$
(ii)	$x = 3 \cos θ - 2 \cos^{3} θ, y = 3 \sin θ - 2 \sin^{3} θ$	(b)	$\frac{- 1}{3 \sqrt{3}}$
(iii)	$x = 3 \cos θ - \cos^{3} θ, y = 3 \sin θ - \sin^{3} θ$	(c)	$\sqrt{3}$
(iv)	$x = a \log \sin θ, y = a \tan θ$	(d)	$\frac{1}{\sqrt{3}}$
		(e)	$\frac{1}{3 \sqrt{3}}$

(i) → c, (ii) → d, (iii) → b, (iv) → a

Incorrect

(i) → c, (ii) → e, (iii) → d, (iv) → a

Incorrect

(i) → d, (ii) → c, (iii) → b, (iv) → a

Incorrect

(i) →d, (ii) → c, (iii) → e, (iv) → b

Incorrect

Q 65MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑦 = 𝑥 \sin 𝑥$ and $\frac{\frac{𝑑 𝑦}{𝑑 𝑥} - \frac{𝑦}{𝑥}}{𝑥 \frac{𝑑 𝑦}{𝑑 𝑥} - 𝑦}$ at $𝑥 = 𝛼$ is 1 , then $𝛼 =$

$\sqrt{\sqrt 2}$

Incorrect

2

Incorrect

1

Incorrect

$1 / \sqrt{\sqrt 2}$

Incorrect

Q 66MathematicsSection A • MCQapplication of derivatives

+1 / -0

A ladder of length 13 m has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 m / \min$ then the speed (in $m / \min$ ) at which upper end falls when the bottom is 5 m away from the wall is

$6 / 5$

Incorrect

$12 / 5$

Incorrect

$5 / 6$

Incorrect

$5 / 12$

Incorrect

Q 67MathematicsSection A • MCQapplication of derivatives

+1 / -0

An angle between the curves $𝑥^{2} - 𝑦^{2} = 4$ and $𝑥^{2} + 𝑦^{2} = 4 \sqrt{\sqrt 2}$ is

$𝜋 / 6$

Incorrect

$𝜋 / 4$

Incorrect

$𝜋 / 3$

Incorrect

$𝜋 / 2$

Incorrect

Q 68MathematicsSection A • MCQapplication of derivatives

+1 / -0

The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is

$384 \sqrt{\sqrt 3} 𝜋$

Incorrect

$768 \sqrt{\sqrt 3} 𝜋$

Incorrect

$\frac{768 𝜋}{\sqrt{\sqrt 3}}$

Incorrect

$\frac{1152 𝜋}{\sqrt{\sqrt 3}}$

Incorrect

Q 69MathematicsSection A • MCQindefinite integration

+1 / -0

$\int \frac{\tan 𝑥}{\sec^{2} 𝑥 {(1 + \sec^{6} 𝑥)}^{\frac{2}{3}}} 𝑑 𝑥 =$

$\frac{- 1}{2} {(1 + \sec^{6} 𝑥)}^{\frac{1}{3}} + 𝐶$

Incorrect

$2 {(1 + \sec^{6} 𝑥)}^{\frac{4}{3}} + 𝐶$

Incorrect

$\frac{- 1}{2} {(1 + \cos^{6} 𝑥)}^{\frac{1}{3}} + 𝐶$

Incorrect

$2 {(1 + \cos^{6} 𝑥)}^{\frac{1}{3}} + 𝐶$

Incorrect

Q 70MathematicsSection A • MCQindefinite integration

+1 / -0

$\int \frac{1}{(𝑥 - 1)^{\frac{5}{7}} (𝑥 + 1)^{\frac{9}{7}}} 𝑑 𝑥 =$

$\frac{7}{4} {(\frac{𝑥 + 1}{𝑥 - 1})}^{\frac{2}{7}} + 𝐶$

Incorrect

$\frac{- 7}{4} {(\frac{𝑥 + 1}{𝑥 - 1})}^{\frac{2}{7}} + 𝐶$

Incorrect

$\frac{7}{4} {(\frac{𝑥 - 1}{𝑥 + 1})}^{\frac{2}{7}} + 𝐶$

Incorrect

$\frac{- 7}{4} {(\frac{𝑥 - 1}{𝑥 + 1})}^{\frac{2}{7}} + 𝐶$

Incorrect

Q 71MathematicsSection A • MCQindefinite integration

+1 / -0

$\int \frac{1 + \sqrt{\sqrt 3} \cot 𝑥}{1 - \sqrt{\sqrt 3} \cot 𝑥} 𝑑 𝑥 =$

$- \frac{𝑥}{2} + \frac{\sqrt{\sqrt 3}}{2} \log ∣ \sin (𝑥 - \frac{𝜋}{3}) ∣ + 𝐶$

Incorrect

$\frac{𝑥}{2} + \frac{\sqrt{\sqrt 3}}{2} \log ∣ \sin (𝑥 - \frac{𝜋}{3}) ∣ + 𝐶$

Incorrect

$- \frac{𝑥}{2} - \frac{\sqrt{\sqrt 3}}{2} \log [\sin (𝑥 - \frac{𝜋}{3})] + 𝐶$

Incorrect

$\frac{𝑥}{2} - \frac{\sqrt{\sqrt 3}}{2} \log ∣ \sin (𝑥 - \frac{𝜋}{3}) ∣ + 𝐶$

Incorrect

Q 72MathematicsSection A • MCQindefinite integration

+1 / -0

$\begin{matrix} If \int \frac{1}{cosec 𝑥 + \cos 𝑥} 𝑑 𝑥 = \frac{1}{2 \sqrt{\sqrt 3}} \log | 𝑓 (𝑥) | \\ - \int \frac{\cos 𝑥 - \sin 𝑥}{2 + \sin 2 𝑥} 𝑑 𝑥 + 𝑐, then at 𝑥 = \frac{𝜋}{3}, | 𝑓 (𝑥) | = \end{matrix}$

