Ap Eapcet 2025 27th May Morning Shift Question Paper Question Paper with Solutions | AP EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQfunctions

+1 / -0

If $𝑓 : 𝑅 \to 𝐴$ , defined by $𝑓 (𝑥) = \cos 𝑥 + \sqrt{\sqrt 3} \sin 𝑥 - 1$ is an onto function then $𝐴 =$

$[- 1, 2]$

Incorrect

$[- \sqrt{\sqrt 3}, \sqrt{\sqrt 3}]$

Incorrect

$[- 3, 1]$

Incorrect

$[- 2, 2]$

Incorrect

Q 2MathematicsSection A • MCQfunctions

+1 / -0

Let $𝑔 (𝑥) = 1 + 𝑥 - [𝑥]$ and $^{'}$

$𝑓 (𝑥) = ⎧⎩⎨ \begin{matrix} - 1, & 𝑥 < 0 \\ 0, & 𝑥 = 0, [𝑥] denotes the greatest integer less \\ 1, & 𝑥 > 0 \end{matrix}$

than or equal to $𝑥$ . Then for all $𝑥, 𝑓 (𝑔 (𝑥)) =$

1

Incorrect

$𝑥$

Incorrect

$𝑓 (𝑥)$

Incorrect

$𝑔 (𝑥)$

Incorrect

Q 3MathematicsSection A • MCQbinomial theorem

+1 / -0

The remainder obtained when $(2 𝑚 + 1)^{2 𝑛} (𝑚, 𝑛 \in 𝑁)$ is divided by 8 is

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

A value of $𝜃$ lying between 0 and $𝜋 / 2$ and satisfying $∣ \begin{matrix} 1 + \sin^{2} 𝜃 & \cos^{2} 𝜃 & 4 \sin 4 𝜃 \\ \sin^{2} 𝜃 & 1 + \cos^{2} 𝜃 & 4 \sin 4 𝜃 \\ \sin^{2} 𝜃 & \cos^{2} 𝜃 & 1 + 4 \sin 4 𝜃 \end{matrix} ∣ = 0$ is

$\frac{5 𝜋}{24}$

Incorrect

$\frac{7 𝜋}{24}$

Incorrect

$\frac{𝜋}{8}$

Incorrect

$\frac{3 𝜋}{8}$

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

If the system of equations $2 𝑥 + 𝑝 𝑦 + 6 𝑧 = 8$ , $𝑥 + 2 𝑦 + 𝑞 𝑧 = 5$ and $𝑥 + 𝑦 + 3 𝑧 = 4$ has infinitely many solutions, then $𝑝 =$

-1

Incorrect

2

Incorrect

3

Incorrect

-3

Incorrect

Q 6MathematicsSection A • MCQmatrices and determinants

+1 / -0

If $𝑥^{𝑎} 𝑦^{𝑏} = 𝑒^{𝑚}, 𝑥^{𝑐} 𝑦^{𝑑} = 𝑒^{𝑛}, Δ_{1} = ∣ \begin{matrix} 𝑚 & 𝑏 \\ 𝑛 & 𝑑 \end{matrix} ∣$ , $Δ_{2} = ∣ \begin{matrix} 𝑎 & 𝑚 \\ 𝑐 & 𝑛 \end{matrix} ∣, Δ_{3} = ∣ \begin{matrix} 𝑎 & 𝑏 \\ 𝑐 & 𝑑 \end{matrix} ∣$ , then the values of $𝑥$ and $𝑦$ are respectively ( $𝑒$ is the base of natural logarithm)

$\frac{Δ_{1}}{Δ_{3}}$ and $\frac{Δ_{2}}{Δ_{3}}$

Incorrect

$\frac{Δ_{2}}{Δ_{1}}$ and $\frac{Δ_{3}}{Δ_{1}}$

Incorrect

$\log (\frac{Δ_{1}}{Δ_{3}})$ and $\log (\frac{Δ_{2}}{Δ_{3}})$

Incorrect

$𝑒^{\frac{Δ_{1}}{Δ_{3}}}$ and $𝑒^{\frac{Δ_{2}}{Δ_{3}}}$

Incorrect

Q 7MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑧$ and $𝑤$ are two non-zero complex numbers such that $| 𝑧 𝑤 | = 1$ and $\arg 𝑧 - \arg 𝑤 = \frac{𝜋}{2}$ , then $\bar{𝑧} 𝑤 =$

$𝑖$

Incorrect

-1

Incorrect

1

Incorrect

$- 𝑖$

Incorrect

Q 8MathematicsSection A • MCQcomplex numbers

+1 / -0

Let $𝑧$ satisfy $| 𝑧 | = 1, 𝑧 = 1 - \bar{𝑧}$ and $Im (𝑧) > 0$

Statement $𝐈 𝑧$ is a real number

Statement II Principal argument of $𝑧$ is $\frac{𝜋}{3}$ .

Then,

Statement I is true, Statement II is true and Statement II is a correct explanation of Statement I

Incorrect

Statement I is true, Statement II is true, but Statement II is not a correct explanation of Statement I

Incorrect

Statement I is false, Statement II is true

Incorrect

Statement I is true, Statement II is false

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝑤_{1}$ and $𝑤_{2}$ are two non-zero complex numbers and $𝑎, 𝑏$ are non-zero real numbers such that $| 𝑎 𝑤_{1} + 𝑏 𝑤_{2} | = | 𝑎 𝑤_{1} - 𝑏 𝑤_{2} |$ , then $\frac{𝑤_{1}}{𝑤_{2}}$ is

a positive real number

Incorrect

a negative real number

Incorrect

zero

Incorrect

purely imaginary number

Incorrect

Q 10MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼$ is the common root of the quadratic equations $𝑥^{2} - 5 𝑥 + 4 𝑎 = 0, 𝑥^{2} - 2 𝑎 𝑥 - 8 = 0$ , where $𝑎 \in 𝑅$ , then the value $𝛼^{4} - 𝛼^{3} + 68$ is

260

Incorrect

250

Incorrect

0

Incorrect

240

Incorrect

Q 11MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼, 𝛽$ are the roots of $𝑥^{2} - 5 𝛾 𝑥 - 6 𝛿 = 0$ and $𝛾, 𝛿$ are the roots of $𝑥^{2} - 5 𝛼 𝑥 - 6 𝛽 = 0$ , then $𝛼 + 𝛽 + 𝛾 + 𝛿 =$

0

Incorrect

125

Incorrect

144

Incorrect

180

Incorrect

Q 12MathematicsSection A • MCQlogarithms

+1 / -0

The equation $𝑥^{\frac{3}{4} {(\log_{2} 𝑥)}^{2} + \log_{2} 𝑥 - \frac{5}{4}} = \sqrt{\sqrt 2}$ has

no real roots

Incorrect

only one real solution

Incorrect

exactly two real solutions

Incorrect

exactly three real solutions

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If $𝛼, 𝛽, 𝛾$ are the roots of the equation $𝑥^{3} + 𝑝 𝑥^{2} + 𝑞 𝑥 + 𝑟 = 0$ , then $(𝛼 + 𝛽) (𝛽 + 𝛾) (𝛾 + 𝛼) =$

$𝑝 - 𝑞 𝑟$

Incorrect

$𝑞 - 𝑟 𝑝$

Incorrect

$𝑟 - 𝑝 𝑞$

Incorrect

$𝑟 + 𝑝 𝑞$

Incorrect

Q 14MathematicsSection A • MCQpermutations and combinations

+1 / -0

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is

$18 \times 7$ !

Incorrect

$24 \times 7!$

Incorrect

$36 \times 7$ !

Incorrect

$72 \times 7$ !

Incorrect

Q 15MathematicsSection A • MCQbinomial theorem

+1 / -0

$\sum_{15}^{𝑟 = 1} 𝑟^{2} (\frac{^{15} 𝐶_{𝑟}}{^{15} 𝐶_{𝑟 - 1}}) =$

560

Incorrect

680

Incorrect

840

Incorrect

1020

Incorrect

Q 16MathematicsSection A • MCQpermutations and combinations

+1 / -0

A string of letters is to be formed by using 4 letters from all the letters of the word "MATHEMATICS". The number of ways this can be done such that two letters are of same kind and the other two are of different kind is

756

Incorrect

252

Incorrect

840

Incorrect

360

Incorrect

Q 17MathematicsSection A • MCQbinomial theorem

+1 / -0

$\frac{1}{81^{𝑛}} -^{2 𝑛} 𝐶_{1} \frac{10}{81^{𝑛}} +^{2 𝑛} 𝐶_{2} \frac{10^{2}}{81^{𝑛}} - \dots + \frac{10^{2 𝑛}}{81^{𝑛}} =$

0

Incorrect

$(- 1)^{𝑛}$

Incorrect

1

Incorrect

81

Incorrect

Q 18MathematicsSection A • MCQbinomial theorem

+1 / -0

If $𝑥$ is positive real number and the first negative term in the expansion of $(1 + 𝑥)^{\frac{27}{5}}$ is $𝑡_{𝑘}$ , then $𝑘 =$

5

Incorrect

6

Incorrect

7

Incorrect

8

Incorrect

Q 19MathematicsSection A • MCQindefinite integration

+1 / -0

If $\frac{𝑥^{2}}{(𝑥^{2} + 2) (𝑥^{4} - 1)} = \frac{𝐴}{𝑥^{2} - 1} + \frac{𝐵}{𝑥^{2} + 1} + \frac{𝐶}{𝑥^{2} + 2}$ , then $𝐴 + 𝐵 - 𝐶 =$

0

Incorrect

$\frac{4}{3}$

Incorrect

$\frac{3}{4}$

Incorrect

2

Incorrect

Q 20MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\cos x+\sin x=\frac{1}{2}$ and $0<x<\pi$ , then $\tan x=$

