Tg Eapcet 2020 14th September Morning Shift Question Paper Question Paper with Solutions | TG EAPCET Mock Test | JeeMate

Q 1MathematicsSection A • MCQfunctions

+1 / -0

Given that for any $𝑛 \in 𝐍$ there exist an odd integer $𝑞$ and a non-negative integer $𝑟$ such that, $𝑛$ can be written uniquely as $𝑛 = 𝑞 \times 2^{𝑟}$ .

Let $𝑓 : 𝐍 \to 𝐍 \times 𝐍$ be function defined by $𝑓 (𝑛) = (𝑟 + 1, \frac{𝑞 + 1}{2})$ . Then,

$𝑓$ is one-one but not onto

Incorrect

$𝑓$ is onto but not one-one

Incorrect

$𝑓$ is a bijection

Incorrect

only $𝑓^{- 1} (1, 1)$ does not exist because $𝑓$ is not a bijection

Incorrect

Q 2MathematicsSection A • MCQfunctions

+1 / -0

If $𝑓 : 𝐑 \to 𝐑$ be defined by $𝑓 (𝑥) = 𝑥 + 2 | 𝑥 + 1 | + 2 | 𝑥 - 1 |$ , then the element in the co-domain, which has unique pre image in the domain is

3

Incorrect

1

Incorrect

2

Incorrect

5

Incorrect

Q 3MathematicsSection A • MCQsequences and series

+1 / -0

If $𝑓 (1) = 3$ , and $𝑓 (𝑛 + 1) - 𝑓 (𝑛) = 3 (4^{𝑛} - 1)$ , then $\forall 𝑛 \in 𝐍$ , $𝑓 (𝑛) =$

$4^{𝑛} - 1$

Incorrect

$4^{𝑛} - 5 𝑛 + 4$

Incorrect

$4^{𝑛} - 3 𝑛 + 2$

Incorrect

$4^{𝑛} + 4 𝑛 - 5$

Incorrect

Q 4MathematicsSection A • MCQmatrices and determinants

+1 / -0

For a square matrix $𝐵$ of order 3 , if $𝐵^{𝑇} = 𝐵^{- 1}$ and $| 𝐵 | = 1$ , then $| 𝐵 - 𝐼 | =$

1

Incorrect

-1

Incorrect

$2 | 𝐵 |$

Incorrect

$∣ 𝐵^{𝑇} ∣ - 1$

Incorrect

Q 5MathematicsSection A • MCQmatrices and determinants

+1 / -0

For $𝛼, 𝛽 \in [0, 2 𝜋]$ and $𝛾 \in [0, 𝜋)$ consider the system of equations

$\begin{matrix} 2 \sin 𝛼 - \cos 𝛽 + 3 \tan 𝛾 = 3 \\ 4 \sin 𝛼 + 2 \cos 𝛽 - 2 \tan 𝛾 = 2 \\ 6 \sin 𝛼 - 3 \cos 𝛽 + \tan 𝛾 = 9 \end{matrix}$

Then, which one of the following is true?

$2 𝛼 - 𝛽 - 𝛾 = 0$

Incorrect

$2 𝛼 + 𝛽 + 𝛾 = 0$

Incorrect

$𝛼 - 2 𝛽 - 𝛾 = 0$

Incorrect

$𝛼 + 2 𝛽 - 𝛾 = 0$

Incorrect

Q 6MathematicsSection A • MCQmatrices and determinants

+1 / -0

$The rank of 𝐴 = ⎡⎣⎢ \begin{matrix} 1 & 𝑥 & 𝑥 + 1 \\ 2 𝑥 & 𝑥^{2} - 𝑥 & 𝑥^{2} + 𝑥 \\ 3 𝑥 (𝑥 - 1) & 𝑥 (𝑥^{2} - 3 𝑥 + 2) & 𝑥 (𝑥^{2} - 1) \end{matrix} ⎤⎦⎥ is$

3; for all $𝑥 \in 𝐑$

Incorrect

2; only for $𝑥 = - 1$

Incorrect

2; for all $𝑥$ except 0, 1 and -1

Incorrect

3; only for $𝑥 = 0$

Incorrect

Q 7MathematicsSection A • MCQcomplex numbers

+1 / -0

$𝑧_{1}, 𝑧_{2}$ are two fixed points on the Argand plane. If $𝑧$ is a complex number such that $| 𝑧 - 𝑧_{1} | + | 𝑧 - 𝑧_{2} | = 𝜆$ , then the locus of $𝑧$ is

a circle when $| 𝑧_{1} - 𝑧_{2} | < 𝜆$

Incorrect

a parabola when $| 𝑧_{1} + 𝑧_{2} | = 𝜆$

Incorrect

an ellipse when $| 𝑧_{1} - 𝑧_{2} | < 𝜆$

Incorrect

a straight line when $| 𝑧_{1} | = | 𝑧_{2} | = 𝜆$

Incorrect

Q 8MathematicsSection A • MCQcircle

+1 / -0

If the four points $𝐴, 𝐵, 𝐶, 𝐷$ in the Argand plane represented respectively by the complex numbers $2 + 𝑖, 4 + 3 𝑖, 2 + 5 𝑖, 3 𝑖$ lie on a circle, then the centre of the circle is

$1 + 2 𝑖$

Incorrect

$3 + 2 𝑖$

Incorrect

$3 + 4 𝑖$

Incorrect

$2 + 3 𝑖$

Incorrect

Q 9MathematicsSection A • MCQcomplex numbers

+1 / -0

The roots of the equation $(𝑥 - 1)^{5} = 32 (𝑥 + 1)^{5}$ are

$\frac{1 + 2 𝑒^{\frac{2 𝑘 𝜋 𝑖}{5}}}{1 - 2 𝑒^{\frac{2 𝑘 𝜋 𝑖}{5}}}, 𝑘 = 1, 2, 3, 4, 5$

Incorrect

$\frac{1 - 2 𝑒^{\frac{2 𝑘 𝜋 𝑖}{5}}}{1 + 2 𝑒^{\frac{2 𝑘 𝜋 𝑖}{5}}}, 𝑘 = 0, 1, 2, 3, 4$

Incorrect

$1, 2 𝜔, 3 𝜔^{2}, 2 𝜔 + 3 𝜔^{2}, 5 𝜔^{2} + 7$

Incorrect

$\frac{3 + 2 𝑒^{\frac{2 (𝑘 + 1) 𝜋 𝑖}{5}}}{3 - 2 𝑒^{\frac{2 (𝑘 + 1) 𝜋 𝑖}{5}}}, 𝑘 = 0, 1, 2, 3, 4$

Incorrect

Q 10MathematicsSection A • MCQcomplex numbers

+1 / -0

If $𝜔$ is a non-real cube root of unity and $𝑥 = 𝜔^{2} - 𝜔 - 3$ , then the value of $𝑥^{4} + 6 𝑥^{3} + 10 𝑥^{2} - 12 𝑥 - 19$ is

5

Incorrect

7

Incorrect

12

Incorrect

-19

Incorrect

Q 11MathematicsSection A • MCQquadratic equations

+1 / -0

The number of integral values of $𝑥$ satisfying $9 𝑥 - 2 < (𝑥 + 2)^{2} < 12 𝑥 - 3$ is

not finite

Incorrect

3

Incorrect

4

Incorrect

5

Incorrect

Q 12MathematicsSection A • MCQcomplex numbers

+1 / -0

Sum of the modulii of the complex roots of the equation $(𝑥^{2} + \frac{1}{𝑥^{2}}) - 5 (𝑥 + \frac{1}{𝑥}) + 6 = 0$ is

5

Incorrect

1

Incorrect

$\frac{1}{2}$

Incorrect

2

Incorrect

Q 13MathematicsSection A • MCQquadratic equations

+1 / -0

If $2 + \sqrt{\sqrt 3}$ is a root of the equation $𝑓 (𝑥) = 𝑥^{4} + 2 𝑥^{3} - 16 𝑥^{2} - 22 𝑥 + 7 = 0$ , then which one of the following is not a root of $𝑓 (𝑥) = 0$ ?

$3 - \sqrt{\sqrt 2}$

Incorrect

$2 - \sqrt{\sqrt 3}$

Incorrect

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

Incorrect

$- 3 - \sqrt{\sqrt 2}$

Incorrect

Q 14MathematicsSection A • MCQcomplex numbers

+1 / -0

Assertion (A) If $𝑎_{1}, 𝑎_{2}, \dots, 𝑎_{𝑛}$ are the $𝑛$ distinct roots of the equation $𝑥^{𝑛} - 2 = 0$ , then $1 + (1 - 𝑎_{1}) (1 - 𝑎_{2}) \dots (1 - 𝑎_{𝑛 - 1}) (1 - 𝑎_{𝑛}) = 0$

Reason (R) If $𝛼_{1}, 𝛼_{2}, \dots, 𝛼_{𝑛}$ are the roots of $𝑓 (𝑥) \equiv 𝑝_{0} 𝑥^{𝑛} + 𝑝_{1} 𝑥^{𝑛 - 1} + 𝑝_{2} 𝑥^{𝑛 - 2} + \dots + 𝑝_{𝑛} = 0$ , then the roots of

$𝑓 (𝑔 (𝑥)) = 0 are g^{- 1} (𝛼_{𝑖}), 𝑖 = 1, 2, 3, \dots, 𝑛$

The correct option among the following is

(A) is true, (R) is true and (R) is the correct explanation for (A).

Incorrect

(A) is true, (R) is true but (R) is not the correct explanation for (A).