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

Incorrect

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

Incorrect

$\frac{6 \sqrt{\sqrt 3} - 2}{\sqrt{\sqrt 3} + 1}$

Incorrect

$\frac{6 \sqrt{\sqrt 3} + 2}{\sqrt{\sqrt 3} + 1}$

Incorrect

Q 73MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{𝜋 / 2}^{0} \frac{𝑥 \tan 𝑥 \sec^{2} 𝑥}{\tan^{4} 𝑥 + 1} 𝑑 𝑥 =$

$𝜋^{2} / 16$

Incorrect

$𝜋^{2} / 4$

Incorrect

$𝜋^{2} / 8$

Incorrect

$𝜋^{2} / 32$

Incorrect

Q 74MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{6}^{3} \frac{\sqrt{\sqrt 𝑥}}{\sqrt{\sqrt 9 - 𝑥} + \sqrt{\sqrt 𝑥}} 𝑑 𝑥 =$

$1 / 2$

Incorrect

$3 / 2$

Incorrect

2

Incorrect

1

Incorrect

Q 75MathematicsSection A • MCQdefinite integration

+1 / -0

$lim_{𝑛 \to \infty} {[(1 + \frac{1}{𝑛^{2}}) (1 + \frac{2^{2}}{𝑛^{2}}) \dots (2)]}^{1 / 𝑛} =$

$2 𝑒^{𝜋 - 4}$

Incorrect

$𝑒^{\frac{𝜋 - 4}{2}}$

Incorrect

$2 𝑒^{\frac{𝜋 - 4}{2}}$

Incorrect

$\frac{1}{2} 𝑒^{\frac{𝜋 - 4}{2}}$

Incorrect

Q 76MathematicsSection A • MCQarea under the curves

+1 / -0

The area (in sq units) of the region bounded by the circle $𝑥^{2} + 𝑦^{2} = 64$ , positive $𝑋$ -axis and the line $𝑦 = \sqrt{\sqrt 3} 𝑥$ is

$16 𝜋 / 3$

Incorrect

$8 𝜋 / 3$

Incorrect

$64 𝜋 / 3$

Incorrect

$32 𝜋 / 3$

Incorrect

Q 77MathematicsSection A • MCQdifferential equations

+1 / -0

If $𝑎$ and $𝑏$ are the arbitrary constants, then the differential equation corresponding to the family of curves given by $𝑦 = 𝑥 [𝑎 \cos (\log 𝑥) + 𝑏 \sin (\log 𝑥)]$ is

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 78MathematicsSection A • MCQdifferential equations

+1 / -0

If the solution for the differential equation $𝑦^{2} 𝑑 𝑥 + (𝑥^{2} - 𝑥 𝑦 - 𝑦^{2}) 𝑑 𝑦 = 0$ at $(2, 1)$ is $𝑥 + 𝑦 = 𝑘 (𝑥 𝑦^{2} - 𝑦^{3})$ , then $𝑘 =$

-3

Incorrect

-4

Incorrect

4

Incorrect

3

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

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

$𝑥 𝑦 = \frac{𝑥^{2}}{2} + 𝐶$

Incorrect

$𝑥 𝑦 = \frac{𝑥^{3}}{3} + 𝐶$

Incorrect

$𝑥 𝑦 = \frac{𝑥^{4}}{4} + 𝐶$

Incorrect

$𝑥 𝑦 = \frac{𝑥^{5}}{5} + 𝐶$

Incorrect

Q 80MathematicsSection A • MCQpermutations and combinations

+1 / -0

The number of ways in which 6 men and 4 women can be seated around a table, so that a particular man and a particular woman never sit adjacent to each other is

9 !

Incorrect

$7 \times 8$ !

Incorrect

$8 \times 8$ !

Incorrect

$6 \times 7$ !

Incorrect

Q 81PhysicsSection A • MCQatoms and nuclei

+1 / -0

Match the following.

(Take the relative strength of the strongest fundamental forces in nature as one)

List-I (Fundamental forces in nature)		List-II (Relative strength)
(A)	Strong nuclear force	(e)	$10^{- 2}$
(B)	Weak nuclear force	(f)	1
(C)	Electromagnetic force	(g)	$10^{10}$
(D)	Gravitational force	(h)	$10^{- 13}$
		(i)	$10^{- 39}$

A-f, B-i, C-e, D-h

Incorrect

A-f, B-h, C-e, D-g

Incorrect

A-f, B-h, C-e, D-i

Incorrect

A-f, B-e, C-h, D-i

Incorrect

Q 82PhysicsSection A • MCQunits and measurements

+1 / -0

A physical quantity $𝑋$ is given by $𝑋 = \frac{2 𝑘^{3} 𝑙^{2}}{𝑚 \sqrt{\sqrt 𝑛}}$ . The percentage errors in the measurements of $𝑘, 𝑙, 𝑚$ and $𝑛$ are $1 %, 2 %, 3 %$ and $4 %$ respectively. The value of $𝑋$ is uncertain by

$8 %$

Incorrect

$10 %$

Incorrect

$12 %$

Incorrect

$14 %$

Incorrect

Q 83PhysicsSection A • MCQmotion in a straight line

+1 / -0

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. The ratio of their velocities is

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

$\sqrt{\sqrt 3} : 2$

Incorrect

$1 : 1$

Incorrect

$1 : 2$

Incorrect

$1 : \sqrt{\sqrt 3}$

Incorrect

Q 84PhysicsSection A • MCQmotion in a plane

+1 / -0

A projectile is given an initial velocity of $\hat{𝐢} + 2 \hat{𝐣} {ms}^{- 1}$ . The cartesian equation of its path is ( $𝑥$ and $𝑦$ are in metres and $𝑔 = 10 {ms}^{- 1}$ )