$\frac{1 + \sqrt{\sqrt 7}}{4}$

Incorrect

$\frac{1 - \sqrt{\sqrt 7}}{4}$

Incorrect

$\frac{4 - \sqrt{\sqrt 7}}{3}$

Incorrect

$- \frac{(4 + \sqrt{\sqrt 7})}{3}$

Incorrect

Q 21MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $\sin 𝜃 + 2 \cos 𝜃 = 1$ and $𝜃$ belongs to 4 th quadrant (not lying on the coordinate axes), then $7 \cos 𝜃 + 6 \sin 𝜃 =$

$\frac{4}{17}$

Incorrect

2

Incorrect

$\frac{7}{17}$

Incorrect

$\frac{4}{5}$

Incorrect

Q 22MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

If $𝐴$ and $𝐵$ are acute angles satisfying $3 \cos^{2} 𝐴 + 2 \cos^{2} 𝐵 = 4$ and $\frac{3 \sin 𝐴}{\sin 𝐵} = \frac{2 \cos 𝐵}{\cos 𝐴}$ , then $𝐴 + 2 𝐵 =$

$\frac{𝜋}{2}$

Incorrect

$\frac{𝜋}{3}$

Incorrect

$\frac{𝜋}{4}$

Incorrect

$\frac{𝜋}{6}$

Incorrect

Q 23MathematicsSection A • MCQtrigonometric equations

+1 / -0

Statement I In the interval $[0, 2 𝜋]$ , the number of common solutions of the equations $2 \sin^{2} 𝜃 - \cos 2 𝜃 = 0$ and $2 \cos^{2} 𝜃 - 3 \sin 𝜃 = 0$ is two.

Statement II The number of solutions of $2 \cos^{2} 𝜃 - 3 \sin 𝜃 = 0$ in $[0, 𝜋]$ is two.

Statement I and Statement II are both true

Incorrect

Statement I is true, Statement II is false

Incorrect

Statement I is false, Statement II is true

Incorrect

Statement I and Statement II are both false

Incorrect

Q 24MathematicsSection A • MCQinverse trigonometric functions

+1 / -0

The equation $\cos^{- 1} (1 - 𝑥) - 2 \cos^{- 1} 𝑥 = \frac{𝜋}{2}$ has

no solution

Incorrect

only one solution

Incorrect

two solutions

Incorrect

more than two solutions

Incorrect

Q 25MathematicsSection A • MCQcomplex numbers

+1 / -0

If $\sinh^{- 1} (2) + \sinh^{- 1} (3) = 𝛼$ , then $\sinh 𝛼 =$

$2 \sqrt{\sqrt 5} + 3 \sqrt{\sqrt 10}$

Incorrect

$2 \sqrt{\sqrt 10} + 4 \sqrt{\sqrt 5}$

Incorrect

$3 \sqrt{\sqrt 10} + 4 \sqrt{\sqrt 5}$

Incorrect

$2 \sqrt{\sqrt 10} + 3 \sqrt{\sqrt 5}$

Incorrect

Q 26MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $𝐴, 𝐵, 𝐶$ are in arithmetic progression, then

$\sqrt{\sqrt 𝑎^{2} - 𝑎 𝑐 + 𝑐^{2}} \cdot \cos (\frac{𝐴 - 𝐶}{2}) =$

$𝑎 + 𝑐$

Incorrect

$\frac{𝑎 + 𝑐}{2}$

Incorrect

$\frac{𝑎 + 𝑐 - 𝑏}{2}$

Incorrect

$𝑎 - 𝑐$

Incorrect

Q 27MathematicsSection A • MCQproperties of triangles

+1 / -0

If in $△ 𝐴 𝐵 𝐶, 𝐵 = 45^{\circ}, 𝑎 = 2 (\sqrt{\sqrt 3} + 1)$ and area of $△ 𝐴 𝐵 𝐶$ is $6 + 2 \sqrt{\sqrt 3}$ sq. units, then the side $𝑏 =$

$8 - 4 \sqrt{\sqrt 3}$

Incorrect

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

Incorrect

$4 \sqrt{\sqrt 2}$

Incorrect

4

Incorrect

Q 28MathematicsSection A • MCQproperties of triangles

+1 / -0

In a $△ 𝐴 𝐵 𝐶$ , if $\sin^{2} 𝐵 = \sin 𝐴$ and $2 \cos^{2} 𝐴 = 3 \cos^{2} 𝐵$ , then the triangle is

acute angled

Incorrect

obtuse angled

Incorrect

right angled

Incorrect

equilateral

Incorrect

Q 29MathematicsSection A • MCQvector algebra

+1 / -0

$𝑃$ is the circumcentre of $△ 𝐴 𝐵 𝐶$ . If the position vectors of $𝐴, 𝐵, 𝐶$ and $𝑃$ are $𝐚, 𝐛, 𝐜, \frac{𝐚 + 𝐛 + 𝐜}{4}$ respectively, then the position vector of the orthocentre of this triangle is

$𝐚 + 𝐛 + 𝐜$

Incorrect

$\frac{𝐚 + 𝐛 + 𝐜}{2}$

Incorrect

$- (\frac{𝐚 + 𝐛 + 𝐜}{2})$

Incorrect

0

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

If the position vectors of $𝐴, 𝐵, 𝐶, 𝐷$ are $\hat{𝐢} + 2 \hat{𝐣} + 2 \hat{𝐤}, 2 \hat{𝐢} - \hat{𝐣}, \hat{𝐢} + \hat{𝐣} + 3 \hat{𝐤}$ and $4 \hat{𝐣} + 5 \hat{𝐤}$ respectively, then the quadrilateral $𝐴 𝐵 𝐶 𝐷$ is a

square

Incorrect

rectangle

Incorrect

rhombus

Incorrect

parallelogram

Incorrect

Q 31MathematicsSection A • MCQvector algebra

+1 / -0

The set of all real values of $𝑐$ so that the angle between the vectors $𝐚 = 𝑐 𝑥 \hat{𝐢} - 6 \hat{𝐣} + 3 \hat{𝐤}$ and $𝐛 = 𝑥 \hat{𝐢} + 2 \hat{𝐣} + 2 𝑐 𝑥 \hat{𝐤}$ is an obtuse angle for all real $𝑥$ is

$(0, \frac{4}{3}]$

Incorrect

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

Incorrect

$(- \frac{2}{3}, 0)$

Incorrect

$[\frac{- 4}{3}, 0]$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐚 = 2 \hat{𝐢} + \hat{𝐣} + 3 \hat{𝐤}, 𝐛 = 3 \hat{𝐢} + 3 \hat{𝐣} + \hat{𝐤}$ and $𝐜 = \hat{𝐢} - 2 \hat{𝐣} + 3 \hat{𝐤}$ be three vectors. If $𝐫$ is a vector such that $𝐫 \times 𝐚 = 𝐫 \times 𝐛$ and $𝐫 \cdot 𝐜 = 18$ , then the magnitude of the orthogonal projection of $4 \hat{𝐢} + 3 \hat{𝐣} - \hat{𝐤}$ on $𝐫$ is

4

Incorrect

6

Incorrect

12

Incorrect

24

Incorrect

Q 33MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐮, 𝐯, 𝐰$ are non-coplanar vectors and $𝑝, 𝑞$ are real numbers, then the equality $[3 𝐮 𝑝 𝐯 𝑝 𝐰] - [𝑝 𝐯 𝐰 𝑞 𝐮] - [2 𝐰 𝑞 𝐯 𝑞 𝐮] = 0$ holds for

exactly one ordered pair of $(𝑝, 𝑞)$

Incorrect

exactly two ordered pairs of $(𝑝, 𝑞)$

Incorrect

all ordered pairs of $(𝑝, 𝑞)$

Incorrect

no ordered pair of $(𝑝, 𝑞)$

Incorrect

Q 34MathematicsSection A • MCQstatistics

+1 / -0

If $\sum_{9}^{𝑖 = 1} (𝑥_{𝑖} - 5) = 9$ and $\sum_{9}^{𝑖 = 1} {(𝑥_{𝑖} - 5)}^{2} = 45$ , then the standard deviation of the nine observations $𝑥_{1}, 𝑥_{2}, \dots, 𝑥_{9}$ is

2

Incorrect

4

Incorrect

3

Incorrect

9

Incorrect

Q 35MathematicsSection A • MCQprobability

+1 / -0

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is $\frac{1}{4}$ and the probability that the second student gets qualified in the same exam is $\frac{2}{5}$ , then the probability that atleast one of them gets qualified in that exam is

$\frac{1}{10}$

Incorrect

$\frac{7}{20}$

Incorrect

$\frac{6}{10}$

Incorrect

$\frac{11}{20}$

Incorrect

Q 36MathematicsSection A • MCQprobability

+1 / -0

For three events $𝐴, 𝐵$ and $𝐶$ of a sample space, $𝑃$ (exactly one of $𝐴$ or $𝐵$ occurs ) $= 𝑃$ (exactly one of $𝐵$ or $𝐶$ occurs) $= 𝑃 ($ exactly one of $𝐶$ or $𝐴$ occurs $) = \frac{1}{4}$ . If probability of all the three events occurring simultaneously is $\frac{1}{16}$ , then the probability that atleast one of the events occur is

$\frac{3}{16}$

Incorrect

$\frac{5}{16}$

Incorrect

$\frac{7}{16}$

Incorrect

$\frac{7}{32}$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

$𝐴$ bag $𝑃$ contains 4 red and 5 black balls another bag Q contains 3 red and 6 black balls. If one ball is drawn at random from bag $𝑃$ and two balls are drawn from bag $𝑄$ , then the probability that out of the three balls drawn two are black and one is red, is

$\frac{25}{54}$

Incorrect

$\frac{25}{64}$

Incorrect

$\frac{27}{64}$

Incorrect

$\frac{35}{54}$

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

On every evening, a student either watches TV or reads a book. The probability of watching TV is $\frac{4}{5}$ If he watches TV, the probability that he will fall asleep is $\frac{3}{4}$ and it is $\frac{1}{4}$ when he reads a book. If the student is found to be asleep on an evening the probability that he watched the TV is

$\frac{11}{13}$

Incorrect

$\frac{12}{13}$

Incorrect

$\frac{2}{13}$

Incorrect

$\frac{4}{13}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

Let $𝑋$ be the random variable taking values $1, 2, \dots 𝑛$ for a fixed positive integer $𝑛$ . If $𝑃 (𝑋 = 𝑘) = \frac{1}{𝑛}$ for $1 \leq 𝑘 \leq 𝑛$ , then the variance of $𝑋$ is

$\frac{𝑛^{2} - 1}{12}$

Incorrect

$\frac{𝑛^{2} + 1}{12}$

Incorrect

$\frac{𝑛^{2} - 1}{6}$

Incorrect

$\frac{(𝑛 + 1) (𝑛 + 2)}{6}$

Incorrect

Q 40MathematicsSection A • MCQprobability

+1 / -0

A radar system can detect an enemy plane in one out of ten consecutive scans.