Incorrect

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

Incorrect

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

Incorrect

Q 15MathematicsSection A • MCQpermutations and combinations

+1 / -0

Let $𝑆_{𝑟} = {𝑥, 𝑦, 𝑧) / 𝑥 + 𝑦 + 𝑧 = 11, 𝑥 \geq 𝑟, 𝑦 \geq 𝑟$ , $𝑧 \geq 𝑟, 𝑥, 𝑦, 𝑧, 𝑟$ are integers $}$ and $𝑛 (𝑆_{𝑟})$ represents the number of elements in $𝑆_{𝑟}$ . Then $𝑛 (𝑆_{2)} + 𝑛 (𝑆_{3}) + 𝑛 (𝑆_{4}) =$

78

Incorrect

27

Incorrect

165

Incorrect

234

Incorrect

Q 16MathematicsSection A • MCQpermutations and combinations

+1 / -0

A certain question paper contains three parts $𝐴, 𝐵, 𝐶$ with four questions in part $𝐴$ , five questions in part $𝐵$ and six questions in part $𝐶$ . A student is required to answer seven questions choosing at least two questions from each part. Then the total number of different ways a student can choose his seven questions for answering, is

1500

Incorrect

1200

Incorrect

1900

Incorrect

2700

Incorrect

Q 17MathematicsSection A • MCQbinomial theorem

+1 / -0

$𝑝, 𝑞$ are two prime numbers. For $𝑛 = 𝑝 𝑞$ , if the expansion ${(\sqrt[4]{\sqrt} + 2 \sqrt[5]{\sqrt})}^{𝑛}$ contains non-zero coefficient of $𝑥^{- 𝑛}$ and $𝑥^{0}$ , then the least value of such $𝑛$ is

82

Incorrect

41

Incorrect

123

Incorrect

62

Incorrect

Q 18MathematicsSection A • MCQbinomial theorem

+1 / -0

The binomial expansion $(7 + 3 𝑥)^{- 2 / 5}$ is valid for all $𝑥$ in the interval $(\frac{- 7}{3}, \frac{7}{3})$ and if the 4 th term of its expansion is $𝑘 𝑥^{3}$ , then $(7^{12 / 5} 𝑘) =$

$\frac{- 2}{125}$

Incorrect

$\frac{- 108}{125}$

Incorrect

$\frac{- 72}{125}$

Incorrect

$- \frac{36}{125}$

Incorrect

Q 19MathematicsSection A • MCQfunctions

+1 / -0

Let $𝐻 (𝑥) = 3 𝑥^{4} + 6 𝑥^{3} - 2 𝑥^{2} + 1$ and $𝑔 (𝑥)$ be a polynomial of degree one. If

$\frac{𝐻 (𝑥)}{(𝑥 - 1) (𝑥 + 1) (𝑥 - 2)} = 𝑓 (𝑥) + \frac{𝑔 (𝑥)}{(𝑥 - 1) (𝑥 + 1) (𝑥 - 2)}$ then

$𝐻 (- 1) + 2 𝐻 (2) - 3 𝐻 (1) =$

$𝑓 (- 1) + 2 𝑓 (2) - 3 𝑓 (1)$

Incorrect

$𝐻 (- 1) + 𝑓 (2) + 𝑔 (3)$

Incorrect

$𝑔 (- 1) + 2 𝑔 (2) - 3 𝑔 (1)$

Incorrect

$𝐻 (1) + 2 𝑓 (2) - 𝑔 (1)$

Incorrect

Q 20MathematicsSection A • MCQtrigonometric equations

+1 / -0

The smallest positive value of $𝑥$ (in degrees) for which $\tan (𝑥 + 100^{\circ}) = \tan (𝑥 + 50^{\circ}) \tan (𝑥) \tan (𝑥 - 50^{\circ})$ is

$15^{\circ}$

Incorrect

$22 \frac{1^{\circ}}{2}$

Incorrect

$75^{\circ}$

Incorrect

$30^{\circ}$

Incorrect

Q 21MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

For $𝑛 \in 𝐍$ , if $𝑓 (𝑛) = (\cos 𝑛 𝑥) (\sec 𝑥)^{𝑛}$ and $𝑔 (𝑛) = (\sin 𝑛 𝑥) (\sec 𝑥)^{𝑛}$ , then $𝑓 (2020) - 𝑓 (2019) + (\tan 𝑥) 𝑔 (2019) =$

$\sin 𝑥$

Incorrect

$\cos 𝑥$

Incorrect

0

Incorrect

1

Incorrect

Q 22MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

$𝜃$ and $𝛼$ lie in $𝑄_{3}$ . If $\cos (𝜃 - 𝛼), \cos 𝜃, \cos (𝜃 + 𝛼)$ are in harmonic progression, then $\cos 𝜃 \sec \frac{𝛼}{2} =$

$- \sqrt{\sqrt 2}$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

$- \sqrt{\sqrt 3}$

Incorrect

$\sqrt{\sqrt 3}$

Incorrect

Q 23MathematicsSection A • MCQtrigonometric equations

+1 / -0

If the possible solution of the equation $2 \cos^{2} 𝑥 + 3 \sin 𝑥 - 3 = 0$ constitute two unequal angles of a triangle, then the third angle of that triangle is

$\frac{𝜋}{2}$

Incorrect

$\frac{𝜋}{3}$

Incorrect

$\frac{𝜋}{6}$

Incorrect

$\frac{𝜋}{4}$

Incorrect

Q 24MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ if $∠ 𝐶 = \frac{𝜋}{2}$ then

$\tan^{- 1} (\frac{𝑎}{𝑏 + 𝑐}) + \tan^{- 1} (\frac{𝑏}{𝑐 + 𝑎}) + \tan^{- 1} (\frac{𝑐}{𝑎 + 𝑏}) =$

$\tan^{- 1} (\frac{𝑟_{3}}{𝑟})$

Incorrect

$\tan^{- 1} (\frac{𝑟_{1} + 𝑟_{2}}{𝑟_{3}})$

Incorrect

$\tan^{- 1} (\frac{1}{𝑟})$

Incorrect

$\tan^{- 1} (\frac{𝑟_{1} + 𝑟_{2} + 𝑟_{3}}{𝑟})$

Incorrect

Q 25MathematicsSection A • MCQinverse trigonometric functions

+1 / -0

If $\sinh (2 \tanh^{- 1} 𝑥) = \frac{11}{60}$ , then $𝑥 =$

-11

Incorrect

$\frac{- 1}{11}$

Incorrect

$\frac{1}{11}$

Incorrect

11

Incorrect

Q 26MathematicsSection A • MCQproperties of triangles

+1 / -0

If the sides of a triangle are in the ratio $\sqrt{\sqrt 3} : \sqrt{\sqrt 5} : \sqrt{\sqrt 8 + \sqrt{\sqrt 15}}$ , then the largest angle in that triangle is

$\frac{2 𝜋}{3}$

Incorrect

$\frac{𝜋}{2}$

Incorrect

$\frac{𝜋}{3}$

Incorrect

$\frac{5 𝜋}{6}$

Incorrect

Q 27MathematicsSection A • MCQproperties of triangles

+1 / -0

In a $△ 𝐴 𝐵 𝐶$ , if $\tan 𝐴 : \tan 𝐵 : \tan 𝐶 = 1 : 2 : 3$ and $\sin 𝐴 : \sin 𝐵 : \sin 𝐶 = \sqrt{\sqrt 5} : 2 \sqrt{\sqrt 2} : 𝑘$ , then $𝑘 =$

$\sqrt{\sqrt 2}$

Incorrect

2

Incorrect

$\sqrt{\sqrt 3}$

Incorrect

3

Incorrect

Q 28MathematicsSection A • MCQproperties of triangles

+1 / -0

In $△ 𝐴 𝐵 𝐶$ , if $𝑅 = \frac{65}{8}, 𝑟 𝑟_{1} = 42$ and $𝑟_{1} - 𝑟 = 6.5$ , then $𝑠 (𝑠 - 𝑎) =$

147

Incorrect

126

Incorrect

105

Incorrect

168

Incorrect

Q 29MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐴 𝐵 𝐶 𝐷$ be a parallelogram and $𝐸$ be the mid-point of $𝐴 𝐵$ . If $𝑃$ is the point of intersection of $𝐷 𝐸$ and $𝐴 𝐶$ , then $\frac{𝐷 𝑃}{𝑃 𝐸} + \frac{𝐴 𝑃}{𝑃 𝐶} =$

$\frac{5}{2}$

Incorrect

$\frac{4}{3}$

Incorrect

$\frac{3}{2}$

Incorrect

$\frac{2}{3}$

Incorrect

Q 30MathematicsSection A • MCQvector algebra

+1 / -0

A vector $𝐚$ has components $2 𝑝$ and 1 with respect to a two dimensional rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise direction. If $𝐚$ has components $𝑝 + 1$ and 1 with respect to the new system, then

$𝑝 = 1$ or $𝑝 = \frac{- 1}{3}$

Incorrect

$𝑝 = - 1$ or $𝑝 = \frac{1}{3}$

Incorrect

$𝑝 = 1$ or $𝑝 = - 1$

Incorrect

$𝑝 = 0$ or $𝑝 = \frac{1}{2}$

Incorrect

Q 31MathematicsSection A • MCQvector algebra

+1 / -0

Let

𝐴 (3 \hat{𝐢} + \hat{𝐣} - \hat{𝐤})

and

𝐵 (13 \hat{𝐢} - 4 \hat{𝐣} + 9 \hat{𝐤})

be two points on a line

𝐿 . 𝐶

and

𝐷

be the points on

𝐿

on either side of

𝐴

at distance of 9 and 6 units respectively and

𝐶

lies between

𝐴

and

𝐵

. Then position vectors of

𝐶

and

𝐷

are respectively

$- 3 \hat{𝐢} + 4 \hat{𝐣} - 7 \hat{𝐤}, 7 \hat{𝐢} - \hat{𝐣} + 3 \hat{𝐤}$

Incorrect

$9 \hat{𝑖} - 2 \hat{𝑗} + 5 \hat{𝑘}, 7 \hat{𝑖} - \hat{𝑗} + 3 \hat{𝑘}$

Incorrect

$- 3 \hat{𝐢} + 4 \hat{𝐣} - 7 \hat{𝐤}, - \hat{𝐢} + 3 \hat{𝐣} - 5 \hat{𝐤}$

Incorrect

$9 \hat{𝐢} - 2 \hat{𝐣} + 5 \hat{𝐤}, - \hat{𝐢} + 3 \hat{𝐣} - 5 \hat{𝐤}$

Incorrect

Q 32MathematicsSection A • MCQvector algebra

+1 / -0

If $𝐚 = 2 𝐮 + 3 𝐯 + 7 𝐰, 𝑏 = 𝐮 + 𝐯 - 2 𝐰$ and $𝐜 = - 𝐮 - 2 𝐯 - 3 𝐰$ then $∣ \frac{[𝐮 𝐯 𝐰]}{[𝐚 𝐛 𝐜]} ∣ (𝐚 + 𝐛 + 𝐜) =$