$𝑦 = 𝑥 - 5 𝑥^{2}$

Incorrect

$𝑦 = 2 𝑥 - 5 𝑥^{2}$

Incorrect

$𝑦 = 2 𝑥 - 15 𝑥^{2}$

Incorrect

$𝑦 = 2 𝑥 - 25 𝑥^{2}$

Incorrect

Q 85PhysicsSection A • MCQcircular motion

+1 / -0

If the radii of circular path of two particles of same mass are in the ratio of $1 : 2$ , then to have a constant centripetal force, the ratio of their speeds should be

$4 : 1$

Incorrect

$1 : \sqrt{\sqrt 2}$

Incorrect

$1 : 4$

Incorrect

$\sqrt{\sqrt 2} : 1$

Incorrect

Q 86PhysicsSection A • MCQvector algebra

+1 / -0

The angle between force $𝐅 = 3 \hat{𝐢} + 4 \hat{𝐣} - 5 \hat{𝐤}$ and displacement $𝐝 = 5 \hat{𝐢} + 4 \hat{𝐣} + 3 \hat{𝐤}$ is

$\cos^{- 1} (0.16)$

Incorrect

$\cos^{- 1} (0.32)$

Incorrect

$\cos^{- 1} (0.24)$

Incorrect

$\cos^{- 1} (0.64)$

Incorrect

Q 87PhysicsSection A • MCQcenter of mass

+1 / -0

A bomb of mass 16 kg explodes into two pieces of masses 4 kg and 12 kg . The velocity of the 12 kg mass is $4 {ms}^{- 1}$ . The kinetic energy of the second piece is

144 J

Incorrect

192 J

Incorrect

96 J

Incorrect

288 J

Incorrect

Q 88PhysicsSection A • MCQrotational motion

+1 / -0

A constant torque acting on a uniform circular wheel changes its angular momentum from $𝐴_{0}$ to $4 𝐴_{0}$ in 4 seconds. The magnitude of the torque is

$\frac{3 𝐴_{0}}{4}$

Incorrect

$𝐴_{0}$

Incorrect

$4 𝐴_{0}$

Incorrect

$12 𝐴_{0}$

Incorrect

Q 89PhysicsSection A • MCQrotational motion

+1 / -0

A particle performs uniform circular motion with an angular momentum $𝐿$ . If the frequency of the particle's motion is doubled and its kinetic energy is halved, then its angular momentum becomes

$2 𝐿$

Incorrect

$4 𝐿$

Incorrect

$\frac{1}{2}$

Incorrect

$\frac{𝐿}{4}$

Incorrect

Q 90PhysicsSection A • MCQsimple harmonic motion

+1 / -0

The displacement of a particle is given by the relation $𝑥 = 4 (\cos 𝜋 𝑡 + \sin 𝜋 𝑡)$ . The amplitude of the particle is

-4

Incorrect

4

Incorrect

$4 \sqrt{\sqrt 2}$

Incorrect

8

Incorrect

Q 91PhysicsSection A • MCQgravitation

+1 / -0

A body of mass $𝑚$ is at height $𝑅$ from the surface of the earth where $𝑅$ is the radius of the earth. If the body is taken from here to a height of $3 𝑅$ from the surface of the earth, the increase in the gravitational potential energy of the body is

( $𝑔$ is acceleration due to gravity on the surface of the earth)

$3 𝑚 𝑔 𝑅$

Incorrect

$\frac{𝑚 𝑔 𝑅}{3}$

Incorrect

$4 𝑚 𝑔 𝑅$

Incorrect

$\frac{𝑚 𝑔 𝑅}{4}$

Incorrect

Q 92PhysicsSection A • MCQelasticity

+1 / -0

The ratio of the areas of cross-sections of three wires is $1 : 2 : 3$ and the ratio of the Young's modulii of their materials is $3 : 2 : 1$ . If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

$4 : 3 : 4$

Incorrect

$1 : 1 : 1$

Incorrect

$9 : 4 : 1$

Incorrect

$3 : 4 : 3$

Incorrect

Q 93PhysicsSection A • MCQfluid mechanics

+1 / -0

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes 5 times its volume at the bottom of the lake. If $𝐻$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is

(The temperature of the water in the lake is same at all points)

2 H

Incorrect

4 H

Incorrect

5 H

Incorrect

3 H

Incorrect

Q 94PhysicsSection A • MCQfluid mechanics

+1 / -0

A water drop breaks into 64 identical droplets of each surface area $10^{- 7} m^{2}$ . If the surface tension of water is $0.07 {Nm}^{- 1}$ , the increase in the surface energy in the process is

$158 \times 10^{- 9} J$

Incorrect

$432 \times 10^{- 9} J$

Incorrect

$216 \times 10^{- 9} J$

Incorrect

$336 \times 10^{- 9} J$

Incorrect

Q 95PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Steam at $100^{\circ} C$ is added to 150 g water to increase its temperature from $20^{\circ} C$ to $40^{\circ} C$ . The total mass of the water at $40^{\circ} C$ is (specific heat capacity of water $= 1 cal g^{- 1}^{\circ} C^{- 1}$ and latent heat of steam $= 540 cal g^{- 1})$

155 g

Incorrect

150 g

Incorrect

145 g

Incorrect

5 g

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are 5.012 m and 5 m respectively at $27^{\circ} C$ . The temperature (in $^{\circ} C$ ) to which iron ring must be heated so as to fit the wooden wheel is

(Coefficient of linear expansion of iron $= 1.2 \times 10^{- 5}^{\circ} C^{- 1})$

200

Incorrect

227

Incorrect

254

Incorrect

300

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Two moles of triatomic gas $(𝛾 = \frac{4}{3})$ at temperature $327^{\circ} C$ expands adiabatically such that its volume becomes 8 times its initial volume. Later the temperature of the gas is doubled in an isochoric process. The total work done in the two processes is

(Where, R is universal gas constant)

$900 𝑅$

Incorrect

$1800 𝑅$

Incorrect

$1200 𝑅$

Incorrect

$300 𝑅$

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

If the temperature of a gas is increased from $27^{\circ} C$ to $159^{\circ} C$ , then the percentage increase in the rms speed of the gas molecules is