The probability that it can detect an enemy plane atleast twice in four consecutive scans is

0.0422

Incorrect

0.0523

Incorrect

0.0535

Incorrect

0.0623

Incorrect

Q 41MathematicsSection A • MCQcircle

+1 / -0

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are $(1, 2)$ and $(4, 5)$ is

$𝑥^{2} + 𝑦^{2} + 5 𝑥 + 7 𝑦 + 14 = 0$

Incorrect

$3 𝑥 + 3 𝑦 - 1 = 0$

Incorrect

$3 𝑥 + 3 𝑦 + 1 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} - 5 𝑥 - 7 𝑦 + 14 = 0$

Incorrect

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

+1 / -0

The coordinate axes are rotated about the origin in the counter clockwise direction through an angle $60^{\circ}$ . If a and $𝑏$ are the intercepts made on the new axes by a straight line whose equation referred to the original axes is $𝑥 + 𝑦 = 1$ , then $\frac{1}{𝑎^{2}} + \frac{1}{𝑏^{2}} =$

2

Incorrect

3

Incorrect

4

Incorrect

6

Incorrect

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

+1 / -0

The image of a point $(2, - 1)$ with respect to the line $𝑥 - 𝑦 + 1 = 0$ is

$(2, - 3)$

Incorrect

$(- 2, 3)$

Incorrect

$(0, 1)$

Incorrect

$(- 1, 0)$

Incorrect

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

+1 / -0

If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle $\frac{𝜋}{4}$ with the negative $𝑋$ -axis in the negative direction, then the equation of that line is

$𝑥 + 𝑦 + 10 \sqrt{\sqrt 2} = 0$

Incorrect

$𝑥 - 𝑦 - 10 \sqrt{\sqrt 2} = 0$

Incorrect

$𝑥 + 𝑦 - 10 \sqrt{\sqrt 2} = 0$

Incorrect

$𝑥 - 𝑦 + 10 \sqrt{\sqrt 2} = 0$

Incorrect

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

+1 / -0

If one of the lines given by the pair of lines $3 𝑥^{2} - 2 𝑦^{2} + 𝑎 𝑥 𝑦 = 0$ is making an angle $60^{\circ}$ with $𝑋$ -axis, then $𝑎 =$

$\sqrt{\sqrt 3}$

Incorrect

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

Incorrect

3

Incorrect

$\frac{1}{3}$

Incorrect

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

+1 / -0

$𝐴$ straight line passing through the origin $𝑂$ meets the parallel lines $4 𝑥 + 2 𝑦 = 9$ and $2 𝑥 + 𝑦 + 6 = 0$ at the points $𝑃$ and $𝑄$ respectively. Then, the point $𝑂$ divides the line segment $𝑃 𝑄$ in the ratio

$1 : 2$

Incorrect

$2 : 1$

Incorrect

$3 : 4$

Incorrect

$4 : 3$

Incorrect

Q 47MathematicsSection A • MCQparabola

+1 / -0

A circle is drawn with its centre at the focus of the parabola $𝑦^{2} = 2 𝑝 𝑥$ such that it touches the directrix of the parabola. Then, a point of intersection of the circle and the parabola is

$(2 𝑝, 2 𝑝)$

Incorrect

$(\frac{𝑝}{2}, - 𝑝)$

Incorrect

$(2 𝑝, - 2 𝑝)$

Incorrect

$(𝑝, \sqrt{\sqrt 2} 𝑝)$

Incorrect

Q 48MathematicsSection A • MCQcircle

+1 / -0

A circle touches both the coordinate axes and the straight line $𝐿 \equiv 4 𝑥 + 3 𝑦 - 6 = 0$ in the first quadrant. If this circle lies below the line $𝐿 = 0$ , then the equation of that circle is

$4 𝑥^{2} + 4 𝑦^{2} - 4 𝑥 - 4 𝑦 + 1 = 0$

Incorrect

$4 𝑥^{2} + 4 𝑦^{2} - 4 𝑥 - 24 𝑦 + 1 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} - 6 𝑥 - 6 𝑦 + 9 = 0$

Incorrect

$𝑥^{2} + 𝑦^{2} - 6 𝑥 - 𝑦 - 9 = 0$

Incorrect

Q 49MathematicsSection A • MCQcircle

+1 / -0

If the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p, 0<p<a$ is $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$ , then $\lambda=$

1

Incorrect

-1

Incorrect

$- 𝑝$

Incorrect

$- 2 𝑝$

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

If the lines $3 𝑥 - 4 𝑦 + 4 = 0$ and $6 𝑥 - 8 𝑦 - 7 = 0$ are the tangents to the same circle, then the area of that circle (in sq. units) is

$\frac{3 𝜋}{4}$

Incorrect

$\frac{16 𝜋}{25}$

Incorrect

$\frac{9 𝜋}{4}$

Incorrect

$\frac{9 𝜋}{16}$

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

Circles are drawn through the point $(2, 0)$ to cut intercepts of length 5 units on the $𝑋$ -axis. If their centre lie in the first quadrant, then their equation is

$3 𝑥^{2} + 3 𝑦^{2} - 27 𝑥 - 2 𝑘 𝑦 + 42 = 0, 𝑘 \in 𝑅^{+}$

Incorrect

$𝑥^{2} + 𝑦^{2} - 2 𝑘 𝑥 - 9 𝑦 + 14 = 0, 𝑘 \in 𝑅^{+}$

Incorrect

$𝑥^{2} + 𝑦^{2} - 9 𝑥 - 2 𝑘 𝑦 + 14 = 0, 𝑘 \in 𝑅^{+}$

Incorrect

$𝑥^{2} + 𝑦^{2} - 9 𝑥 - 2 𝑘 𝑦 - 42 = 0, 𝑘 \in 𝑅^{+}$

Incorrect

Q 52MathematicsSection A • MCQparabola

+1 / -0

If the locus of a point that divides a chord of slope 2 of the parabola $𝑦^{2} = 4 𝑥$ internally in the ratio $1 : 2$ is a parabola, then its vertex is

$(\frac{2}{9}, \frac{8}{9})$

Incorrect

$(\frac{1}{9}, \frac{3}{9})$

Incorrect

$(\frac{4}{9}, \frac{8}{9})$

Incorrect

$(\frac{2}{9}, \frac{4}{9})$

Incorrect

Q 53MathematicsSection A • MCQellipse

+1 / -0

Assertion (A) The length of the latus rectum of an ellipse is 4 . The focus and its corresponding directrix are respectively $(1, - 2)$ and $3 𝑥 + 4 𝑦 - 15 = 0$ . Then, its eccentricity is $\frac{1}{2}$ .

Reason $(R)$ Length of the perpendicular drawn from focus of an ellipse to its corresponding directrix is $\frac{𝑎 (1 - 𝑒^{2})}{𝑒}$ .

Then, which one of the following is correct?

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

Incorrect

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

Incorrect

(A) is true, (R) is false

Incorrect

(A) is false, (R) is true

Incorrect

Q 54MathematicsSection A • MCQhyperbola

+1 / -0

If the eccentricity of the hyperbola $\frac{𝑥^{2}}{𝑎^{2}} - \frac{𝑦^{2}}{𝑏^{2}} = 1$ passing through the point $(4, 6)$ is 2 , then the equation of the tangent to this hyperbola at $(4, 6)$ is

$2 𝑥 - 3 𝑦 + 10 = 0$

Incorrect

$3 𝑥 - 2 𝑦 = 0$

Incorrect

$𝑥 - 2 𝑦 + 8 = 0$

Incorrect

$2 𝑥 - 𝑦 - 2 = 0$

Incorrect

Q 55MathematicsSection A • MCQhyperbola

+1 / -0

A hyperbola passes through the point $𝑃 (\sqrt{\sqrt 2}, \sqrt{\sqrt 3})$ and has foci at $(\pm 2, 0)$ . Then, the point that lies on the tangent drawn to this hyperbola at $𝑃$ is

$(\sqrt{\sqrt 3}, \sqrt{\sqrt 2})$

Incorrect

$(- \sqrt{\sqrt 2}, - \sqrt{\sqrt 3})$

Incorrect

$(2 \sqrt{\sqrt 2}, 3 \sqrt{\sqrt 3})$

Incorrect

$(3 \sqrt{\sqrt 2}, 2 \sqrt{\sqrt 3})$

Incorrect

Q 56MathematicsSection A • MCQ3d geometry

+1 / -0

The circumradius of the triangle formed by the points $(2, - 1, 1), (1, - 3, - 5)$ and $(3, - 4, - 4)$ is