$12 (𝐮 + 𝐯 + 𝐰)$

Incorrect

$3 (𝐮 + 𝐯 + 𝐰)$

Incorrect

$\frac{2}{3} (𝐮 + 𝐯 + 𝐰)$

Incorrect

$\frac{1}{3} (𝑢 + 𝑣 + 𝑤)$

Incorrect

Q 33MathematicsSection A • MCQvector algebra

+1 / -0

Let $𝐕 = 2 \hat{𝐢} + \hat{𝐣} - \hat{𝐤}$ and $𝐖 = \hat{𝐢} + 3 \hat{𝐤}$ . If $𝐔$ is a unit vector, then the maximum value of $[𝐔 𝐕 𝐖]$ is

-1

Incorrect

$\sqrt{\sqrt 10} + \sqrt{\sqrt 16}$

Incorrect

$\sqrt{\sqrt 59}$

Incorrect

$\sqrt{\sqrt 60}$

Incorrect

Q 34MathematicsSection A • MCQ3d geometry

+1 / -0

$𝐿_{1}$ is a line passing through the points with position vectors $\hat{𝐢} - 2 \hat{𝐣} - \hat{𝐤}$ and $4 \hat{𝐢} - 3 \hat{𝐤} . 𝐿_{2}$ is a line passing through the points with position vectors $\hat{𝐢} + 2 \hat{𝐣} - \hat{𝐤}$ and $2 \hat{𝐢} - 4 \hat{𝐣} - 5 \hat{𝐤}$ . Then the distance between $𝐿_{1}$ and $𝐿_{2}$ is

0

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{4}{3}$

Incorrect

$\frac{2}{3}$

Incorrect

Q 35MathematicsSection A • MCQstatistics

+1 / -0

The mean and standard deviation of 100 observations $𝑥_{1}, 𝑥_{2}, \dots, 𝑥_{100}$ were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. Then the correct value of $\sum_{100}^{𝑖 = 1} 𝑥_{2}^{𝑖} =$

3990

Incorrect

161701

Incorrect

162601

Incorrect

4000

Incorrect

Q 36MathematicsSection A • MCQstatistics

+1 / -0

The coefficient of variation of the first 5 prime numbers is

$\frac{400}{7}$

Incorrect

$\frac{406}{7}$

Incorrect

$\frac{416}{7}$

Incorrect

$\frac{425}{8}$

Incorrect

Q 37MathematicsSection A • MCQprobability

+1 / -0

A person tossing a biased coin indefinitely wins the game by getting head for the first time. The probability that he wins the game in odd number of tosses is $3 / 4$ . If 5 such coins are tossed at a time then the probability that head appears on all the coins is

$\frac{32}{3125}$

Incorrect

$\frac{243}{3125}$

Incorrect

$\frac{1}{243}$

Incorrect

$\frac{32}{243}$

Incorrect

Q 38MathematicsSection A • MCQprobability

+1 / -0

Let $𝐵 (𝛼, 𝛽, 𝛾)$ represents that a bag $𝐵$ contains $𝛼$ red balls, $𝛽$ green balls and $𝛾$ blue balls. Given $𝐵_{1} (2, 3, 2), 𝐵_{2} (3, 2, 2), 𝐵_{3} (2, 2, 3)$ . A die is rolled. If the die shows up 2 or 3 or 5 , then a ball will be drawn at random from bag $𝐵_{1}$ . If the die shows up 4 or 6 , then a ball will be drawn at random from bag $𝐵_{2}$ . If the die shows up 1 , then from bag $𝐵_{3}$ a ball will be drawn at random. Then the probability of drawing a green ball from a bag thus chosen is

$\frac{2}{7}$

Incorrect

$\frac{5}{14}$

Incorrect

$\frac{3}{5}$

Incorrect

$\frac{2}{3}$

Incorrect

Q 39MathematicsSection A • MCQprobability

+1 / -0

If the coefficients $𝑎$ and $𝑏$ of a quadratic expression $𝑥^{2} + 𝑎 𝑥 + 𝑏$ are chosen from the sets $𝐴 = {3, 4, 5}$ and $𝐵 = {1, 2, 3, 4}$ respectively, then the probability that the equation $𝑥^{2} + 𝑎 𝑥 + 𝑏 = 0$ has real roots is

$\frac{1}{6}$

Incorrect

$\frac{5}{6}$

Incorrect

$\frac{3}{4}$

Incorrect

$\frac{7}{12}$

Incorrect

Q 40MathematicsSection A • MCQprobability

+1 / -0

A random variable $𝑋$ has the following probability distribution

$\begin{matrix} 𝑋 = 𝑥 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 𝑃 (𝑋 = 𝑥) & 0.15 & 0.23 & 𝐾 & 0.10 & 0.20 & 0.08 & 0.07 & 0.05 \end{matrix}$

For the event $𝐸 = {𝑋 / 𝑋$ is a prime number $}$ and the event $𝐹 = {𝑋 / 𝑋 < 4}$ , the probability $𝑃 (𝐸 \cup 𝐹) =$

0.35

Incorrect

0.57

Incorrect

0.87

Incorrect

0.77

Incorrect

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

+1 / -0

If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other, then the points $𝑃 (𝑥, 𝑦)$ on such lines satisfy

$𝑥 + 𝑦 > 4$

Incorrect

$4 𝑥 𝑦 > 1$

Incorrect

$4 𝑥 𝑦 < 1$

Incorrect

$𝑥 + 𝑦 = 4$

Incorrect

Q 42MathematicsSection A • MCQhyperbola

+1 / -0

Suppose the axes $𝑋$ and $𝑌$ are obtained by rotating the axes $𝑥$ and $𝑦$ an angle $𝜃$ . If the equation $𝑥^{2} + 2 \sqrt{\sqrt 3} 𝑥 𝑦 - 𝑦^{2} = 4 𝑎^{2}$ is transformed to $𝑋^{2} - 𝑌^{2} = 2 𝑎^{2}$ with respect to the $𝑋 𝑌$ -axes, then $𝜃$ is equal to

$45^{\circ}$

Incorrect

$60^{\circ}$

Incorrect

$90^{\circ}$

Incorrect

$30^{\circ}$

Incorrect

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

+1 / -0

If the lines drawn along the diagonals of the two squares formed by two pairs of lines $𝑥^{2} - 3 | 𝑥 | + 2 = 0$ and $𝑦^{2} - 3 𝑦 + 2 = 0$ form a square $𝐴 𝐵 𝐶 𝐷$ , then the equations of two adjacent sides of the square $𝐴 𝐵 𝐶 𝐷$ are

$𝑥 + 𝑦 = - 3, 𝑥 - 𝑦 = 3$

Incorrect

$𝑥 + 𝑦 = 0, 𝑥 - 𝑦 = 3$

Incorrect

$𝑥 + 𝑦 = 3, 𝑥 - 𝑦 = - 3$

Incorrect

$𝑥 - 𝑦 = 0, 𝑥 + 𝑦 = - 3$

Incorrect

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

+1 / -0

If $𝜋 / 3$ is the angle between the straight lines $𝑝 𝑥 + 𝑞 𝑦 + 𝑟 = 0$ and $𝑥 \sin 𝛼 + 𝑦 \cos 𝛼 = 𝑟 (𝑟 \neq 0)$ which meet at a point $𝐴$ and the straight line $𝑥 \cos 𝛼 - 𝑦 \sin 𝛼 = 0$ also passes through the point $𝐴$ , then

$𝑝^{2} + 𝑞^{2} = 4$

Incorrect

$𝑝^{2} + 𝑞^{2} = 2$

Incorrect

$𝑝^{2} + 𝑞^{2} = 𝑟^{2}$

Incorrect

$𝑝^{2} + 𝑞^{2} = 2 𝑟^{2}$

Incorrect

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

+1 / -0

The distance between the point $(2, 1)$ and the image of the point $(3, - 1)$ with respect to the line $2 𝑥 + 𝑦 - 1 = 0$ is

$\sqrt{\sqrt \frac{37}{5}}$

Incorrect

$\sqrt{\sqrt \frac{81}{5}}$

Incorrect

$\sqrt{\sqrt \frac{89}{5}}$

Incorrect

$\sqrt{\sqrt \frac{29}{5}}$

Incorrect

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

+1 / -0

Let $𝑂 𝐴 𝐵 𝐶$ be a parallelogram. The equation of one diagonal $𝐴 𝐶$ is $𝑥 + 𝑦 - 1 = 0$ and the combined equation of the sides $𝑂 𝐴, 𝑂 𝐶$ is $2 𝑥^{2} - 𝑦^{2} = 0$ . If $𝐺$ is centroid of the triangle $𝑂 𝐴 𝐶$ , then $𝐵 𝐺 =$

$2 \sqrt{\sqrt 5}$

Incorrect

$\frac{4}{3} \sqrt{\sqrt 5}$

Incorrect

$\frac{2}{3} \sqrt{\sqrt 15}$

Incorrect

$\frac{4}{9} \sqrt{\sqrt 5}$

Incorrect

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

+1 / -0

The acute angle between the pair of straight lines joining the origin to the points of intersection of the line $𝑥 + 𝑦 - 1 = 0$ with the pair of straight lines $𝑘 𝑥^{2} + 8 𝑥 𝑦 - 3 𝑦^{2} + 2 𝑥 - 4 𝑦 - 1 = 0$ is

$\frac{𝜋}{2}$

Incorrect

$\frac{𝜋}{4}$

Incorrect

$\cos^{- 1} (\frac{1}{\sqrt{\sqrt 10}})$

Incorrect

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

Incorrect

Q 48MathematicsSection A • MCQcircle

+1 / -0

The centre and radius of the circumcircle of the triangle formed by the lines $2 𝑥 + 3 𝑦 = 10, 𝑦 = 𝑥$ and the $𝑋$ -axis are respectively.