5

Incorrect

10

Incorrect

15

Incorrect

20

Incorrect

Q 99PhysicsSection A • MCQwaves

+1 / -0

A source emitting sound is tied to one end of a string of length 50 cm and is rotated with an angular speed of $40 rad s^{- 1}$ in the horizontal plane. The ratio of the maximum and minimum frequencies of the sound heard by an observer standing at a distance of 10 m from the fixed end of the string is

(speed of sound in air $= 340 {ms}^{- 1}$ )

$2 : 1$

Incorrect

$4 : 3$

Incorrect

$6 : 5$

Incorrect

$9 : 8$

Incorrect

Q 100PhysicsSection A • MCQwaves

+1 / -0

One end of a string is tied to the ceiling of a lift and a load is attached at the bottom end of the string. When the lift is moving upwards with an acceleration of 2.1 ${ms}^{- 2}$ , the speed of the transverse wave at the lower end of the string is $88 {ms}^{- 1}$ . If the lift moves downwards with an acceleration of $1.9 {ms}^{- 2}$ , the speed of the transverse wave at the lower end of the string is $(𝑔 = 10 {ms}^{- 2})$

$88 {ms}^{- 1}$

Incorrect

$102 {ms}^{- 1}$

Incorrect

$119 {ms}^{- 1}$

Incorrect

$72 {ms}^{- 1}$

Incorrect

Q 101PhysicsSection A • MCQray optics

+1 / -0

The focal lengths of the objective and the eyepiece of a compound microscope are 2 cm and 3 cm respectively and the distance between them is 15 cm . The final image formed by the eyepiece is at infinity. The distances of the object and the image produced by the object from the objective lens are respectively.

$2.4 cm, 12 cm$

Incorrect

$2.4 cm, 15 cm$

Incorrect

$2.3 cm, 12 cm$

Incorrect

$2.3 cm, 3 cm$

Incorrect

Q 102PhysicsSection A • MCQwave optics

+1 / -0

In a single slit diffraction, the slit is illuminated with light of wavelength

6000 \overset{o}{A}

. If the slit were illuminated by a light of wavelength

𝜆

the angular width of the central maximum decreases by

30 %

. Then

𝜆

is

6000 \overset{o}{A}

Incorrect

4200 \overset{o}{A}

Incorrect

3000 \overset{o}{A}

Incorrect

1800 \overset{o}{A}

Incorrect

Q 103PhysicsSection A • MCQelectrostatics

+1 / -0

A hollow spherical shell of radius $𝑟$ has a uniform charge density $𝜎$ . It is kept in a cube of edge $3 𝑟$ such that the centres of the cube and the shell coincide. Then the electric flux coming out of one face of a cube is ( $𝜀_{0} =$ permittivity of free space)

$\frac{𝜋 𝑟^{2} 𝜎}{𝜀_{0}}$

Incorrect

$\frac{5 𝜀_{0}}{2 𝜋 𝑟^{2} 𝜎}$

Incorrect

$\frac{𝜋 𝑟^{2} 𝜎}{6 𝜀_{0}}$

Incorrect

$\frac{2 𝜋 𝑟^{2} 𝜎}{3 𝜀_{0}}$

Incorrect

Q 104PhysicsSection A • MCQcapacitor

+1 / -0

The circuit shows two capacitor $𝐴$ and $𝐵$ of capacitances $𝐶$ and $2 𝐶$ respectively.

When they are fully charged, the cell is removed and the capacitors are connected with their plates of opposite polarities touching each other. Then

(i) Charge on $𝐴$ is $\frac{4 𝐶 𝐸}{9}$

(ii) Charge on $𝐵$ is zero

(iii) Loss of energy in this process is $(𝐶 𝐸^{2} / 3)$

The correct statement/s is/are

qImage--capacitor-electromagnetism-Jeemate

(i) and (ii) are correct.

Incorrect

(ii) and (iii) are correct.

Incorrect

(i), (ii) and (iii) are correct.

Incorrect

(iii) alone is correct.

Incorrect

Q 105PhysicsSection A • MCQcurrent electricity

+1 / -0

A uniform conducting wire $𝐴 𝐵$ of length 5 m and resistance $5 Ω$ is connected as shown in the circuit. If the balancing point is obtained at 3 m from $𝐴$ , then the value of $𝐸$ is

qImage--current-electricity-electromagnetism-Jeemate

1.5 V

Incorrect

3 V

Incorrect

0.67 V

Incorrect

1.33 V

Incorrect

Q 106PhysicsSection A • MCQcurrent electricity

+1 / -0

In the given circuit, the equivalent resistance between $𝐴$ and $𝐵$ is

qImage--current-electricity-electromagnetism-Jeemate

$3 Ω$

Incorrect

$4 Ω$

Incorrect

$4.5 Ω$

Incorrect

$5 Ω$

Incorrect

Q 107PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A square loop of side $𝑎$ and carrying a current $𝐼$ is suspended from an insulating hanger of a spring balance as shown in figure. The transverse magnetic field $𝐵$ directed into the paper occurs only at the bottom side of the loop. When direction of current in the loop is reversed, the change in the reading of spring balance is

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

$𝑙 𝑎 𝐵$

Incorrect

$2 / 𝑎 𝐵$

Incorrect

$\frac{𝑙 𝑎 𝐵}{2}$

Incorrect

$\frac{3}{2} laB$

Incorrect

Q 108PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A current carrying loop is placed in a uniform magnetic field $𝐵$ in different orientations I, II, III and IV as shown in the figure. The correct order of decreasing potential energy is

( $\hat{𝐧} =$ unit vector normal to the plane of the loop) qImage--moving-charges-and-magnetism-electromagnetism-Jeemate