$\frac{\sqrt{\sqrt 35}}{2}$

Incorrect

$\frac{\sqrt{\sqrt 25}}{3}$

Incorrect

$\sqrt{\sqrt 41}$

Incorrect

$\frac{\sqrt{\sqrt 41}}{2}$

Incorrect

Q 57MathematicsSection A • MCQ3d geometry

+1 / -0

Let $𝐴 (2, 3, 5), 𝐵 (- 1, 3, 2)$ and $𝐶 (𝜆, 5, 𝜇)$ be the vertices of $△ 𝐴 𝐵 𝐶$ . If the median through the vertex $𝐴$ is equally inclined to the coordinate axes, then

$5 𝜆 - 8 𝜇 = 0$

Incorrect

$8 𝜆 - 5 𝜇 = 0$

Incorrect

$10 𝜆 - 7 𝜇 = 0$

Incorrect

$7 𝜆 - 10 𝜇 = 0$

Incorrect

Q 58MathematicsSection A • MCQ3d geometry

+1 / -0

Equation of the plane passing through the origin and perpendicular to the planes $𝑥 + 2 𝑦 - 𝑧 = 1$ and $3 𝑥 - 4 𝑦 + 𝑧 = 5$ is

$𝑥 + 2 𝑦 - 5 𝑧 = 0$

Incorrect

$𝑥 - 2 𝑦 + 5 𝑧 = 0$

Incorrect

$𝑥 + 2 𝑦 + 5 𝑧 = 0$

Incorrect

$3 𝑥 + 𝑦 - 5 𝑧 = 0$

Incorrect

Q 59MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

$lim_{𝑥 \to \frac{𝜋}{4}} \frac{2 \sqrt{\sqrt 2} - (\cos 𝑥 + \sin 𝑥)^{3}}{1 - \sin 2 𝑥} =$

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

Incorrect

$\frac{3}{2}$

Incorrect

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

Incorrect

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

Incorrect

Q 60MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

Let $[𝑥]$ denote the greatest integer less than or equal to $𝑥$ . Then,

$lim_{𝑥 \to 2^{+}} (\frac{[𝑥]^{3}}{3} - {[\frac{𝑥}{3}]}^{3}) =$

0

Incorrect

$\frac{8}{3}$

Incorrect

$\frac{64}{27}$

Incorrect

$\frac{1}{3}$

Incorrect

Q 61MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If the function $𝑓$ defined by

$𝑓 (𝑥) = ⎧⎩⎨⎪⎪ \begin{matrix} \frac{1 - \cos 4 𝑥}{𝑥^{2}}, & 𝑥 < 0 \\ 𝑎, & 𝑥 = 0 \\ \frac{\sqrt{\sqrt 𝑥}}{\sqrt{\sqrt 16 + \sqrt{\sqrt 𝑥}} - 4}, & 𝑥 > 0 \end{matrix}$

is continuous at $𝑥 = 0$ , then $𝑎 =$

1

Incorrect

2

Incorrect

4

Incorrect

8

Incorrect

Q 62MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

The domain of the derivative of the function $𝑓 (𝑥) = \frac{𝑥}{1 + | 𝑥 |}$ is

$[0, \infty)$

Incorrect

$(- \infty, 0)$

Incorrect

$(- \infty, \infty)$

Incorrect

$(0, \infty)$

Incorrect

Q 63MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑥 = \sqrt{\sqrt 2^{{cosec}^{- 1} 𝑡}}$ and $𝑦 = \sqrt{\sqrt 2^{\sec^{- 1} 𝑡}}, | 𝑡 | \geq 1$ , then $\frac{𝑑 𝑦}{𝑑 𝑥} =$

$\frac{𝑥}{𝑦}$

Incorrect

$\frac{𝑦}{𝑥}$

Incorrect

$- \frac{𝑦}{𝑥}$

Incorrect

$- \frac{𝑥}{𝑦}$

Incorrect

Q 64MathematicsSection A • MCQdifferentiation

+1 / -0

If $(𝑎 + \sqrt{\sqrt 2} 𝑏 \cos 𝑥) (𝑎 - \sqrt{\sqrt 2} 𝑏 \cos 𝑦) = 𝑎^{2} - 𝑏^{2}$ , where $𝑎 > 𝑏 > 0$ , then at $(\frac{𝜋}{4}, \frac{𝜋}{4}), \frac{𝑑 𝑦}{𝑑 𝑥} =$

$\frac{𝑎 + 𝑏}{𝑎 - 𝑏}$

Incorrect

$\frac{𝑎 - 𝑏}{𝑎 + 𝑏}$

Incorrect

$\frac{𝑎 - 2 𝑏}{𝑎 + 2 𝑏}$

Incorrect

$\frac{2 𝑎 + 𝑏}{2 𝑎 - 𝑏}$

Incorrect

Q 65MathematicsSection A • MCQapplication of derivatives

+1 / -0

Consider the quadratic equation $𝑎 𝑥^{2} + 𝑏 𝑥 + 𝑐 = 0$ , where $2 𝑎 + 3 𝑏 + 6 𝑐 = 0$ and let $𝑔 (𝑥) = \frac{𝑎 𝑥^{3}}{3} + \frac{𝑏 𝑥^{2}}{2} + 𝑐 𝑥$

Statement I The given quadratic equation $𝑎 𝑥^{2} + 𝑏 𝑥 + 𝑐 = 0$ has atleast one root in $(0, 1)$ .

Statement II Rolle's theorem is applicable to $𝑔 (𝑥) on$ [0, 1].

Then

Statement I is false, Statement II is true

Incorrect

Statement I is true, Statement II is false

Incorrect

Statement I is true, Statement II is true but Statement IIs not a correct explanation of Statement I

Incorrect

Statement I is true, Statement II is true and Statement I is a correct explanation of Statement I

Incorrect

Q 66MathematicsSection A • MCQapplication of derivatives

+1 / -0

The difference between the absolute maximum and absolute minimum values of the function $𝑓 (𝑥) = 2 𝑥^{3} - 15 𝑥^{2} + 36 𝑥 - 30$ on $[- 1, 4]$ is

80

Incorrect

1

Incorrect

85

Incorrect

4

Incorrect

Q 67MathematicsSection A • MCQapplication of derivatives

+1 / -0

If $𝑓 (𝑥) = 𝑥 𝑒^{𝑥 (1 - 𝑥)}, 𝑥 \in 𝑅$ , then $𝑓 (𝑥)$ is

increasing on $[- \frac{1}{2}, 1]$

Incorrect

decreasing on $𝑅$

Incorrect

increasing on $𝑅$

Incorrect

decreasing on $[- \frac{1}{2}, 1]$

Incorrect

Q 68MathematicsSection A • MCQapplication of derivatives

+1 / -0

The angle between the curves $𝑦^{2} = 𝑥$ and $𝑥^{2} = 𝑦$ at the point $(1, 1)$ is

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

Incorrect

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

Incorrect

$90^{\circ}$

Incorrect

$45^{\circ}$

Incorrect

Q 69MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int \frac{5 \tan 𝑥}{\tan 𝑥 - 2} 𝑑 𝑥 = 𝑎 𝑥 + 𝑏 \log | \sin 𝑥 - 2 \cos 𝑥 | + 𝑐$ , then $𝑎 + 𝑏 =$

2

Incorrect

3

Incorrect

4

Incorrect

-1

Incorrect

Q 70MathematicsSection A • MCQindefinite integration

+1 / -0

$\int 𝑥 \cos^{- 1} (\frac{1 - 𝑥^{2}}{1 + 𝑥^{2}}) 𝑑 𝑥 (𝑥 > 0) =$

$- 𝑥 + (1 + 𝑥^{2}) \tan^{- 1} 𝑥 + 𝐶$

Incorrect

$𝑥 - (1 + 𝑥^{2}) \cot^{- 1} 𝑥 + 𝐶$

Incorrect

$- 𝑥 + (1 + 𝑥^{2}) \cot^{- 1} 𝑥 + 𝐶$

Incorrect

$𝑥 - (1 + 𝑥^{2}) \tan^{- 1} 𝑥 + 𝐶$

Incorrect

Q 71MathematicsSection A • MCQindefinite integration

+1 / -0

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

$- 2 \sqrt{\sqrt \frac{1 + \sqrt{\sqrt 𝑥}}{1 - \sqrt{\sqrt 𝑥}}} + 𝐶$

Incorrect

$- \sqrt{\sqrt \frac{1 - \sqrt{\sqrt 𝑥}}{1 + \sqrt{\sqrt 𝑥}}} + 𝐶$

Incorrect

$- 2 \sqrt{\sqrt \frac{1 - \sqrt{\sqrt 𝑥}}{1 + \sqrt{\sqrt 𝑥}}} + 𝐶$

Incorrect

$2 \sqrt{\sqrt \frac{1 + \sqrt{\sqrt 𝑥}}{1 - \sqrt{\sqrt 𝑥}}} + 𝐶$

Incorrect

Q 72MathematicsSection A • MCQindefinite integration

+1 / -0

$\int \sin^{- 1} (\sqrt{\sqrt \frac{𝑥}{𝑎 + 𝑥}}) 𝑑 𝑥 =$

$(𝑎 + 𝑥) \tan^{- 1} \sqrt{\sqrt \frac{𝑥}{𝑎}} + 𝑎 𝑥 + 𝐶$

Incorrect

$(𝑎 + 𝑥) \tan^{- 1} \sqrt{\sqrt \frac{𝑥}{𝑎}} + \sqrt{\sqrt 𝑎 𝑥} + 𝐶$

Incorrect

$(𝑎 + 𝑥) \tan^{- 1} \sqrt{\sqrt \frac{𝑎}{𝑥}} - \sqrt{\sqrt 𝑎 𝑥} + 𝐶$

Incorrect

$(𝑎 + 𝑥) \tan^{- 1} \sqrt{\sqrt \frac{𝑥}{𝑎}} - \sqrt{\sqrt 𝑎 𝑥} + 𝐶$

Incorrect

Q 73MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int \frac{𝑥}{𝑥 \tan 𝑥 + 1} 𝑑 𝑥 = \log 𝑓 (𝑥) + 𝑘$ , then $𝑓 (\frac{𝜋}{4}) =$