$(\frac{- 5}{2}, \frac{3}{2}), \frac{\sqrt{\sqrt 34}}{2}$

Incorrect

$(\frac{5}{2}, 2), \frac{\sqrt{\sqrt 41}}{2}$

Incorrect

$(\frac{5}{2}, \frac{- 1}{2}), \sqrt{\sqrt \frac{13}{2}}$

Incorrect

$(\frac{1}{2}, \frac{- 5}{2}), \sqrt{\sqrt \frac{13}{2}}$

Incorrect

Q 49MathematicsSection A • MCQcircle

+1 / -0

If the straight 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 square units) is

$\frac{9 𝜋}{4}$

Incorrect

$\frac{9 𝜋}{16}$

Incorrect

$\frac{25 𝜋}{9}$

Incorrect

$\frac{121 𝜋}{25}$

Incorrect

Q 50MathematicsSection A • MCQcircle

+1 / -0

In the List-I each item contains equations of two circles, List-II contains the number of common tangents for each pair of circles given in List-I. Match the items of List-I with those of the items of List-II

$List-I$		$List-II$
A.	$\begin{matrix} 𝑥^{2} + 𝑦^{2} + 2 𝑥 + 8 𝑦 - 23 = 0 \\ 𝑥^{2} + 𝑦^{2} - 4 𝑥 - 10 𝑦 + 19 = 0 \end{matrix}$	I.	0
B.	$\begin{matrix} 𝑥^{2} + 𝑦^{2} = 1 \\ 𝑥^{2} + 𝑦^{2} - 2 𝑥 - 6 𝑦 + 6 = 0 \end{matrix}$	II.	1
C.	$\begin{matrix} 𝑥^{2} + 𝑦^{2} - 8 𝑥 + 2 𝑦 = 0 \\ 𝑥^{2} + 𝑦^{2} - 2 𝑥 - 16 𝑦 + 25 = 0 \end{matrix}$	III.	2
D.	$\begin{matrix} 𝑥^{2} + 𝑦^{2} = 4 \\ 𝑥^{2} + 𝑦^{2} - 2 𝑥 = 0 \end{matrix}$	IV.	3
		V.	4

$The correct match is$

A	B	C	D
V	I	III	II

Incorrect

A	B	C	D
IV	I	III	II

Incorrect

A	B	C	D
IV	V	III	II

Incorrect

A	B	C	D
III	IV	I	IV

Incorrect

Q 51MathematicsSection A • MCQcircle

+1 / -0

$(0, \frac{3}{4})$ is the radical centre of the circles $𝑆_{1} : 𝑥^{2} + 𝑦^{2} - 2 𝑥 + 6 𝑦 = 0, 𝑆_{2} : 𝑥^{2} + 𝑦^{2} + 2 𝑔 𝑥 - 2 𝑦 + 6 = 0$ and $𝑆_{3} : 𝑥^{2} + 𝑦^{2} - 12 𝑥 + 2 𝑓 𝑦 + 3 = 0$ . If $𝑆_{2}$ and $𝑆_{3}$ intersect orthogonally, then $(𝑔, 𝑓) =$

$(\frac{- 11}{12}, 1)$

Incorrect

$(1, \frac{- 21}{2})$

Incorrect

$(0, \frac{- 9}{2})$

Incorrect

$(- 1, \frac{- 7}{12})$

Incorrect

Q 52MathematicsSection A • MCQcircle

+1 / -0

For the circles $(𝑥 - 𝑎)^{2} + 𝑦^{2} = 𝑎^{2}$ and $𝑥^{2} + (𝑦 - 𝑎)^{2} = 𝑎^{2}$ , where $𝑎 > 0$ , which one of the following is not true?

mid-point of the common chord is $(\frac{𝑎}{2}, \frac{𝑎}{2})$

Incorrect

length of the common chord is $(\sqrt{\sqrt 2} 𝑎)$

Incorrect

the circles intersect at $(0, 0)$ and $(𝑎, 𝑎)$

Incorrect

common chord is at a distance of $(\sqrt{\sqrt 2} 𝑎)$ units from the centres of given circles

Incorrect

Q 53MathematicsSection A • MCQparabola

+1 / -0

If $𝑆 (𝑎, 𝑏)$ is a fixed point and $𝑃 (𝛼, 𝛽)$ is such a variable point that $4 [(𝑥 - 𝑎)^{2} + (𝑦 - 𝑏)^{2}] = (𝛼 𝑥 + 𝛽 𝑦 + 7)^{2}$ represents a parabola, then the locus of $𝑃 (𝛼, 𝛽)$ is

$𝛽^{2} = 4 𝛼$

Incorrect

$𝛼^{2} + 𝛽^{2} = 4$

Incorrect

$\frac{𝛼^{2}}{4} + \frac{𝛽^{2}}{2} = 1$

Incorrect

$(𝛼 + 𝛽)^{2} = 4$

Incorrect

Q 54MathematicsSection A • MCQparabola

+1 / -0

If $𝑃 (- 3, 2)$ is an end point of the focal chord $𝑃 𝑄$ of the parabola $𝑦^{2} + 4 𝑥 + 4 𝑦 = 0$ , then the slope of the normal drawn at $𝑄$ is

$\frac{- 1}{2}$

Incorrect

2

Incorrect

$\frac{1}{2}$

Incorrect

-2

Incorrect

Q 55MathematicsSection A • MCQellipse

+1 / -0

Equation of a common tangent to the circle $𝑥^{2} + 𝑦^{2} = 4$ and to the ellipse $2 𝑥^{2} + 25 𝑦^{2} = 50$ is

$\sqrt{\sqrt 2} 𝑥 + \sqrt{\sqrt 21} 𝑦 + \sqrt{\sqrt 23} = 0$

Incorrect

$\sqrt{\sqrt 2} 𝑥 - \sqrt{\sqrt 21} 𝑦 + 2 \sqrt{\sqrt 23} = 0$

Incorrect

$\sqrt{\sqrt 19} 𝑥 - \sqrt{\sqrt 2} 𝑦 + 2 \sqrt{\sqrt 21} = 0$

Incorrect

$\sqrt{\sqrt 19} 𝑥 - 𝑦 + 2 \sqrt{\sqrt 20} = 0$

Incorrect

Q 56MathematicsSection A • MCQellipse

+1 / -0

The $𝜃$ is the angle made by the common tangent to the circle $𝑥^{2} + 𝑦^{2} = 16$ and the ellipse $\frac{𝑥^{2}}{25} + \frac{𝑦^{2}}{9} = 1$ with positive $𝑋$ -axis, then $\cos 2 𝜃 =$

$\frac{- 2}{3}$

Incorrect

$\frac{5}{6}$

Incorrect

$\frac{- 1}{8}$

Incorrect

$\frac{1}{8}$

Incorrect

Q 57MathematicsSection A • MCQhyperbola

+1 / -0

For the hyperbola $𝑥^{2} - 𝑦^{2} - 4 𝑥 + 2 𝑦 + 𝑐 = 0$ , if the focus is $𝑆 (2 + 2 \sqrt{\sqrt 2}, 𝑘)$ and the directrix that is adjacent to $𝑆$ is $𝑥 = 2 + \sqrt{\sqrt 2}$ , then $𝑐 =$

0

Incorrect

-1

Incorrect

1

Incorrect

2

Incorrect

Q 58MathematicsSection A • MCQ3d geometry

+1 / -0

The quadrilateral formed by the points $𝐴 (1, 2, 5), 𝐵 (- 1, 6, 1), 𝐶 (3, 4, - 3)$ and $𝐷 (5, 0, 1)$ is a

Parallelogram

Incorrect

Rectangle

Incorrect

Square

Incorrect

Rhombus

Incorrect

Q 59MathematicsSection A • MCQ3d geometry

+1 / -0

A line with direction cosines proportional to $2, 1, 2$ meets the line $𝐿_{1}$ passing through $(0, - 1, 0)$ with direction ratios $1, 1, 1$ at $𝐴 (𝑥, 𝑦, 𝑧)$ and another line $𝐿_{2}$ at $𝐵 (1, 1, 1)$ then $𝑥 + 𝑦 + 𝑧 =$

7

Incorrect

8

Incorrect

9

Incorrect

10

Incorrect

Q 60MathematicsSection A • MCQ3d geometry

+1 / -0

If a plane $𝜋$ passes through the point $(- 1, 6, 2)$ is perpendicular to the planes $𝑥 + 2 𝑦 + 2 𝑧 - 5 = 0$ and $3 𝑥 + 3 𝑦 + 2 𝑧 - 8 = 0$ , then, the perpendicular distance from the point $(1, - 1, 1)$ to the plane $𝜋$ is

$\frac{20}{\sqrt{\sqrt 29}}$

Incorrect

$\frac{21}{\sqrt{\sqrt 29}}$

Incorrect

$\frac{27}{\sqrt{\sqrt 29}}$

Incorrect

$\sqrt{\sqrt 29}$

Incorrect

Q 61MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

If $𝑓 : 𝐑 \to 𝐑$ and $𝑔 : 𝐑 \to 𝐑$ be defined by $𝑓 (𝑥) = {\begin{matrix} 𝑥 + 2, & 𝑥 > 0 \\ 2 - 𝑥, & 𝑥 \leq 0 \end{matrix}$ and $𝑔 (𝑥) = ⎧⎩⎨⎪⎪ \begin{matrix} 𝑥^{2} - 2 𝑥 - 2, & 1 \leq 𝑥 < 2 \\ 𝑥 - 7 & 𝑥 \geq 2 \\ 𝑥 + 5, & 𝑥 < 1 \end{matrix}$ then $lim_{𝑥 \to 0} 𝑔 \circ 𝑓 (𝑥)$

is equal to -7

Incorrect

is equal to -5

Incorrect

is equal to 2

Incorrect

does not exist

Incorrect

Q 62MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

Define $𝑓 : 𝑅 \to 𝑅$ by $𝑓 (𝑥) = ⎧⎩⎨ \begin{matrix} (𝑥 - 𝑎) \frac{𝑒^{\frac{1}{(𝑥 - 𝑎)}} - 1}{\frac{1}{(𝑥 - 𝑎)}} + 1 & for 𝑥 \neq 𝑎 \\ 0, at 𝑥 = 𝑎 \end{matrix}$

Then which one of the following is true?