I, III, II, IV

Incorrect

I, I I, I I I, I V

Incorrect

I, IV, II, III

Incorrect

III, IV, I, II

Incorrect

Q 109PhysicsSection A • MCQmagnetism and matter

+1 / -0

A bar magnet of magnetic moment $2 A - m^{2}$ lies aligned with the direction of a uniform magnetic field of 0.3 T . The amount of work required by an external torque to turn the magnet so as to align its magnetic moment normal to the field direction is

0.15 J

Incorrect

0.3 J

Incorrect

0.6 J

Incorrect

1.2 J

Incorrect

Q 110PhysicsSection A • MCQelectromagnetic induction

+1 / -0

A conducting rod is moving towards right with a velocity $𝑣$ in a uniform magnetic field $𝐵$ . If the direction of induced current $𝑖$ is as shown in the figure, then the direction of $𝐵$ is

qImage--electromagnetic-induction-electromagnetism-Jeemate

in the plane of the paper towards right

Incorrect

in the plane of the paper towards left

Incorrect

perpendicular to the plane of the paper and into the paper

Incorrect

perpendicular to the plane of the paper and out of the paper

Incorrect

Q 111PhysicsSection A • MCQalternating current

+1 / -0

A coil has a resistance of $30 Ω$ and an inductive reactance of $20 Ω$ at 50 Hz frequency. If an AC source of $200 V, 100 Hz$ is connected across the coil, the current in the coil is

$2 𝐴$

Incorrect

$\frac{20}{\sqrt{\sqrt 13}} A$

Incorrect

4 A

Incorrect

8 A

Incorrect

Q 112PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A current $𝑖$ is flowing through a wire of length ' $𝐿$ '. If it is made into a circular loop of one turn, then its magnetic moment is

$\frac{𝐿_{2}^{𝑖}}{4 𝜋}$

Incorrect

$\frac{𝐿^{2}}{4 𝜋}$

Incorrect

$\frac{4 𝜋}{𝐿^{2} 𝑖}$

Incorrect

$4 𝜋 𝐿^{2} 𝑖$

Incorrect

Q 113PhysicsSection A • MCQatoms and nuclei

+1 / -0

Energy released in the fission of a single uranium nucleus is 200 MeV . Then the number of fissions per second to produce 5 mW power is

$1.56 \times 10^{8}$

Incorrect

$1.56 \times 10^{13}$

Incorrect

$3.12 \times 10^{8}$

Incorrect

$3.12 \times 10^{13}$

Incorrect

Q 114PhysicsSection A • MCQelectromagnetic waves

+1 / -0

Match the electromagnetic radiations given in List-I with their uses given in List-II

List-I		List-II
(A)	$𝑋$ -rays	(P)	Remote switches
(B)	UV-rays	(Q)	Finger prints in forensic Labs
(C)	Radiowaves	(R)	Crystal structure study
(D)	IR-rays	(S)	TV communication system

A-Q, B-R, C-P, D-S

Incorrect

A-R, B-Q, C-S, D-P

Incorrect

A-R, B-S, C-Q, D-P

Incorrect

A-S, B-R, C-Q, D-P

Incorrect

Q 115PhysicsSection A • MCQatoms and nuclei

+1 / -0

The ratio of longest wavelengths of the spectral lines in the Lyman and Balmer series of hydrogen spectrum is

$\frac{3}{23}$

Incorrect

$\frac{5}{27}$

Incorrect

$\frac{7}{29}$

Incorrect

$\frac{9}{31}$

Incorrect

Q 116PhysicsSection A • MCQdual nature of radiation

+1 / -0

The graph given in the figure shows the variation of photo current $(𝐼)$ and the applied voltage ( $𝑉$ ) for two different materials and for two different intensities of the incident radiations. Then the curves which represent the same material are

qImage--dual-nature-of-radiation-modern-physics-Jeemate

1 and 3

Incorrect

1 and 4

Incorrect

2 and 3

Incorrect

3 and 4

Incorrect

Q 117PhysicsSection A • MCQatoms and nuclei

+1 / -0

Half-life of a radioactive substance $𝐴$ is two times the half-life of another radioactive substance $𝐵$ . Initially the number of nuclei of $𝐴$ and $𝐵$ are $𝑁_{𝐴}$ and $𝑁_{𝐵}$ respectively. After three half-lives of $𝐴$ , the number of nuclei of both are equal. Then $𝑁_{𝐴} / 𝑁_{𝐵}$ is

$1 / 3$

Incorrect

$1 / 4$

Incorrect

$1 / 6$

Incorrect

$\frac{1}{8}$

Incorrect

Q 118PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

When an $𝑛$ -type semiconductor is heated

number of electrons increases while that of electrons decreases

Incorrect

number of holes increases while that of electrons decreases

Incorrect

number of holes and electrons do not change

Incorrect

number of holes and electrons increases equally

Incorrect

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

5 logic gates are connected as shown in the figure. If $𝐴$ and $𝐵$ are the inputs, $𝑌$ is the output then the truth table of the circuit is

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

$\begin{matrix} A & B & Y \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 1 & 0 \end{matrix}$

Incorrect

$\begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 1 & 1 \end{matrix}$

Incorrect

$\begin{matrix} 𝐴 & 𝐵 & 𝑌 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}$

Incorrect

$\begin{matrix} 𝐀 & 𝐁 & 𝐘 \\ 0 & 0 & 1 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}$

Incorrect

Q 120PhysicsSection A • MCQcommunication systems

+1 / -0

Consider the following statements regarding digital signals

(i) provide a continuous set of values

(ii) represent values as discrete steps

(iii) can utilise binary system

(iv) are in the form of rectangular waves

Then the true statements are

(i), (ii)

Incorrect

(ii), (iii)

Incorrect

(ii), (iii), (iv)

Incorrect

(i), (ii), (iii), (iv)

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

A 100 W bulb emits light of wavelength

$𝑥 \overset{o}{A}$ . What is the value of $𝑥$ , if the number of photons emitted is $2.0 \times 10^{20} s^{- 1}$ ?