$\frac{𝜋}{4 \sqrt{\sqrt 2}}$

Incorrect

$𝜋 + \frac{𝜋}{2 \sqrt{\sqrt 2}}$

Incorrect

$\frac{𝜋 + 4}{4 \sqrt{\sqrt 2}}$

Incorrect

$\frac{𝜋 - 4}{4 \sqrt{\sqrt 2}}$

Incorrect

Q 74MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{1}^{0} \frac{2 𝑥 + 5}{𝑥^{2} + 3 𝑥 + 2} 𝑑 𝑥 =$

$\log (\frac{16}{3})$

Incorrect

0

Incorrect

$\log (\frac{3}{16})$

Incorrect

$4 \log 2 - 2 \log 3$

Incorrect

Q 75MathematicsSection A • MCQarea under the curves

+1 / -0

The area (in sq units) of the region given by $𝑅 = {(𝑥, 𝑦); \frac{𝑦^{2}}{2} \leq 𝑥 \leq 𝑦 + 4}$ is

16

Incorrect

18

Incorrect

24

Incorrect

30

Incorrect

Q 76MathematicsSection A • MCQdefinite integration

+1 / -0

$\int_{1}^{0} 𝑥^{\frac{5}{2}} (1 - 𝑥)^{\frac{3}{2}} 𝑑 𝑥 =$

$\frac{5 𝜋}{256}$

Incorrect

$\frac{3 𝜋}{256}$

Incorrect

$\frac{3 𝜋}{128}$

Incorrect

$\frac{5 𝜋}{128}$

Incorrect

Q 77MathematicsSection A • MCQdefinite integration

+1 / -0

$lim_{𝑛 \to \infty} [\begin{matrix} \frac{1}{𝑛^{2}} \sec^{2} \frac{1}{𝑛^{2}} + \frac{2}{𝑛^{2}} \sec^{2} \frac{4}{𝑛^{2}} + \frac{3}{𝑛^{2}} \sec^{2} \\ \frac{9}{𝑛^{2}} + \dots + \frac{1}{𝑛^{2}} \sec^{2} 1 \end{matrix}] =$

$\tan^{- 1} 1$

Incorrect

$\frac{1}{2} \tan^{- 1} 1$

Incorrect

$\frac{1}{2} \tan 1$

Incorrect

$\frac{1}{2} \sec 1$

Incorrect

Q 78MathematicsSection A • MCQdifferential equations

+1 / -0

The general solution of the differential equation $(𝑥 \sin \frac{𝑦}{𝑥}) 𝑑 𝑦 = (𝑦 \sin \frac{𝑦}{𝑥} - 𝑥) 𝑑 𝑥$ is

$\cos (\frac{𝑦}{𝑥}) = \log | 𝑥 | + 𝐶$

Incorrect

$\cos (\frac{𝑦}{𝑥}) = \frac{1}{𝑥} + 𝐶$

Incorrect

$\cos (\frac{𝑥}{𝑦}) = \log | 𝑦 | + 𝐶$

Incorrect

$\cos \frac{𝑦}{𝑥} = \frac{2}{𝑥} + 𝐶$

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

The general solution of the differential equation $\cos (𝑥 + 𝑦) 𝑑 𝑦 = 𝑑 𝑥$ is

$𝑦 = \tan (\frac{𝑥 + 𝑦}{2}) + 𝐶$

Incorrect

$𝑦 = \sec (\frac{𝑥 + 𝑦}{2}) + 𝐶$

Incorrect

$𝑦 = 𝑥 \sec (\frac{𝑦}{𝑥}) + 𝐶$

Incorrect

$𝑦 = - \cos^{- 1} (\frac{𝑦}{𝑥}) + 𝐶$

Incorrect

Q 80MathematicsSection A • MCQdifferential equations

+1 / -0

If $𝐴 𝑥^{3} + 𝐵 𝑥 𝑦 = 4$ ( $𝐴$ and $𝐵$ are arbitrary constants) is the general solution of the differential equation $𝐹 (𝑥) \frac{𝑑^{2} 𝑦}{𝑑 𝑥^{2}} + 𝐺 (𝑥) \frac{𝑑 𝑦}{𝑑 𝑥} - 2 𝑦 = 0$ , then $𝐹 (𝑙) + 𝐺 (𝑙) =$

1

Incorrect

0

Incorrect

4

Incorrect

9

Incorrect

Q 81PhysicsSection A • MCQunits and measurements

+1 / -0

The physical quantity having the dimensions of the square root of the ratio of the kinetic energy and surface tension is

distance

Incorrect

time

Incorrect

temperature

Incorrect

mass

Incorrect

Q 82PhysicsSection A • MCQmotion in a straight line

+1 / -0

If the displacement ( $𝑠$ in metre) of a moving particle in terms of time $(𝑡$ in second $) 𝑠 = 𝑡^{3} - 6 𝑡^{2} + 18 𝑡 + 9$ , then the minimum velocity attained by the particle is

$29 {ms}^{- 1}$

Incorrect

$5 {ms}^{- 1}$

Incorrect

$6 {ms}^{- 1}$

Incorrect

$12 {ms}^{- 1}$

Incorrect

Q 83PhysicsSection A • MCQwork power and energy

+1 / -0

If a force $(𝛽 \hat{𝐢} + 2 \hat{𝐣} + 5 \hat{𝐤}) N$ acting on a body displaces it through $(2 \hat{𝐢} + 2 \hat{𝐣} + 1 \hat{𝐤}) m$ , then the work done by the force on the body is

40 J

Incorrect

20 J

Incorrect

15 J

Incorrect

25 J

Incorrect

Q 84PhysicsSection A • MCQmotion in a plane

+1 / -0

If two bodies $𝐴$ and $𝐵$ are projected with same velocity but with different angles $𝜃_{1}$ and $𝜃_{2}$ respectively with the horizontal such that both will have same range, then the ratio of times of flight of the bodies $𝐴$ and $𝐵$ is

$\sin 𝜃_{2}$

Incorrect

$\sin 𝜃_{1}$

Incorrect

$\tan 𝜃_{2}$

Incorrect

$\tan 𝜃_{1}$

Incorrect

Q 85PhysicsSection A • MCQlaws of motion

+1 / -0

The apparent weight of a girl of mass 30 kg when she is in a lift moving vertically upwards with an acceleration of $2 {ms}^{- 2}$ is (Acceleration due to gravity $= 10 {ms}^{- 2}$ )

60 N

Incorrect

30 N

Incorrect

240 N

Incorrect

360 N

Incorrect

Q 86PhysicsSection A • MCQcircular motion

+1 / -0

If a stone of mass 0.5 kg tied to one end of a wire is whirled in a circular path of radius 2 m with a speed $40 rev / \min$ in a horizontal plane, then the tension in the wire is nearly

14.8 N

Incorrect

12.4 N

Incorrect

17.5 N

Incorrect

20.8 N

Incorrect

Q 87PhysicsSection A • MCQwork power and energy

+1 / -0

A body is projected vertically upwards with a velocity of $20 {ms}^{- 1}$ . If the potential energy of the body at a height of 5 m from the ground is 100 J , then the kinetic energy of the body at a height of 10 m from the ground is

(Acceleration due to gravity $= 10 {ms}^{- 2}$ )

200 J

Incorrect

300 J

Incorrect

150 J

Incorrect

250 J

Incorrect

Q 88PhysicsSection A • MCQcenter of mass

+1 / -0

A body falls freely on to a hard horizontal surface. If the coefficient of restitution between the surface and the body is 0.8 , then the ratio of the maximum height to which the body rises after second impact and the initial height of the body is

$256 : 625$

Incorrect

$64 : 125$

Incorrect

$16 : 25$

Incorrect

$4 : 5$

Incorrect

Q 89PhysicsSection A • MCQcenter of mass

+1 / -0

Two bodies of masses $𝑀$ and $4 𝑀$ initially at rest, start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $𝑣_{0}$ is

zero

Incorrect

$- 𝑣_{0}$

Incorrect

$2 𝑣_{0}$

Incorrect

$- 4 𝑣_{0}$

Incorrect

Q 90PhysicsSection A • MCQrotational motion

+1 / -0

The angular velocity of a body changes from $6 rad s^{- 1}$ to $21 rad s^{- 1}$ in a time of 1.5 s . If the moment of inertia of the body is $g m^{2}$ , then the rate of change of angular momentum of the body is

0.12 Nm

Incorrect

0.6 Nm

Incorrect

1 Nm

Incorrect

0.8 Nm

Incorrect

Q 91PhysicsSection A • MCQsimple harmonic motion

+1 / -0

If the displacement of a particle executing simple harmonic motion is given by $𝑥 = 0.5 \cos (125.6 𝑡)$ , then the time period of oscillation of the particle is nearly (Here, $𝑥$ is displacement in metre and $𝑡$ is time in second)

1 s

Incorrect

2 s

Incorrect

0.09 s

Incorrect

0.05 s

Incorrect

Q 92PhysicsSection A • MCQsimple harmonic motion

+1 / -0

The amplitude of a damped harmonic oscilator becomes $50 %$ of its initial value in a time of 12 s . If the amplitude of the oscillator at a time of 36 s is $𝑥 %$ of its initial amplitude, then the value of $𝑥$ is