Left and right limits of $𝑓$ at $𝑥 = 𝑎$ are equal and they are not equal to $𝑓 (𝑎)$

Incorrect

Both left and right limits of $𝑓$ at $𝑥 = 𝑎$ exist and are not equal

Incorrect

The function $𝑓 (𝑥)$ is continuous at $𝑥 = 𝑎$

Incorrect

The function $𝑓 (𝑥)$ has a simple discontinuity at a point other than $𝑎$

Incorrect

Q 63MathematicsSection A • MCQdifferentiation

+1 / -0

If ${Lt}_{ℎ \to 0} \frac{𝑓 (𝑥 + ℎ) - 𝑓 (𝑥)}{ℎ} = 𝑒^{𝑥} (𝑥 + 1)$ and $𝑓 (0) = 0$ , then $\frac{𝑑}{𝑑 𝑥} (𝑓 (𝑥) 𝑒^{- 𝑥}) + \frac{𝑑}{𝑑 𝑥} (\frac{𝑓 (𝑥)}{𝑥}) =$

$𝑒^{𝑥} + 1$

Incorrect

$𝑥^{2} 𝑒^{𝑥} + 𝑥$

Incorrect

$𝑥 𝑒^{𝑥} + 1$

Incorrect

$𝑥^{2} 𝑒^{𝑥}$

Incorrect

Q 64MathematicsSection A • MCQlimits continuity and differentiability

+1 / -0

Let $𝑓, 𝑔 : 𝐑 \to 𝐑$ be functions defined by

$𝑓 (𝑥) = {\begin{matrix} 𝑥 \sin (\frac{1}{𝑥}), & for 𝑥 \neq 0 \\ 0, & for 𝑥 = 0 \end{matrix}$

and $𝑔 (𝑥) = 𝑥 𝑓 (𝑥)$

Consider the following statements

(i) $𝑓 (𝑥)$ is continuous at $𝑥 = 0$ but not differentiable at $𝑥 = 0$

(ii) $𝑔 (𝑥)$ is differentiable at $𝑥 = 0$ , but $𝑔^{1} (𝑥)$ is not continuous at $𝑥 = 0$

Then, which one of the following is true?

(i) is true; but (ii) is false

Incorrect

Both (i) and (ii) are true

Incorrect

(i) is false, but (ii) is true

Incorrect

Both (i) and (ii) are false

Incorrect

Q 65MathematicsSection A • MCQdifferentiation

+1 / -0

If $𝑦 (𝑥) = \tan^{- 1} (\frac{\sqrt{\sqrt 1 + 𝑎^{2} 𝑥^{2}} - 1}{𝑎 𝑥})$ and $(1 + 𝑎^{2} 𝑥^{2}) 𝑦^{''} + 𝑔 (𝑥) 𝑦^{'} = 0$ then, the sum of the roots of the equation $1 + 𝑎^{2} 𝑥^{2} + 𝑔 (𝑥) = 0$ is

$2 𝑎$

Incorrect

$- 2 𝑎^{2}$

Incorrect

2

Incorrect

-2

Incorrect

Q 66MathematicsSection A • MCQapplication of derivatives

+1 / -0

A vessel in the shape of an inverted cone of height 10 ft and semi vertical angle $30^{\circ}$ is full of water. Due to a hole at the vertex, the slant height of the water in the vessel is decreasing at a constant rate of $\frac{1}{\sqrt{\sqrt 3}}$ feet per minute. The rate (in cu. feet/min) at which the volume of water in the vessel is decreasing, when the volume of water is $\frac{8 𝜋}{\sqrt{\sqrt 3}}$ cubic feet, is

$\frac{2 𝜋}{\sqrt{\sqrt 3}}$

Incorrect

$2 𝜋$

Incorrect

$2 𝜋 \sqrt{\sqrt 3}$

Incorrect

$𝜋 \sqrt{\sqrt 3}$

Incorrect

Q 67MathematicsSection A • MCQapplication of derivatives

+1 / -0

The area (in sq. units) of the triangle formed by the tangent and normal drawn to the curve ${(\frac{𝑥}{3})}^{𝑛} + {(\frac{𝑦}{4})}^{𝑛} = 2$ at $(3, 4)$ and $𝑥$ -axis is

$\frac{100}{3}$

Incorrect

48

Incorrect

$\frac{50}{3}$

Incorrect

144

Incorrect

Q 68MathematicsSection A • MCQapplication of derivatives

+1 / -0

If the curves $𝑎 𝑥^{2} + 𝑏 𝑦^{2} = 1$ and $𝑐 𝑥^{2} + 𝑑 𝑦^{2} = 1$ intersect orthogonally, then $\frac{𝑏 - 𝑎}{𝑑 - 𝑐} =$

$\frac{𝑎}{𝑐} \cdot \frac{𝑏}{𝑑}$

Incorrect

$\frac{𝑎 + 𝑏}{𝑐 + 𝑑}$

Incorrect

1

Incorrect

0

Incorrect

Q 69MathematicsSection A • MCQtrigonometric ratios and identities

+1 / -0

The ratio of the maximum and minimum values attained by the function $𝑓 (𝑥) = 1 + 2 \sin 𝑥 + 3 \cos^{2} 𝑥, 0 \leq 𝑥 \leq \frac{2 𝜋}{3}$ is

$3 : 1$

Incorrect

$13 : 9$

Incorrect

$9 : 4$

Incorrect

$8 : 13$

Incorrect

Q 70MathematicsSection A • MCQindefinite integration

+1 / -0

If $5 (𝑓 (𝑥))^{2} = 𝑥 𝑓 (𝑥) + 30$ and

$\begin{matrix} \int \frac{(3 𝑥^{3} + (1 - 30 𝑥^{2}) 𝑓 (𝑥))}{(10 𝑓 (𝑥) - 𝑥) {(𝑥^{3} - 𝑓 (𝑥))}^{2}} 𝑑 𝑥 \\ = \frac{𝐴}{𝐵 𝑥^{3} + 𝐷 𝑓 (𝑥)} + 𝐶 then 𝐴 + 𝐵 + 𝐷 = \end{matrix}$

2

Incorrect

1

Incorrect

$\frac{1}{2}$

Incorrect

-1

Incorrect

Q 71MathematicsSection A • MCQindefinite integration

+1 / -0

If $\int 𝑥 [\log (1 + 𝑥)]^{3} 𝑑 𝑥 = \frac{(1 + 𝑥)^{2}}{16} (𝑓 (𝑥)) + (1 + 𝑥) (𝑔 (𝑥))$ , then

$𝑓 (𝑥) + 𝑔 (𝑥) =$

$\log (1 + 𝑥) [6 + 9 (\log (1 + 𝑥)) - 7 (\log (1 + 𝑥))^{2}] + 𝐶$

Incorrect

$\log (1 + 𝑥) 𝑥^{3} + 7 (\log (1 + 𝑥))^{2} + 4 \log (1 + 𝑥) + 𝐶$

Incorrect

$12 - 18 \log (1 + 𝑥) + 15 (\log (1 + 𝑥))^{2} - 9 (\log (1 + 𝑥))^{3} + 𝐶$

Incorrect

$6 \log (1 + 𝑥) - 9 (\log (1 + 𝑥))^{2} + 7 (\log (1 + 𝑥))^{3} + 𝐶$

Incorrect

Q 72MathematicsSection A • MCQindefinite integration

+1 / -0

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

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

Incorrect

$\log ∣ 𝑥 + \sqrt{\sqrt 1 + 𝑥^{2}} ∣ + 𝐶$

Incorrect

$𝑥 + \sqrt{\sqrt 1 + 𝑥^{2}} + 𝐶$

Incorrect

$\frac{{(𝑥 + \sqrt{\sqrt 1 + 𝑥^{2}})}^{2}}{2} + 𝐶$

Incorrect

Q 73MathematicsSection A • MCQindefinite integration

+1 / -0

$\int {[\frac{𝑥^{4} - 𝑥}{𝑥^{20}}]}^{1 / 4} 𝑑 𝑥 =$

$\frac{4}{15} {(\frac{{(𝑥^{3} - 1)}^{5}}{𝑥^{15}})}^{1 / 4} + 𝐶$

Incorrect

$\frac{4}{15} {(\frac{𝑥^{4} + 1}{𝑥^{4}})}^{1 / 4} + 𝐶$

Incorrect

$\frac{\sqrt{\sqrt 𝑥^{4} + 𝑥^{2} + 1}}{𝑥} + 𝐶$

Incorrect

$\frac{3}{4} (𝑥^{4 / 3} + 𝑥^{1 / 3}) + 𝐶$

Incorrect

Q 74MathematicsSection A • MCQdefinite integration

+1 / -0

$\begin{matrix} lim_{𝑛 \to \infty} [\frac{𝑛^{3 / 2}}{𝑛^{5 / 2}} - \frac{𝑛^{1 / 2}}{𝑛^{3 / 2}} + \frac{𝑛^{3 / 2}}{(𝑛 + 2)^{5 / 2}} - \frac{𝑛^{1 / 2}}{(𝑛 + 3)^{3 / 2}} \\ + \frac{𝑛^{3 / 2}}{(𝑛 + 4)^{5 / 2}} - \frac{𝑛^{1 / 2}}{(𝑛 + 6)^{3 / 2}} + \dots + \frac{𝑛^{3 / 2}}{(𝑛 + 2 (𝑛 - 1))^{5 / 2}} \\ - \frac{𝑛^{1 / 2}}{(𝑛 + 3 (𝑛 - 1))^{3 / 2}}] = \end{matrix}$