$(ℎ = 6.63 \times 10^{- 34} Js, 1 W = 1 {Js}^{- 1})$

3578

Incorrect

4978

Incorrect

3978

Incorrect

4578

Incorrect

Q 122ChemistrySection A • MCQatomic structure

+1 / -0

The ratio of the difference in energy between the first and second Bohr orbits to that between the second and third orbit is

$\frac{5}{27}$

Incorrect

$\frac{27}{5}$

Incorrect

$\frac{4}{9}$

Incorrect

$\frac{9}{4}$

Incorrect

Q 123ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Assertion (A) First ionisation enthalpy of oxygen is less than that of nitrogen.

Reason (R) Atoms with half-filled or completely filled orbitals are less stable.

The correct option among the following is

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 124ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

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

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 125ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

Arrange the molecules $B_{2}, {He}_{2}, N_{2}$ and $C_{2}$ in the increasing order of their bond order values.

$C_{2} < {He}_{2} < B_{2} < N_{2}$

Incorrect

$N_{2} < B_{2} < C_{2} < {He}_{2}$

Incorrect

${He}_{2} < B_{2} < C_{2} < N_{2}$

Incorrect

${He}_{2} < C_{2} < N_{2} < B_{2}$

Incorrect

Q 126ChemistrySection A • MCQstates of matter

+1 / -0

Two containers $𝐴$ and $𝐵$ contain ${CO}_{2}$ gas. Pressure, volume and absolute temperature of the gas in $𝐴$ are 4 times more compared to that in $𝐵$ . The mass of the gas in $𝐵$ is $𝑥 g$ , then the mass of the gas in $𝐴$ will be

$\frac{𝑥}{2} 𝑔$

Incorrect

$4 \times 𝑔$

Incorrect

$2 \times g$

Incorrect

$16 \times g$

Incorrect

Q 127ChemistrySection A • MCQredox reactions

+1 / -0

The oxidation states of three carbon atoms in carbon suboxide $(C_{3} O_{2})$ respectively are

$+ 2, 0, + 2$

Incorrect

$+ 2, 0, + 4$

Incorrect

$+ 4, + 2, + 2$

Incorrect

$- 2, + 2, 0$

Incorrect

Q 128ChemistrySection A • MCQthermodynamics

+1 / -0

At $𝑇 (K) 2$ mole of an ideal gas is allowed to expand reversibly and isothermally from a pressure of 10 atmospheres to 1 atmosphere. The work done (in kJ ) is $(𝑅 = 8.3 {JK}^{- 1} {mol}^{- 1})$

$- 3.82 \times 10^{- 1} \times 𝑇$

Incorrect

$- 4.82 \times 10^{- 1} \times 𝑇$

Incorrect

$- 2.82 \times 10^{- 2} \times 𝑇$

Incorrect

$- 3.82 \times 10^{- 2} \times 𝑇$

Incorrect

Q 129ChemistrySection A • MCQionic equilibrium

+1 / -0

At 298 K the molar solubility of $Cd (OH)_{2}$ in $0.1 M {KOH}_{OH}$ solution is $𝑥 \times 10^{- 𝑦}$ . The values of $𝑥$ and $𝑦$ are respectively.

(At $298 K, 𝐾_{𝑠 𝑝}$ of $Cd (OH)_{2} = 2.5 \times 10^{- 14}$ )

$2.5, 14$

Incorrect

25,13

Incorrect

25,14

Incorrect

$2.5, 16$

Incorrect

Q 130ChemistrySection A • MCQp block elements

+1 / -0

Zeolite is a silicate of two metal ions $𝑋$ and $𝑌 . 𝑋$ and $𝑌$ are respectively

${Ca}^{2 +}, {Na}^{+}$

Incorrect

${Mg}^{2 +}, {Na}^{+}$

Incorrect

${Na}^{+}, {Al}^{3 +}$

Incorrect

${Ca}^{2 +}, {Mg}^{2 +}$

Incorrect

Q 131ChemistrySection A • MCQs block elements

+1 / -0

Identify the incorrect reaction from the following.

$2 {NaNO}_{3} ⟶ 2 {NaNO}_{2} + O_{2}$

Incorrect

$2 {LiNO}_{3} ⟶ 2 {LiNO}_{2} + O_{2}$

Incorrect

$2 Pb {({NO}_{3})}_{2} ⟶ 2 PbO + 4 {NO}_{2} + O_{2}$

Incorrect

${Mg}_{2} C_{3} + H_{2} O ⟶ {CH}_{3} C \equiv CH + Mg (OH)_{2}$

Incorrect

Q 132ChemistrySection A • MCQatomic structure

+1 / -0

In the reaction I and II the covalencies of Be and Al in $𝑋$ and $𝑌$ are respectively

I. $Be (OH)_{2} + \underset{(Excess)}{NaOH} ⟶ 𝑋$

II. $Al (OH)_{3} + \underset{(Excess)}{NaOH} ⟶ 𝑌$

4,6

Incorrect

4,4

Incorrect

6, 4

Incorrect

3,6

Incorrect

Q 133ChemistrySection A • MCQperiodic classification of elements

+1 / -0

Tha atomic radius of gallium is less than that of aluminium. This is due to

greater shielding power of s-electrons of gallium atom.

Incorrect

poor shielding power of s-electrons of gallium.

Incorrect

poor shielding power of $𝑑$ -electrons of gallium.

Incorrect

greater shielding power of $𝑑$ -electrons of gallium.

Incorrect

Q 134ChemistrySection A • MCQp block elements

+1 / -0

Which of the following has lowest melting point?

Si

Incorrect

Ge

Incorrect

Sn

Incorrect

Pb

Incorrect

Q 135ChemistrySection A • MCQhydrocarbons

+1 / -0

Arrange the following in the correct order of their acidic strength.