25

Incorrect

12.5

Incorrect

37.5

Incorrect

8

Incorrect

Q 93PhysicsSection A • MCQgravitation

+1 / -0

The escape velocity of a body from a planet of mass $𝑀$ and radius $𝑅$ is $14 km s^{- 1}$ . The escape velocity of the body from another planet having same mass and diameter 8 R (in $km s^{- 1}$ ) is

7

Incorrect

10.5

Incorrect

14

Incorrect

28

Incorrect

Q 94PhysicsSection A • MCQelasticity

+1 / -0

The stress-strain graph of two wires $𝐴$ and $𝐵$ is shown in the figure. If $𝑌_{𝐴}$ and $𝑌_{𝐵}$ are Young's moduli of materials of wires $𝐴$ and $𝐵$ respectively, then

qImage--elasticity-mechanics-Jeemate

$𝑌_{𝐴} = 3 𝑌_{𝐵}$

Incorrect

$𝑌_{𝐴} = 𝑌_{𝐵}$

Incorrect

$𝑌_{𝐵} = 3 𝑌_{𝐴}$

Incorrect

$𝑌_{𝐵} = 2 𝑌_{𝐴}$

Incorrect

Q 95PhysicsSection A • MCQfluid mechanics

+1 / -0

If two soap bubbles each of radius 2 cm combine in vacuum under isothermal conditions, then the radius of the new bubble formed is

$\sqrt{\sqrt 2} cm$

Incorrect

$2 \sqrt{\sqrt 2} cm$

Incorrect

0.5 cm

Incorrect

2 cm

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $4 : 1$ . If the free face of brass is at $0^{\circ} C$ and that of copper is at $100^{\circ} C$ , then the temperature of their interface is

$80^{\circ} C$

Incorrect

$20^{\circ} C$

Incorrect

$60^{\circ} C$

Incorrect

$40^{\circ} C$

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

The efficiency of a Carnot's heat engine is $\frac{1}{3}$ . If the temperature of the source is decreased by $50^{\circ} C$ and the temperature of the sink is increased by $25^{\circ} C$ , the efficiency of the engine becomes $\frac{3}{16}$ . The initial temperature of the sink is

325 K

Incorrect

375 K

Incorrect

350 K

Incorrect

300 K

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

The change in internal energy of given mass of a gas, when its volume changes from $𝑉$ to $3 𝑉$ at constant pressure $𝑝$ is

( $𝛾 =$ Ratio of the specific heat capacities of the gas)

$\frac{𝑝 𝑉}{𝛾 - 1}$

Incorrect

$\frac{2 𝑝 𝑉}{𝛾 - 1}$

Incorrect

$\frac{3 𝑝 𝑉}{𝛾 - 1}$

Incorrect

$\frac{𝑝 𝑉}{2 𝛾 - 1}$

Incorrect

Q 99PhysicsSection A • MCQheat and thermodynamics

+1 / -0

A monoatomic gas at a pressure of 100 kPa expands adiabatically such that its final volume becomes 8 times its initial volume. If the work done during the process is 180 J , then the initial volume of the gas is

$1600 {cm}^{3}$

Incorrect

$800 {cm}^{3}$

Incorrect

$1200 {cm}^{3}$

Incorrect

$2000 {cm}^{3}$

Incorrect

Q 100PhysicsSection A • MCQheat and thermodynamics

+1 / -0

If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature $𝑇$ , then the total internal energy of the mixture is (neglect vibrational modes and $𝑅 =$ Universal gas constant)

$11 𝑅 𝑇$

Incorrect

$12.5 𝑅 𝑇$

Incorrect

$13.5 𝑅 𝑇$

Incorrect

15.5 RT

Incorrect

Q 101PhysicsSection A • MCQwaves

+1 / -0

A sound wave of frequency 500 Hz travels between two points $𝑋$ and $𝑌$ separated by a distance of 600 m in a time of 2 s . The number of waves between the points $𝑋$ and $𝑌$ are

1000

Incorrect

1500

Incorrect

300

Incorrect

600

Incorrect

Q 102PhysicsSection A • MCQray optics

+1 / -0

A ray of light incidents at an angle of $60^{\circ}$ on the first face of a prism. The angle of the prism is $30^{\circ}$ and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second face, then the refractive index of the material of the prism is

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

Incorrect

$\frac{3}{2}$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

$\sqrt{\sqrt 3}$

Incorrect

Q 103PhysicsSection A • MCQwave optics

+1 / -0

In an experiment, two polariods are arranged such that the intensity of the polarised light emerged from the second polaroid is $37.5 %$ of the intensity of the unpolarised light incident on the first polaroid. Then the angle between the axes of the two polaroids is

$60^{\circ}$

Incorrect

$90^{\circ}$

Incorrect

$45^{\circ}$

Incorrect

$30^{\circ}$

Incorrect

Q 104PhysicsSection A • MCQelectrostatics

+1 / -0

If two particles $𝐴$ and $𝐵$ of charges $1.6 \times 10^{- 19} C$ and $3.2 \times 10^{- 19} C$ respectively are separated by a distance of 3 cm in air, then the magnitude of electrostatic force on particle $𝐴$ due to particle $𝐵$ is

$5.12 \times 10^{- 22} N$

Incorrect

$5.12 \times 10^{- 32} N$

Incorrect

$5.12 \times 10^{- 12} N$

Incorrect

$5.12 \times 10^{- 25} N$

Incorrect

Q 105PhysicsSection A • MCQelectrostatics

+1 / -0

If four charges $+ 12 nC, - 20 nC, + 32 nC$ and -15 nC are arranged at the four vertices of a square of side $\sqrt{\sqrt 2} m$ , then the net electric potential at the centre of the square due to these four charges is

72 V

Incorrect

81 V

Incorrect

64 V

Incorrect

36 V

Incorrect

Q 106PhysicsSection A • MCQcapacitor

+1 / -0

Four capacitors are connected as shown in the figure. If $𝐶_{1}, 𝐶_{2}, 𝐶_{3}$ and $𝐶_{4}$ are in the ratio of $1 : 2 : 3 : 4$ , then the ratio of the charges on the capacitors $𝐶_{2}$ and $𝐶_{4}$ is

qImage--capacitor-electromagnetism-Jeemate

$1 : 4$

Incorrect

$2 : 3$

Incorrect

$6 : 11$

Incorrect

$3 : 22$

Incorrect

Q 107PhysicsSection A • MCQcurrent electricity

+1 / -0

In the given circuit, the internal resistance of the cell is zero. If $𝑖_{1}$ and $𝑖_{2}$ are the readings of the ammeter when the key $(𝐾)$ is opened and closed respectively, then $𝑖_{1} : 𝑖_{2} =$

qImage--current-electricity-electromagnetism-Jeemate

$2 : 1$

Incorrect

$3 : 10$

Incorrect

$3 : 5$

Incorrect

$1 : 2$

Incorrect

Q 108PhysicsSection A • MCQcurrent electricity

+1 / -0

In a meter bridge, the null point is located at 20 cm from left end of the wire when resistances $𝑅$ and $𝑆$ are connected in the left and right gaps respectively. If the resistance $𝑆$ is shunted with $60 Ω$ resistance, the null point shifted by 5 cm , then the values of $𝑅$ and $𝑆$ are respectively

$24 Ω, 6 Ω$

Incorrect

$6 Ω, 24 Ω$

Incorrect

$5 Ω, 20 Ω$

Incorrect

$20 Ω, 5 Ω$

Incorrect

Q 109PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

If a wire of length ' $𝐿$ ' carrying a current ' $𝑖$ ' is bent in the shape of a semi-circular arc as shown in the figure, then the magnetic field at centre of the arc is

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

\frac{𝜋 𝜇_{0} 𝑖}{4 𝐿}

Incorrect

\frac{𝜋 𝜇_{0} 𝑖}{2 𝐿}

Incorrect

\frac{𝜇_{0}^{𝑗}}{2 𝜋 𝐿}

Incorrect

\frac{𝜇_{0} 𝑖}{4 𝜋 𝐿}

Incorrect

Q 110PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A galvanometer having 30 divisions has a current sensitivity of $0.0625 \frac{𝑑 𝑖 𝜈}{𝜇 𝐴}$ . If it is converted into a voltmeter to read a maximum of 6 V , then the resistance of that voltmeter is

$7.5 k Ω$

Incorrect

$12.5 k Ω$

Incorrect

$6 k Ω$

Incorrect

$5 k Ω$

Incorrect

Q 111PhysicsSection A • MCQmagnetism and matter

+1 / -0

If the given figure shows the relation between magnetic field ( $𝐵$ -along $𝑌$ -axis) and magnetic intensity ( $𝐻$ -along $𝑋$ -axis) of a ferromagnetic material, then the point that represents coercivity of the material is

qImage--magnetism-and-matter-electromagnetism-Jeemate

$𝑃$

Incorrect

$𝑄$

Incorrect

$𝑅$

Incorrect

$𝑆$

Incorrect

Q 112PhysicsSection A • MCQelectromagnetic induction

+1 / -0

A coil having 100 square loops each of side 10 cm is placed such that its plane is normal to a magnetic field, which is changing at a rate of $0.7 {Ts}^{- 1}$ . The emf induced in the coil is

0.2 V

Incorrect

0.4 V

Incorrect

0.7 V

Incorrect

1 V

Incorrect

Q 113PhysicsSection A • MCQalternating current

+1 / -0

An AC source of internal resistance $10^{3} Ω$ is connected to a transformer. The ratio of the number of turns in the primary to the number of turns in the secondary to match the source to a load resistance of $10 Ω$ is

$1 : 10$

Incorrect

$10 : 1$

Incorrect

$2 : 5$

Incorrect

$5 : 2$

Incorrect

Q 114PhysicsSection A • MCQelectromagnetic waves

+1 / -0

If $11 %$ of the power of a 200 W bulb is converted to visible radiation, then the intensity of the light at a distance of 100 cm from the bulb is