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

Incorrect

$\frac{- 1}{9 \sqrt{\sqrt 3}}$

Incorrect

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

Incorrect

$\frac{1}{9 \sqrt{\sqrt 3}}$

Incorrect

Q 75MathematicsSection A • MCQdefinite integration

+1 / -0

$lim_{𝑛 \to \infty} [\frac{𝑛 + 3}{𝑛^{2} + 1^{2}} + \frac{𝑛 + 6}{𝑛^{2} + 2^{2}} + \frac{𝑛 + 9}{𝑛^{2} + 3^{2}} + \dots + \frac{2}{𝑛}] =$

$\frac{𝜋}{4} + \frac{3}{2} \ln 2$

Incorrect

$\frac{𝜋}{2} + \frac{3}{4} \ln 2$

Incorrect

$\frac{𝜋}{4} - \frac{3}{2} \ln 2$

Incorrect

$\frac{𝜋}{4} + \frac{1}{2} \ln 2$

Incorrect

Q 76MathematicsSection A • MCQarea under the curves

+1 / -0

If the area lying in the first quadrant and bounded by the circle $𝑥^{2} + 𝑦^{2} - 4 𝑥 = 0$ , the parabola $𝑦^{2} = 𝑥$ and the $𝑋$ -axis is $𝐴$ , then $6 𝐴 - 9 \sqrt{\sqrt 3} =$

$𝜋$

Incorrect

$2 𝜋$

Incorrect

$3 𝜋$

Incorrect

$4 𝜋$

Incorrect

Q 77MathematicsSection A • MCQdifferential equations

+1 / -0

If the order and degree of the differential equation corresponding to the family of curves $(𝑥 - 2)^{2} + (𝑦 - 𝑎)^{2} = 𝑏^{2}$ , (where $𝑎$ and $𝑏$ are parameters) are $𝑚$ and $𝑛$ respectively, then $𝑚^{2} + 𝑛 =$

7

Incorrect

5

Incorrect

4

Incorrect

3

Incorrect

Q 78MathematicsSection A • MCQdifferential equations

+1 / -0

Consider the differential equation $\frac{𝑑 𝑦}{𝑑 𝑥} = \frac{1}{𝑎 𝑥 + 4 𝑦 + 7}$ and the following statements

A. The given differential equation is linear in $𝑥$ .

B. The given differential equation is not linear in $𝑦$ .

C. The given differential equation is linear in $𝑦$ .

D. $𝑒^{𝑎 𝑥}$ is the integrating factor of the given differential equation.

Which one of the following options is true?

Only C and D are true

Incorrect

Only B and D are true

Incorrect

Only $𝐵$ and $𝐴$ are true

Incorrect

Only A and C are true

Incorrect

Q 79MathematicsSection A • MCQdifferential equations

+1 / -0

The solution of the differential equation $𝑥 \cos 𝑥 \frac{𝑑 𝑦}{𝑑 𝑥} + (𝑥 \sin 𝑥 + \cos 𝑥) 𝑦 = 1$ is

$𝑥 \sec 𝑥 - 𝑦 \tan 𝑥 = 𝐶$

Incorrect

$𝑥^{2} 𝑦 \cos 𝑥 - \tan 𝑥 = 𝐶$

Incorrect

$𝑥 𝑦 \sec 𝑥 + 𝑦 \tan 𝑥 = 𝐶$

Incorrect

$𝑥 𝑦 \sec 𝑥 - \tan 𝑥 = 𝐶$

Incorrect

Q 80PhysicsSection A • MCQelectromagnetic waves

+1 / -0

Choose the correct statement.

Photons carry some momentum because, they have a finite rest mass.

Incorrect

Electromagnetic force is weaker than weak nuclear force but stronger than gravitational force.

Incorrect

Weak nuclear force is responsible for the stability of nuclei.

Incorrect

Electromagnetic force acts over large distances and does not need any intervening medium.

Incorrect

Q 81PhysicsSection A • MCQunits and measurements

+1 / -0

The dimension of $\frac{𝐸^{2}}{𝜇_{0}}$ in mass $(𝑀)$ , length $(𝐿)$ and time

$(𝑇)$ is $(𝐸 =$ electric field,

$𝜇_{0} =$ permeability of free space)

$[M^{2} L^{3} T^{- 2} A^{2}]$

Incorrect

$[{MLT}^{- 4}]$

Incorrect

$[{ML}^{3} T^{- 2}]$

Incorrect

$[𝑀 𝐿^{4} T^{- 4}]$

Incorrect

Q 82PhysicsSection A • MCQmotion in a straight line

+1 / -0

A body moves in a straight line with speed $𝑣_{1}$ and $𝑣_{2}$ for distance which are in ratio $1 : 2$ . Find the average speed.

$3 𝑣_{1} + 𝑣_{2}$

Incorrect

$𝑣_{2} + 2 𝑣_{1}$

Incorrect

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

Incorrect

$\frac{3 𝑣_{1} 𝑣_{2}}{𝑣_{2} - 2 𝑣_{2}}$

Incorrect

Q 83PhysicsSection A • MCQwork power and energy

+1 / -0

A block of mass $𝑚$ placed on a rough horizontal plane is pulled by a constant power $𝑃$ . The coefficient of friction between the block and the surface is $𝜇$ . The maximum velocity of the block will be

$\frac{𝜇 𝑃}{𝑚 𝑔}$

Incorrect

$\frac{𝜇 𝑚 𝑔}{𝑃}$

Incorrect

$𝜇 𝑚 𝑔 𝑃$

Incorrect

$\frac{𝑃}{𝜇 𝑚 𝑔}$

Incorrect

Q 84PhysicsSection A • MCQcircular motion

+1 / -0

Consider a particle is moving with a minimum speed $𝑣$ at highest point of vertical circle of radius $𝑅$ . If the radius of the circle doubled the corresponding minimum speed will be

$𝑣$

Incorrect

$\frac{𝑣}{\sqrt{\sqrt 2}}$

Incorrect

$\sqrt{\sqrt 3} V$

Incorrect

$\sqrt{\sqrt 2} V$

Incorrect

Q 85PhysicsSection A • MCQmotion in a plane

+1 / -0

A ball is projected with a velocity $5 m / s$ , so that its horizontal range is twice the greatest height attained. The value of range is

10 m

Incorrect

2 m

Incorrect

4 m

Incorrect

5 m

Incorrect

Q 86PhysicsSection A • MCQlaws of motion

+1 / -0

A block rests on a fixed wedge inclined at an angle $𝜃$ . The coefficient of friction between the block and plane is $𝜇$ . The maximum value of $𝜃$ for the block to remain motionless on the

wedge is

qImage--laws-of-motion-mechanics-Jeemate

$𝜇 = \tan 𝜃$

Incorrect

$𝜇 = \sin 𝜃$

Incorrect

$𝜇 = \cos 𝜃$

Incorrect

$𝜇 = \cot 𝜃$

Incorrect

Q 87PhysicsSection A • MCQlaws of motion

+1 / -0

A block of mass 4 kg at rest on a rough inclined plane making an angle of $𝜃$ with the horizontal. The coefficient of static friction between the block and plane is 0.5 and the frictional force on the block is 14.14 N , find the value of $𝜃$ ?

$30^{\circ}$

Incorrect

$45^{\circ}$

Incorrect

$60^{\circ}$

Incorrect

$15^{\circ}$

Incorrect

Q 88PhysicsSection A • MCQcenter of mass

+1 / -0

Two blocks of equal masses are connected with a massless spring of spring constant $2500 N / m^{2}$ and length 10 cm at rest on the frictionless horizontal plane. If a constant horizontal force 10 N is applied as shown in the figure, find the maximum distance between the blocks.

qImage--center-of-mass-mechanics-Jeemate

10.8 cm

Incorrect

10.4 cm

Incorrect

10.6 cm

Incorrect

10.0 cm

Incorrect

Q 89PhysicsSection A • MCQwork power and energy

+1 / -0

The graph of potential energy $𝑈 (𝑥)$ versus distance $𝑥$ is shown in the following figure. The force $𝐹$ versus distance $𝑥$ graph will be represented by (assume, that the force is conservative)

qImage--work-energy-and-power-mechanics-Jeemate

Incorrect

qImage--work-energy-and-power-mechanics-Jeemate

Incorrect

qImage--work-energy-and-power-mechanics-Jeemate

Incorrect

qImage--work-energy-and-power-mechanics-Jeemate

Incorrect

Q 90PhysicsSection A • MCQmotion in a plane

+1 / -0

A point moves in the $𝑥 𝑦$ -plane according to the following equation, $𝑥 = 𝑎 \sin 𝜔 𝑡, 𝑦 = 𝑎 (1 - \cos 𝜔 𝑡)$ , where $𝑎$ and $𝜔$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

$𝜋 / 2$

Incorrect

$𝜋 / 3$

Incorrect

$𝜋$

Incorrect

$2 𝜋$

Incorrect

Q 91PhysicsSection A • MCQcircular motion

+1 / -0

Assume proton is rotating along a circular path of radius 1 m under a centrifugal force of $4 \times 10^{- 12} N$ . If the mass of proton is $1.6 \times 10^{- 27} kg$ , then its angular velocity of rotation is

$5 \times 10^{7} rad / s$

Incorrect

$10^{15} rad / s$

Incorrect

$2.5 \times 10^{7} rad / s$

Incorrect

$5 \times 10^{14} rad / s$

Incorrect

Q 92PhysicsSection A • MCQsimple harmonic motion

+1 / -0

A particle is exhibiting simple harmonic motion has its displacement $𝑥$ and velocity $𝑣$ related as $4 𝑣^{2} = 25 - 𝑥^{2}$ . The time period of SHM is

$𝜋 s$

Incorrect

$2 𝜋 s$

Incorrect

$3 𝜋 s$

Incorrect

$4 𝜋 s$

Incorrect

Q 93PhysicsSection A • MCQgravitation

+1 / -0

If the escape velocity on earth is $11.2 km / s$ , its value for a planet having double the radius and 8 time the mass of earth is

$22.4 km / s$

Incorrect

$24.3 km / s$

Incorrect

$26.6 km / s$

Incorrect

$44.8 km / s$

Incorrect

Q 94PhysicsSection A • MCQelasticity

+1 / -0

If the bulk modulus of water is $2 \times 10^{9} {Nm}^{- 2}$ , then the required pressure to reduce the given volume of water by $2 %$ is

$2 \times 10^{7} {Nm}^{- 2}$

Incorrect

$4 \times 10^{7} {Nm}^{- 2}$

Incorrect

$8 \times 10^{6} {Nm}^{- 2}$

Incorrect

$5 \times 10^{7} {Nm}^{- 2}$

Incorrect

Q 95PhysicsSection A • MCQunits and measurements

+1 / -0

The surface tension of 70 dynes $/ cm$ is equal to

$70 N / m$

Incorrect

$70 \times 10^{- 3} N / m$

Incorrect

$7 \times 10^{2} N / m$

Incorrect

$7 \times 10^{3} N / m$

Incorrect

Q 96PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Assertion A thermos bottle consists of a double walled glass vessel with the space between the two walls evacuated, so that the heat transfer between the contents of the bottle and outside is minimised.