I. $H_{2} C = {CH}_{2}$

II. $CH \equiv CH$

III. ${CH}_{3} - C \equiv CH$

IV. ${CH}_{3} - {CH}_{3}$

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 136ChemistrySection A • MCQhydrocarbons

+1 / -0

$C_{3} H_{4} + H_{2} O {\to\leftarrow}_{333 K}^{{Hg}^{2 +} / H^{+}} [𝑋] \overset{Tautomerisation}{⇌} 𝑌$

$𝑋$ and $𝑌$ are respectively

unsaturated alcohol, aldehyde

Incorrect

saturated alcohol, ketone

Incorrect

unsaturated alcohol, ketone

Incorrect

saturated alcohol, aldehyde

Incorrect

Q 137ChemistrySection A • MCQhydrocarbons

+1 / -0

Addition of HBr to propene in presence of a peroxide takes place contrary to Markownikoff rule. This can be explained by the mechanism involving

electrophile

Incorrect

free radical

Incorrect

nucleophile

Incorrect

carbene

Incorrect

Q 138ChemistrySection A • MCQhydrocarbons

+1 / -0

The rate of attack of an electrophile is least when $𝑋$ in the given compound is

qImage--hydrocarbons-organic-chemistry-Jeemate

$- {NO}_{2}$

Incorrect

$- {CH}_{3}$

Incorrect

$- 𝑂 𝐻$

Incorrect

$- {NH}_{2}$

Incorrect

Q 139ChemistrySection A • MCQsolid state

+1 / -0

In the structure of a solid, W atoms are located at the cube corners of the unit cell, O atoms are located at the cube edges and Na atoms at the cube centres. The formula of the compound is

${NaWO}_{3}$

Incorrect

${NaWO}_{2}$

Incorrect

${Na}_{2} W_{2} O_{2}$

Incorrect

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

Incorrect

Q 140ChemistrySection A • MCQsolutions

+1 / -0

An aqueous solution of a non-volatile solute boils at ${100.17}^{\circ} C$ . The temperature at which this solution will freeze (in $^{\circ} C$ ) is

$\begin{matrix} (𝐾_{𝑏} (H_{2} O) = {0.512}^{\circ} C kg {mol}^{- 1}, \\ 𝐾_{𝑓} (H_{2} O) = {1.86}^{\circ} C kg {mol}^{- 1}) \end{matrix}$

-0.62

Incorrect

-0.512

Incorrect

-1.24

Incorrect

-1.86

Incorrect

Q 141ChemistrySection A • MCQchemical kinetics

+1 / -0

A possible mechanism for the gaseous reaction $2 H_{2} + 2 NO ⟶ 2 H_{2} O + N_{2}$ is

Step 1:2 $NO ⇌ N_{2} O_{2}$

Step 2 : $N_{2} O_{2} + H_{2} ⟶ N_{2} O + H_{2} O$ (slow)

Step 3: $N_{2} O + H_{2} ⟶ N_{2} + H_{2} O$

The rate law for this reaction is

$𝑅 = 𝑘 [NO]^{2} {[H_{2}]}^{2}$

Incorrect

$𝑅 = 𝑘 [NO] {[H_{2}]}^{2}$

Incorrect

$𝑅 = 𝑘 [NO]^{1 / 2} [H_{2}]$

Incorrect

$𝑅 = 𝑘 [NO]^{2} [H_{2}]$

Incorrect

Q 142ChemistrySection A • MCQelectrochemistry

+1 / -0

The reduction potential of a half-cell consisting of a Pt electrode immersed in $2.0 M {Fe}^{2 +}$ and $0.02 M {Fe}^{3 +}$ solution (in V) is

Given : $(\frac{2.303 𝑅 𝑇}{𝐹} = 0.059, 𝐸_{\circ}^{{Fe}^{3 +} ∣ {Fe}^{2 +}} = 0.771 V)$

0.543

Incorrect

0.653

Incorrect

0.733

Incorrect

0.822

Incorrect

Q 143ChemistrySection A • MCQsurface chemistry

+1 / -0

The sol prepared by Bredig's arc method is $𝑋$ and the charge of sol particles of it is $𝑞 . 𝑋$ and $𝑞$ are respectively

metal sol, -ve

Incorrect

metal sol, $+ 𝑣 𝑒$

Incorrect

metal sulphide sol, -ve

Incorrect

${TiO}_{2}$ sol, +ve

Incorrect

Q 144ChemistrySection A • MCQmetallurgy

+1 / -0

The metal which is refined by Mond process is $(𝑋)$ , by van Arkel process is $(𝑌)$ and by zone refining is $(𝑍), 𝑋, 𝑌$ and Z respectively are

$Ni, Zr, Ga$

Incorrect

$Zr, Ni, Ga$

Incorrect

$Ga, Ni, Zr$

Incorrect

$Ni, Ga, Zr$

Incorrect

Q 145ChemistrySection A • MCQd and f block elements

+1 / -0

The product formed during thermal decomposition of ammonium dichromate are

$O_{2}, H_{2} O, Cr (OH)_{3}$

Incorrect

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

Incorrect

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

Incorrect

$N_{2} O, Cr (OH)_{3}$

Incorrect

Q 146ChemistrySection A • MCQp block elements

+1 / -0

Among the hydrides of group 16 elements, the hydride $𝑋$ has lowest boiling point and the hydride $𝑌$ has highest boiling point. $𝑋$ and $𝑌$ respectively are

$H_{2} Te, H_{2} Se$

Incorrect

$H_{2} O, H_{2} Te$

Incorrect

$H_{2} S, H_{2} Te$

Incorrect

$H_{2} S, H_{2} O$

Incorrect

Q 147ChemistrySection A • MCQp block elements

+1 / -0

Sodium nitrite with hydrochloric acid gives water alongwith two nitrogen oxides. They are

$NO, {NO}_{2}$

Incorrect

${NO}_{2}, N_{2} O_{3}$

Incorrect

${NO}_{2}, N_{2} O$

Incorrect

$NO, N_{2} O_{5}$

Incorrect

Q 148ChemistrySection A • MCQp block elements

+1 / -0

Identify the incorrect statement about the interhalogen compounds.