$10.5 W m^{- 2}$

Incorrect

$5.25 W m^{- 2}$

Incorrect

$3.5 {Wm}^{- 2}$

Incorrect

$1.75 W m^{- 2}$

Incorrect

Q 115PhysicsSection A • MCQdual nature of radiation

+1 / -0

The de-Broglie wavelength associated with an electron accelerated through a potential difference of $\frac{200}{3} V$ is nearly

$25 \overset{o}{A}$

Incorrect

$2.5 \overset{o}{A}$

Incorrect

$15 \overset{o}{A}$

Incorrect

$1.5 \overset{o}{A}$

Incorrect

Q 116PhysicsSection A • MCQatoms and nuclei

+1 / -0

The ratio of the shortest wavelengths of Bracket and Balmer series of hydrogen atom is

$2 : 1$

Incorrect

$3 : 2$

Incorrect

$4 : 1$

Incorrect

$6 : 5$

Incorrect

Q 117PhysicsSection A • MCQatoms and nuclei

+1 / -0

If the binding energy per nucleon of deuteron $(_{1} H^{2})$ is 1.15 MeV and an $𝛼$ -particle has a binding energy of 7.1 MeV per nucleon, then the energy released per nucleon in the given reaction is

$_{1} H^{2} +_{1} H^{2} \to_{2} {He}^{4} + Q$

23.8 MeV

Incorrect

26.1 MeV

Incorrect

5.95 MeV

Incorrect

28.9 MeV

Incorrect

Q 118PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

In a transistor, if the collector current is $98 %$ of emitter current, then the ratio of the base and collector currents is

$1 : 98$

Incorrect

$1 : 1$

Incorrect

$1 : 49$

Incorrect

$1 : 99$

Incorrect

Q 119PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

In the given circuit, if $𝐴 = 0, 𝐵 = 1$ and $𝐶 = 1$ are inputs, then the values of $𝑦_{1}$ and $𝑦_{2}$ are respectively qImage--semiconductor-devices-and-logic-gates-modern-physics-Jeemate

1.1

Incorrect

0.1

Incorrect

0.0

Incorrect

1.0

Incorrect

Q 120PhysicsSection A • MCQcommunication systems

+1 / -0

In amplitude modulation, if a message signal of 5 kHz 2 is modulated by a carrier wave of frequency 900 kHz , then the frequencies of the side bands are

$905 kHz, 895 kHz$

Incorrect

$900 kHz, 800 kHz$

Incorrect

$800 kHz, 700 kHz$

Incorrect

$1000 kHz, 900 kHz$

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

The wavelength of a particular electron transition for ${He}^{+}$ is 100 nm . The wavelength (in $Å$ ) of H atom for the same transition is

1000

Incorrect

100

Incorrect

4000

Incorrect

2000

Incorrect

Q 122ChemistrySection A • MCQatomic structure

+1 / -0

The energy of second Bohr orbit of hydrogen atom is -3.4 eV . The energy of the fourth Bohr orbit of the ${He}^{+}$ ion will be

-3.4 eV

Incorrect

-13.6 eV

Incorrect

-6.8 eV

Incorrect

-0.85 eV

Incorrect

Q 123ChemistrySection A • MCQperiodic classification of elements

+1 / -0

$Observe the following data :$

$\begin{matrix} Ion & 𝑄^{𝑎 +} & 𝑋^{𝑏 +} & 𝑌^{𝑐 +} & 𝑍^{𝛼 +} \\ Radius (pm) & 53 & 66 & 40 & 100 \end{matrix}$

$𝑄^{𝑎 +}, 𝑋^{𝑏 +}, 𝑌^{𝑐 +}, 𝑍^{𝑑 +}$ are respectively

${Mg}^{2 +}, {Al}^{3 +}, {Na}^{+}, {Si}^{4 +}$

Incorrect

${Al}^{3 +}, {Si}^{4 +}, {Mg}^{2 +}, {Na}^{+}$

Incorrect

${Mg}^{2 +}, {Si}^{4 +}, {Al}^{3 +}, {Na}^{+}$

Incorrect

${Al}^{3 +}, {Mg}^{2 +}, {Si}^{4 +}, {Na}^{+}$

Incorrect

Q 124ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

$Which of the following sets are correctly matched?$

$\begin{matrix} Molecule & Hybridisation & Geometry \\ I. & {BrF}_{5} & 𝑠 𝑝^{3} 𝑑^{2} & Square pyramidal \\ II. & {XeF}_{6} & 𝑠 𝑝^{3} 𝑑^{3} & Distorted octahedral \\ III. & {SF}_{4} & 𝑑 𝑠 𝑝^{2} & Square planar \\ IV. & {PbCl}_{2} & 𝑠 𝑝 & Linear \end{matrix}$

I and IV

Incorrect

II and III

Incorrect

III and IV

Incorrect

I and II

Incorrect

Q 125ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

The order of dipole moments of $H_{2} O (𝐴), {CHCl}_{3} (𝐵)$ and ${NH}_{3} (𝐶)$ is

$B<A<C$

Incorrect

$B<C<A$

Incorrect

$C<B<A$

Incorrect

$C<A<B$

Incorrect

Q 126ChemistrySection A • MCQstates of matter

+1 / -0

Identify the correct graph for an ideal gas $(𝑦$ -axis $=$ compressibility factor, $𝑍 : 𝑥$ -axis $=$ pressure, $𝑝)$

qImage--states-of-matter-physical-chemistry-Jeemate

Incorrect

qImage--states-of-matter-physical-chemistry-Jeemate

Incorrect

qImage--states-of-matter-physical-chemistry-Jeemate

Incorrect

qImage--states-of-matter-physical-chemistry-Jeemate

Incorrect

Q 127ChemistrySection A • MCQstates of matter

+1 / -0

Identify the correct statements from the following:

I. Glass is an extremely viscous liquid.

II. Increase in temperature decreases the surface tension of liquids.

III. Compressibility factor for an ideal gas is zero.

I, II and III

Incorrect

I and II only

Incorrect

I and III only

Incorrect

II and III only

Incorrect

Q 128ChemistrySection A • MCQredox reactions

+1 / -0

Identify the correct statements about the following stoichiometric equation.

$𝑎 P_{4} + 𝑏^{-} OH + 𝑐 H_{2} O ⟶ 𝑑 {PH}_{3} + 𝑒 H_{2} {PO}_{-}^{2}$

I. $𝑎 + 𝑏 + 𝑐 = 5$

II. $𝑏 + 𝑐 - 𝑒 = 3$

III. The oxidation state of P in $H_{2} {PO}_{-}^{2}$ is +l .

I, II and III

Incorrect

I and II only

Incorrect

I and III only

Incorrect

II and III only

Incorrect

Q 129ChemistrySection A • MCQthermodynamics

+1 / -0

5 moles of a gas is allowed to pass through a series of changes as shown in the graph, in a cyclic process. The processes $𝐶 \to 𝐴, 𝐵 \to 𝐶$ and $𝐴 \to 𝐵$ respectively are

qImage--thermodynamics-physical-chemistry-Jeemate

isothermal, isochoric, isobaric

Incorrect

isochoric, isobaric. isothermal

Incorrect

isobaric, isochoric, isothermal

Incorrect

isothermal, isobaric, isochoric

Incorrect

Q 130ChemistrySection A • MCQthermodynamics

+1 / -0

1 mole of an ideal gas is allowed to expand isothermally and reversibly from $1 L$ to 5 L at 300 K . The change in enthalpy (in kJ ) is $(𝑅 = 8.3 {JK}^{- 1} {mol}^{- 1})$

1.74

Incorrect

2.48

Incorrect

0.0

Incorrect

4.22

Incorrect

Q 131ChemistrySection A • MCQchemical equilibrium

+1 / -0

Consider the following equilibrium reaction in gaseous state at $𝑇 (K)$ .

$𝐴 + 2 𝐵 ⇌ 2 𝐶 + 𝐷$

The initial concentration of $𝐵$ is 1.5 times that of $𝐴$ . At equilibrium, the concentrations of $𝐴$ and $𝐵$ are equal. The equilibrium constant for the reaction is

6

Incorrect

16

Incorrect

12

Incorrect

4

Incorrect

Q 132ChemistrySection A • MCQionic equilibrium

+1 / -0

At $𝑇 (K) 𝐾_{sp}$ of two ionic salts $𝑀 𝑋_{2}$ and $𝑀 𝑋$ is $5 \times 10^{- 13}$ and $1.6 \times 10^{- 11}$ respectively. The ratio of molar solubility of $𝑀 𝑋_{2}$ and $𝑀 𝑋$ is

12.5

Incorrect

1.25

Incorrect

6.25

Incorrect

7.50

Incorrect

Q 133ChemistrySection A • MCQhydrogen

+1 / -0

Consider the following.

Statement ${IH}_{2} O_{2}$ acts as an oxidising as well as reducing agent in both acidic and basic mediim.

Statement $II 10 V H_{2} O_{2}$ sample means it contains $6 % (\frac{𝑤}{𝑣}) H_{2} O_{2}$ .

The correct answer is

Both statement-I and statement-II are correct

Incorrect

Statement-I is correct, but statement-II is not correct

Incorrect

Statement-I is not correct, but statement-II is correct

Incorrect

Both statement-I and statement-II are not correct.

Incorrect

Q 134ChemistrySection A • MCQs block elements

+1 / -0

Identify the correct statements from the following.

I. All alkaline earth metals give hydrides on heating with hydrogen.

II. Calcium hydroxide is used to purify sugar.

III.

{BeCl}_{2}

is a dimer in gaseous phase.