Reason The vacuum between the two walls inhibits the heat transfer by radiation mechanism.

Which of the following is correct?

Assertion is true, Reason is true and Reason is the correct explanation for Assertion.

Incorrect

Assertion is true, Reason is true but Reason is not the correct explanation for Assertion.

Incorrect

Assertion is true but Reason is false.

Incorrect

Assertion is false but Reason is true.

Incorrect

Q 97PhysicsSection A • MCQheat and thermodynamics

+1 / -0

How much heat energy is supplied when 5 kg of water at $20^{\circ} C$ is brought to its boiling point? (Assume, specific heat of water $= 4.2 J / g^{\circ} C$ )

1680 kJ

Incorrect

1740 kJ

Incorrect

1680 J

Incorrect

1740 J

Incorrect

Q 98PhysicsSection A • MCQheat and thermodynamics

+1 / -0

What is the name of ideal-gas process in which no heat is transferred?

Isochoric

Incorrect

Isothermal

Incorrect

Isobaric

Incorrect

Adiabatic

Incorrect

Q 99PhysicsSection A • MCQheat and thermodynamics

+1 / -0

Mean free path of molecules in a polyatomic gas is independent of

number density of the molecules

Incorrect

volume of the molecule

Incorrect

temperature of the gas

Incorrect

gas constant $𝑅$

Incorrect

Q 100PhysicsSection A • MCQsimple harmonic motion

+1 / -0

Three masses $700 g, 500 g$ and 400 g are suspended at the end of a spring shown in figure and are in equilibrium. When the 700 g mass is removed, the system oscillates with a time period of 3 s . If 500 g mass is further removed, then it will oscillate with a period of

qImage--simple-harmonic-motion-mechanics-Jeemate

1 s

Incorrect

2 s

Incorrect

3 s

Incorrect

$\sqrt{\sqrt \frac{12}{5}} s$

Incorrect

Q 101PhysicsSection A • MCQray optics

+1 / -0

A thin prism of angle $6^{\circ}$ made of glass of refractive index 1.5 is combined with another prism made of refractive index 1.75 to produce dispersion without deviation. Then, the angle of the second prism is

$5^{\circ}$

Incorrect

$8^{\circ}$

Incorrect

$4^{\circ}$

Incorrect

$6^{\circ}$

Incorrect

Q 102PhysicsSection A • MCQray optics

+1 / -0

A small object is placed in the air, at a distance 45 cm from a convex refracting surface of radius of curvature 15 cm . If the surface separates air from glass of refractive index 1.5, then the position of image is

100 cm

Incorrect

120 cm

Incorrect

125 cm

Incorrect

135 cm

Incorrect

Q 103PhysicsSection A • MCQwave optics

+1 / -0

Which of the following phenomena produces the colour in soap bubble?

Diffraction

Incorrect

Interference

Incorrect

Polarisation

Incorrect

Refraction

Incorrect

Q 104PhysicsSection A • MCQelectrostatics

+1 / -0

Choose the incorrect statement.

Gauss's law applies to a closed surface of any shape.

Incorrect

According to Gauss's law, if a closed surface encloses no charge, electric field must vanish everywhere on the surface.

Incorrect

Gauss's law can be derived from Coulomb's law.

Incorrect

According to Gauss's law, the net number of lines crossing any closed surface in an outward direction is proportional to the net charge on surface.

Incorrect

Q 105PhysicsSection A • MCQelectrostatics

+1 / -0

In a regular polygon of 10 sides, each corner is at a distance $𝑅$ from the centre. Identical charges are placed at 9 corners. At the centre, the magnitude of electric field is $𝐸$ and the potential is $𝑉$ . The ratio $\frac{𝑉}{𝐸}$ is

$10 𝑅$

Incorrect

$\frac{9}{𝑅}$

Incorrect

$\frac{9}{10} 𝑅$

Incorrect

$9 𝑅$

Incorrect

Q 106PhysicsSection A • MCQcurrent electricity

+1 / -0

The resistance of a wire is $20 Ω$ . It is stretched, so that the length becomes three times, then the new resistance of the wire will be

$200 Ω$

Incorrect

$160 Ω$

Incorrect

$120 Ω$

Incorrect

$180 Ω$

Incorrect

Q 107PhysicsSection A • MCQcurrent electricity

+1 / -0

In a meter bridge the resistances $𝑅$ and $𝑆$ are such that the null point is found at a distance of 40 cm from one end. If a resistance of $10 Ω$ is connected in parallel with shunt $𝑆$ , then the null point occurs at 90 cm from the same end. The values of the two resistances $𝑅$ and $𝑆$ respectively are

$2.5 Ω, 3.5 Ω$

Incorrect

$3.5 Ω, 2.5 Ω$

Incorrect

$1.5 Ω, 2.5 Ω$

Incorrect

$83.3 Ω, 125 Ω$

Incorrect

Q 108PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

Two similar coils which are separated by 2 m having radius of 1 m and number of turns 80 have a common axis. Calculate the strength of magnetic field at a point midway between them on their common axis when a current is 0.2 A .

$0.04 \sqrt{\sqrt 2}$

Incorrect

$\sqrt{\sqrt 2}$

Incorrect

$\frac{0.04}{\sqrt{\sqrt 2}}$

Incorrect

$\frac{\sqrt{\sqrt 2}}{0.04}$

Incorrect

Q 109PhysicsSection A • MCQmoving charges and magnetism

+1 / -0

A particle of mass $𝑚$ and charge $𝑄$ moving with a speed $𝑣$ in a circular path of radius $𝑅$ has magnetic moment $𝜇$ . If the mass of the particle is doubled and maintains the same speed while revolving in the same circular path, then the magnetic moment will be

doubled

Incorrect

halved

Incorrect

tripled

Incorrect

unchanged

Incorrect

Q 110PhysicsSection A • MCQmagnetism and matter

+1 / -0

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 G experiences a torque of 0.016 Nm . The magnetic moment of the bar magnet is

$0.4 {Am}^{2}$

Incorrect

$0.5 {Am}^{2}$

Incorrect

$0.6 {Am}^{2}$

Incorrect

$0.7 {Am}^{2}$

Incorrect

Q 111PhysicsSection A • MCQelectromagnetic induction

+1 / -0

Two concentric circular coils, one of small radius $𝑟$ and the other of large radius $𝑅$ are placed co-axially with centres coinciding. If the radius $𝑟$ is changed by $2 %$ , then the change in mutual inductance of the arrangement is (assume, $𝑟 ≪ 𝑅$ )

$2 %$

Incorrect

$1.5 %$

Incorrect

$4 %$

Incorrect

$0 %$

Incorrect

Q 112PhysicsSection A • MCQalternating current

+1 / -0

A $𝐿 - 𝐶 - 𝑅$ series circuit is connected to a source of alternating current. At resonance, the applied voltage and the current flowing through the circuit will have a phase difference of

$𝜋$

Incorrect

$\frac{𝜋}{2}$

Incorrect

$\frac{𝜋}{4}$

Incorrect

$0^{\circ}$

Incorrect

Q 113PhysicsSection A • MCQdual nature of radiation

+1 / -0

A radiation of energy $𝐸$ falls on a perfectly reflecting surface. The momentum transferred to the surface is (let $𝑐 \equiv$ speed of light)

$\frac{𝐸}{𝐶}$

Incorrect

$\frac{2 𝐸}{𝑐}$

Incorrect

$𝐸 𝐶$

Incorrect

$\frac{𝐸}{𝑐^{2}}$

Incorrect

Q 114PhysicsSection A • MCQdual nature of radiation

+1 / -0

According to the photoelectric effect, the plot of kinetic energy of the emitted photo-electrons from a metal versus the frequency of the incident radiation gives a straight line whose slope

is the same for all metals and independent of the intensity of radiation

Incorrect

depends only on the intensity of radiation

Incorrect

depends both on the intensity of the radiation and the metal used

Incorrect

depends on the nature of metals used

Incorrect

Q 115PhysicsSection A • MCQatoms and nuclei

+1 / -0

The shortest wavelength in Lyman series is

912 \overset{o}{A}

. Then, the longest wavelength in the series must be

9120 \overset{o}{A}

Incorrect

1824 \overset{o}{A}

Incorrect

1216 \overset{o}{A}

Incorrect

2432 \overset{o}{A}

Incorrect

Q 116PhysicsSection A • MCQatoms and nuclei

+1 / -0

Half-life of radioactive sample is 24 h . If a newly prepared radioactive sample shows 4 times the allowed and safe value of radio activity, the minimum time after which one can work safely with the source is

48 h

Incorrect

96 h

Incorrect

8 h

Incorrect

72 h

Incorrect

Q 117PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

The current gain of a transistor is 0.98 . If the transistor is used in a common emitter arrangement what would be the change in collector current corresponding to a change of 0.5 mA in the base current?