ICl is more reactive than $I_{2}$ .

Incorrect

They are diamagnetic in nature.

Incorrect

The products of ICl and water are $HI + HOCl$ .

Incorrect

They act as fluorinating agents.

Incorrect

Q 149ChemistrySection A • MCQd and f block elements

+1 / -0

In +2 oxidation state, which of the following lanthanoids act as reducing agents?

$Ce, \Pr$

Incorrect

Eu, Gd

Incorrect

Eu, Yb

Incorrect

Lu, Er

Incorrect

Q 150ChemistrySection A • MCQcoordination compounds

+1 / -0

The sum of oxidation state and co-ordination number of central metal atom is maximum with respect to which of the following complex?

$K_{3} [Cr {(C_{2} O_{4})}_{3}]$

Incorrect

$[Cr (CO)_{6}]$

Incorrect

$K_{2} [{PtCl}_{6}]$

Incorrect

$K_{4} [Fe (CN)_{6}]$

Incorrect

Official Correct Answer:Option (C)

Step-by-Step Solution:

Compound	Coordination no. (a)	Oxidation no. (b)	Sum ( $a + b$ )
$K_{3} [Cr {(C_{2} O_{4})}_{3}]$	6 ( $C_{2} O_{4}^{2 -}$ is bidentate ligand)	$\begin{matrix} + 1 \times 3 + x \\ 3 \times (- 2) = 0 \\ x = + 3 \end{matrix}$	9
$Cr (CO)_{6}$	6	$x + 0 \times 6 = 0$	6
$K_{2} [{PtCl}_{6}]$	6	$\begin{matrix} 1 (2) + x + (- 1) 6 \\ x = + 4 \end{matrix}$	10
$K_{4} [Fe (CN)_{6}]$	6	$\begin{matrix} (1 \times 4) + x \\ + (- 1) \times 6 = 0 \\ x = + 2 \end{matrix}$	8

Thus, the sum of oxidation state and coordination number of central metal atom is maximum in $K_{2} [{PtCl}_{6}]$ .

Q 151ChemistrySection A • MCQpolymers

+1 / -0

$Match the following.$

$\begin{matrix} List-I (Polymer type) & List-II (Example) \\ A. & Fibre & I. & Bakelite \\ B. & Elastomer & II. & Polystyrene \\ C. & Thermosetting polymer & III. & Neoprene \\ D. & Thermosplastic polymer & IV. & Dacron \end{matrix}$

The correct answer is

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 152ChemistrySection A • MCQbiomolecules

+1 / -0

From the following, the correct statements about polysaccharides are

I. Starch is a polymer of $𝛼 - D (+)$ -glucose.

II. Amylose component of starch is not soluble in water.

III. Amylose is a branched chain polymer of $𝛼 - D (+)$ -glucose.

IV. Cellulose is a straight chain polymer of $𝛽 - D (+)$ -glucose units.

I and IV only

Incorrect

II and III only

Incorrect

II and IV only

Incorrect

I and III only

Incorrect

Q 153ChemistrySection A • MCQchemistry in everyday life

+1 / -0

Which of the following acts as antihistamine?

Heroin

Incorrect

Dimetapp

Incorrect

Nardil

Incorrect

Veronal

Incorrect

Q 154ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

Identify the halogen exchange reaction from the following.

Sandmeyer reaction

Incorrect

Swarts reaction

Incorrect

Stephen reaction

Incorrect

Wurtz reaction

Incorrect

Q 155ChemistrySection A • MCQalcohols phenols and ethers

+1 / -0

Identify the major product $𝑌$ in the given reaction sequence.

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

Incorrect

${CH}_{3} - {CH}_{2} - {CH}_{2} OH$

Incorrect

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

Incorrect

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

Incorrect

Q 156ChemistrySection A • MCQaldehyde and ketone

+1 / -0

Conversion of $𝑋$ into $𝑌$ is an example of the reaction

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

Rosenmund reduction

Incorrect

Clemmensen reduction

Incorrect

Wolff-Kishner reduction

Incorrect

Stephen reduction

Incorrect

Q 157ChemistrySection A • MCQaldehyde and ketone

+1 / -0

The main reactants involved in Etard reaction are

Toluene $+ {CrO}_{2} {Cl}_{2}$

Incorrect

Toluene $+ {CrO}_{3} + {({CH}_{3} CO)}_{2} O$

Incorrect

Toluene $+ {Cl}_{2} / ℎ 𝑣$

Incorrect

Benzene $+ CO + HCl /$ Anhy. ${AlCl}_{3}$

Incorrect

Q 158ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

$The major product ’ 𝑍 ’ in the reaction sequence is$

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 159ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

Arrange the following in the order of decreasing basicity.

I. $RN = CH 𝑅^{1}$

II. $RC \equiv N$

III. ${RNH}_{2}$

I $>$ III $>$ II

Incorrect

III $>$ I $>$ II

Incorrect

II $>$ III $>$ I

Incorrect

II $>$ I $>$ III

Incorrect

Q 160ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

Which one of the following gives a foul-smelling substance when treated with chloroform and alcoholic KOH ?

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Case I	Case II
$1 + 1 + 3$	$1 + 2 + 2$	Total
$1 + 3 + 1$	$2 + 2 + 1$	$= 192 + 432$
$3 + 1 + 1$	$2 + 1 + 2$	$= 624$
$= 3 \times^{4} C_{1} \times^{4} C_{1} \times^{4} C_{3}$	$= 3 \times^{4} C_{1}$
$= 3 \times 4 \times 4 \times 4$	$\times^{4} C_{2} \times^{4} C_{2}$
$= 192$	$= 3 \times 4 \times 6 \times 6$
	$= 432$

TG EAPCET 2023 14th May Evening Shift Question Paper with Solutions