I and III only

Incorrect

II and III only

Incorrect

I, II, III

Incorrect

I and II only

Incorrect

Q 135ChemistrySection A • MCQp block elements

+1 / -0

Select the correct statements from the following

(A) Aluminium liberates $H_{2}$ gas with dil. HCl but not with aqueous NaOH .

(B) Formula of sodium metaborate is ${Na}_{3} {BO}_{3}$ .

(C) Boric acid is a weak monobasic acid.

(D) For thallium, +1 state is more stable than +3 state.

A and B

Incorrect

B and C

Incorrect

C and D

Incorrect

A and D

Incorrect

Q 136ChemistrySection A • MCQp block elements

+1 / -0

The number of amphoteric oxides from the following is ${CO}_{2}, {GeO}_{2}, {SnO}_{2}, {PbO}_{2}$ , $CO, GeO, SnO, PbO$

3

Incorrect

4

Incorrect

6

Incorrect

5

Incorrect

Q 137ChemistrySection A • MCQenvironmental chemistry

+1 / -0

Which of the following statements is not correct?

Catalytic converters present in automobiles prevent the release of nitrogen oxide to the atmosphere.

Incorrect

Photochemical smog is a mixture of smoke, fog and ${SO}_{2}$ .

Incorrect

Chlorofluorocarbons damage ozone layer.

Incorrect

Acid rain corrodes water pipes resulting in the leaching of heavy metals into the drinking water.

Incorrect

Q 138ChemistrySection A • MCQhydrocarbons

+1 / -0

Consider the sets I, II and III. Identify the set(s) which is (are) correctly matched.

I. Staggered ethane > eclipsed ethane ..........torsional strain.

II. 2, 2-dimethylbutane > 2-methylpentane ......... boiling point

III. cis-but-2-ene > trans-but-2-ene ......... dipole moment

I, II only

Incorrect

II, III only

Incorrect

III only

Incorrect

I, II and III

Incorrect

Q 139ChemistrySection A • MCQcompounds containing nitrogen

+1 / -0

What are $𝐵$ and $𝐶$ respectively in the following set of reactions?

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 140ChemistrySection A • MCQsolid state

+1 / -0

The crystal system with edge lengths $𝑎 \neq 𝑏 \neq 𝑐$ and axial angles $𝛼 = 𝛽 = 𝛾 = 90^{\circ}$ is ' $𝑥$ ' and number of Bravais lattices for it is ' $𝑦$ '. $𝑥$ and $𝑦$ are

cubic : 3

Incorrect

monoclinic : 2

Incorrect

orthorhombic : 4

Incorrect

trigonal : 2

Incorrect

Q 141ChemistrySection A • MCQsolutions

+1 / -0

A solution is prepared by adding 124 g of ethylene glycol (molar mass $= 62 g {mol}^{- 1}$ ) to $𝑥 g$ of water to get 10 m solution. What is the value of $𝑥$ (in g )?

100

Incorrect

400

Incorrect

800

Incorrect

200

Incorrect

Q 142ChemistrySection A • MCQsolutions

+1 / -0

The following graph is obtained for an ideal solution containing a non-volatile solute $𝑥$ -and $𝑦$ -axis represent, respectively qImage--liquid-solution-physical-chemistry-Jeemate

mole fraction of solute, vapour pressure of solute

Incorrect

mole fraction of solvent, vapour pressure of solution

Incorrect

mole fraction of solute, vapour pressure of solution

Incorrect

concentration of solution, vapour pressure of solution

Incorrect

Q 143ChemistrySection A • MCQelectrochemistry

+1 / -0

Observe the following statements about dry cell

I. It is a primary battery.

II. Zinc vessel acts as cathode.

III. A paste of moist ${NH}_{4} Cl, {MnO}_{2}$ and ${ZnCl}_{2}$ , is present between two electrodes

IV. The potential of this cell is 1.5 V .

The correct statements are

I, II, III and IV

Incorrect

I, II and III only

Incorrect

I, III and IV only

Incorrect

II, III and IV only

Incorrect

Q 144ChemistrySection A • MCQchemical kinetics

+1 / -0

For a reaction, the graph of $\ln 𝑘$ (on $𝑦$ -axis) and $\frac{1}{𝑇}$ (on $𝑥$ -axis) is a straight line with a slope $- 2 \times 10^{4} K$ . The activation energy of the reaction (in $kJ {mol}^{- 1}$ ) is ( $𝑅 = 8.3 {JK}^{- 1} {mol}^{- 1}$ )

332

Incorrect

432

Incorrect

166

Incorrect

216

Incorrect

Q 145ChemistrySection A • MCQsurface chemistry

+1 / -0

Match the following

$List-I (Reaction)$		$List-II (Catalyst)$
(A)	Hydrogenation of vegetable oils	I.	Ni
(B)	Decomposition of potassium chlorate	II.	${MnO}_{2}$
(C)	Oxidation of ${SO}_{2}$ in lead chamber process	III.	Pt
(D)	Oxidation of ammonia in Ostwald's process	(IV)	$NO (𝑔)$

The correct answer is

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 146ChemistrySection A • MCQsurface chemistry

+1 / -0

The critical micelle concentration (CMC) of a soap solution is $5 \times 10^{- 4} mol L^{- 1}$ . Identify the correct statements about this solution.

I. The micelle is stable if the soap solution concentration is $10^{- 7} mol L^{- 1}$ .

II. The micelle is stable if the soap solution concentration is higher than $5 \times 10^{- 4} mol L^{- 1}$ .

III. Micelles are also known as associated colloids.

I, II and III

Incorrect

I and II only

Incorrect

I and III only

Incorrect

II and III only

Incorrect

Q 147ChemistrySection A • MCQmetallurgy

+1 / -0

The metal purified by Mond process is $𝑋$ . The number of unpaired electrons in $𝑋$ is

5

Incorrect

4

Incorrect

3

Incorrect

2

Incorrect

Q 148ChemistrySection A • MCQp block elements

+1 / -0

Complete hydrolysis of xenon hexafluoride gives HF along with compound $𝑋$ . The hybridisation in $𝑋$ is

$𝑠 𝑝^{3}$

Incorrect

$𝑠 𝑝$

Incorrect

$𝑠 𝑝^{2}$

Incorrect

$𝑠 𝑝^{3} 𝑑$

Incorrect

Q 149ChemistrySection A • MCQredox reactions

+1 / -0

${KMnO}_{4}$ oxidises hydrogen sulphide in acidic medium, The number of moles of ${KMnO}_{4}$ which react with one mole of hydrogen sulphide is

2

Incorrect

4

Incorrect

0.4

Incorrect

2.5

Incorrect

Q 150ChemistrySection A • MCQcoordination compounds

+1 / -0

Identify the set which does not have ambidentate ligand(s)

${NO}_{-}^{2}, {CN}^{-}, C_{2} O_{2 -}^{4}$

Incorrect

$C_{2} O_{2 -}^{4}, H_{2} O, {SO}_{2 -}^{4}$

Incorrect

${SCN}^{-}, {NH}_{3}, {CH}_{3} {COO}^{-}$

Incorrect

${CN}^{-}, {SCN}^{-}, {CH}_{3} {NH}_{2}$

Incorrect

Q 151ChemistrySection A • MCQpolymers

+1 / -0

The number of linear and crosslinked polymers in the following respectively are

Novolac, Nylon 6,6, Bakelite, PVC, melamine

1, 4

Incorrect

4,1

Incorrect

2,3

Incorrect

3,2

Incorrect

Q 152ChemistrySection A • MCQbiomolecules

+1 / -0

Which of the following represents the correct structure of $𝛽 - 𝐷 - (-)$ - fructofuranose?

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 153ChemistrySection A • MCQbiomolecules

+1 / -0

Which of the following statement is not correct for glucose?

Glucose does not give Schiff's test.

Incorrect

Glucose exists in two crystalline forms $𝛼$ - and $𝛽$ -

Incorrect

The pentaacetate of glucose does not react with ${NH}_{2} OH$ .

Incorrect

Glucose forms addition product with ${NaHSO}_{3}$ .

Incorrect

Q 154ChemistrySection A • MCQchemistry in everyday life

+1 / -0

The synthetic detergent used in tooth paste is of type $𝑋$ . Animal starch is $𝑌 . 𝑋$ and $𝑌$ respectively are

anionic, amylose

Incorrect

non-ionic, cellulose

Incorrect

anionic, glycogen

Incorrect

cationic, amylopectin

Incorrect

Q 155ChemistrySection A • MCQaldehyde and ketone

+1 / -0

What are $𝑋$ and $𝑌$ respectively in the following sets of reactions?

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 156ChemistrySection A • MCQhaloalkanes and haloarenes

+1 / -0

Identify the two reactions $𝐴 (I \to II)$ and $𝐵 (I \to III)$ respectively in the following set of reactions.

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

Fittig : Friedel-Crafts

Incorrect

Wurtz-Fittig : Friedel-Crafts

Incorrect

Wurtz-Fittig : Stephen

Incorrect

Friedel-Crafts : Swarts

Incorrect

Q 157ChemistrySection A • MCQalcohols phenols and ethers

+1 / -0

An alcohol, $𝑋 (C_{5} H_{12} O)$ in the presence of $Cu / 573 K$ gives $𝑌 (C_{5} H_{10})$ . The reactants required for the preparation of $𝑋$ are

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

Incorrect

$HCHO, {({CH}_{3})}_{3} CMgBr$

Incorrect

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

Incorrect

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

Incorrect

Q 158ChemistrySection A • MCQaldehyde and ketone

+1 / -0

A carbonyl compound $𝑋 (C_{8} H_{8} O)$ undergoes disproportionation with conc. KOH on heating. Product of $𝑋$ with $Zn - Hg / HCl$ is $𝑌$ and product of $𝑋$ with ${NaBH}_{4}$ is Z . What are $𝑌$ and Z respectively?