24.5 mA

Incorrect

47.5 mA

Incorrect

32.5 mA

Incorrect

28.5 mA

Incorrect

Q 118PhysicsSection A • MCQsemiconductor devices and logic gates

+1 / -0

In a $𝑝 - 𝑛 - 𝑝$ transistor, the current carriers are

acceptor ions

Incorrect

donor ions

Incorrect

free electrons

Incorrect

holes

Incorrect

Q 119PhysicsSection A • MCQcommunication systems

+1 / -0

The function of a detector is to demodulate the modulated carrier wave and the steps for this process are

demodulation and filtering

Incorrect

demodulation and rectification

Incorrect

rectification and filtering

Incorrect

regeneration and filtering

Incorrect

Q 120ChemistrySection A • MCQatomic structure

+1 / -0

Maximum number of electrons in a subshell with $𝑛 = 4$ and $𝑙 = 3$ is

10

Incorrect

12

Incorrect

14

Incorrect

16

Incorrect

Q 121ChemistrySection A • MCQatomic structure

+1 / -0

From the following sets of quantum numbers, which set is possible?

$𝑛 = 1, 𝑙 = 0, 𝑚_{𝑙} = + 1, 𝑚_{𝑠} = - \frac{1}{2}$

Incorrect

$𝑛 = 1, 𝑙 = 1, 𝑚_{𝑙} = 0 𝑚_{𝑠} = + \frac{1}{2}$

Incorrect

$𝑛 = 3, 𝑙 = 1, 𝑚_{𝑙} = 0, 𝑚_{𝑠} = + \frac{1}{2}$

Incorrect

$𝑛 = 3, 𝑙 = 3, 𝑚_{𝑙} = - 3, 𝑚_{𝑠} = + \frac{1}{2}$

Incorrect

Q 122ChemistrySection A • MCQperiodic classification of elements

+1 / -0

What is the correct order of atomic radius of $Al, Na, B$ and Be ?

$Be < Na < Al < B$

Incorrect

$B < Be < Al < Na$

Incorrect

AI $< Be < B < Na$

Incorrect

$Na < Al < B < Be$

Incorrect

Q 123ChemistrySection A • MCQp block elements

+1 / -0

Find the element, which displays greater ability to form $𝑝 𝜋 - 𝑝 𝜋$ multiple bonds to itself and to other elements in the same block.

Na

Incorrect

Mg

Incorrect

Li

Incorrect

N

Incorrect

Q 124ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

Which of the sulphur compound follows the octet rule?

$H_{2} {SO}_{4}$

Incorrect

${SF}_{6}$

Incorrect

${SCl}_{2}$

Incorrect

${SF}_{4}$

Incorrect

Q 125ChemistrySection A • MCQthermodynamics

+1 / -0

$Δ_{𝑟} 𝐻$ of which reaction correctly represents the lattice enthalpy of $NaCl (𝑠)$ ?

$NaCl (s) ⟶ Na (g) + Cl (g)$

Incorrect

$NaCl (s) ⟶ {Na}^{+} (g) + {Cl}^{-} (g)$

Incorrect

$Na (𝑔) + Cl (𝑔) ⟶ NaCl (𝑠)$

Incorrect

${Na}^{+} (𝑔) + {Cl}^{-} (𝑔) ⟶ NaCl (s)$

Incorrect

Q 126ChemistrySection A • MCQstates of matter

+1 / -0

The volume of a given amount of gas at $27^{\circ} C$ at constant pressure is $420 {cm}^{3}$ . If the temperature is reduced by $20^{\circ} C$ at constant pressure, what will be the volume of the gas?

$350 {cm}^{3}$

Incorrect

$392 {cm}^{3}$

Incorrect

$450 {cm}^{3}$

Incorrect

$480 {cm}^{3}$

Incorrect

Q 127ChemistrySection A • MCQstates of matter

+1 / -0

The compressibility factor $𝑍 = \frac{𝑝 𝑉}{𝑛 𝑅 𝑇}$ for hydrogen gas a 273 K and 1 atm pressure is

zero

Incorrect

one

Incorrect

greater than one

Incorrect

between zero and one

Incorrect

Q 128ChemistrySection A • MCQredox reactions

+1 / -0

In the following reaction mixtures,

I. $Cu / {CuSO}_{4} + Ag / {Ag}_{2} {SO}_{4}$

II. $Zn / {ZnSO}_{4} + Cu / {CuSO}_{4}$

copper respectively undergoes

reduction and reduction

Incorrect

oxidation and reduction

Incorrect

reduction and oxidation

Incorrect

oxidation and oxidation

Incorrect

Q 129ChemistrySection A • MCQsome basic concepts of chemistry

+1 / -0

The molecular mass of sucrose $(C_{12} H_{22} O_{11})$ is

312 g

Incorrect

355 g

Incorrect

342 g

Incorrect

308 g

Incorrect

Q 130ChemistrySection A • MCQthermodynamics

+1 / -0

In which of the processes, the entropy will decrease

$H_{2} (g) ⟶ 2 H (g)$

Incorrect

Liquid water crystallises to ice

Incorrect

Temperature of ice is raised from 10 K to 115 K

Incorrect

$2 {NaHCO}_{3}$ (s) $⟶ {Na}_{2} {CO}_{3}$ (s) $+ {CO}_{2}$ (g) $+ H_{2} O$ (s)

Incorrect

Q 131ChemistrySection A • MCQchemical equilibrium

+1 / -0

For a given equilibrium reaction, addition of inert argon gas at constant volume can shift the equilibrium in

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

forward direction

Incorrect

backward direction

Incorrect

remain unaffected

Incorrect

initially forward and then backward direction

Incorrect

Q 132ChemistrySection A • MCQchemical equilibrium

+1 / -0

For the given equilibrium reaction

$H_{2} (g) + I_{2} (g) ⇌ 2 HI (g)$

Choose the correct equation to calculate $𝐾_{𝑝}$ .

$𝐾_{𝑝} = 𝐾_{𝐶}$

Incorrect

$𝐾_{𝑝} = 𝐾_{𝐶} (𝑅 𝑇)$

Incorrect

$𝐾_{𝑝} = 𝐾_{𝐶} (𝑅 𝑇)$

Incorrect

$𝐾_{𝑝} = 𝐾_{𝐶} (𝑅 𝑇)^{2}$

Incorrect

Q 133ChemistrySection A • MCQhydrogen

+1 / -0

When calcium carbide is reacted with heavy water, which of the following product(s) will be formed

I. ${CD}_{4}$

II. $C_{2} D_{2}$

III. $Ca (OD)_{2}$

IV. ${Ca}_{2} \cdot D_{2} O$

I and IV

Incorrect

II and III

Incorrect

I, II and III

Incorrect

I, II, III and IV

Incorrect

Q 134ChemistrySection A • MCQs block elements

+1 / -0

Which alkali metal emits blue colour light in flame test?

Cs

Incorrect

Li

Incorrect

Na

Incorrect

K

Incorrect

Q 135ChemistrySection A • MCQp block elements

+1 / -0

$Match the following :$

$\begin{matrix} List-I \\ (Compounds) \end{matrix}$		$\begin{matrix} List-II \\ (Uses) \end{matrix}$
A.	Boron-10	I.	Antiseptic
B.	Borax	II.	Bullet proof vest
C.	Boron-fibre	III.	Neutron absorber
D.	Orthoboric-acid	IV.	Heat resistance glasses

The correct match is

A	B	C	D
I	IV	II	III

Incorrect

A	B	C	D
I	III	II	IV

Incorrect

A	B	C	D
III	IV	II	I

Incorrect

A	B	C	D
III	I	II	IV

Incorrect

Q 136ChemistrySection A • MCQp block elements

+1 / -0

Glass reacts with HF to produce

${SiF}_{4}$

Incorrect

${Na}_{2} {SiO}_{3}$

Incorrect

$H_{2} {SiO}_{3}$

Incorrect

Silicones

Incorrect

Q 137ChemistrySection A • MCQenvironmental chemistry

+1 / -0

Which of the following molecules react with haemoglobin of the blood to produce toxic effect?

Carbon monoxide

Incorrect

Carbon dioxide

Incorrect

Oxygen

Incorrect

Nitrogen

Incorrect

Q 138ChemistrySection A • MCQiupac nomenclature

+1 / -0

$The IUPAC name of the following compound is$

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

3, 3-dimethylcyclohex-1-en-5-ol

Incorrect

4, 4-dimethylcyclohex-1-en-2-ol

Incorrect

3, 3-dimethylcyclohex-5-en-1-ol

Incorrect

5,5-dimethylcyclohex-2-en-1-ol

Incorrect

Q 139ChemistrySection A • MCQhydrocarbons

+1 / -0

When ${CH}_{3} Br$ and $C_{2} H_{5} Br$ are subjected to Wurtz reaction, the maximum number of possible alkane product(s) formed is/are

1

Incorrect

2

Incorrect

3

Incorrect

4

Incorrect

Q 140ChemistrySection A • MCQhydrocarbons

+1 / -0

Maximum number of bromine atoms present in the final product $𝑃$ upon complete bromination are

qImage--hydrocarbons-organic-chemistry-Jeemate

4

Incorrect

6

Incorrect

10

Incorrect

8

Incorrect

Q 141ChemistrySection A • MCQsolid state

+1 / -0

A cubic structure is formed where atoms of element $𝑋$ are occupied at corner of cube and also at face centers. Atoms of element $𝑌$ are present at body center and at the edge centers. If all the atoms are removed along a plane passing through the middle of the cube (bisecting the four edges), the formula will become

$𝑋 𝑌_{2}$

Incorrect

$𝑋_{4} 𝑌_{3}$

Incorrect

$𝑋 𝑌$

Incorrect

$𝑋_{2} 𝑌_{3}$

Incorrect

Q 142ChemistrySection A • MCQionic equilibrium

+1 / -0

pH of 0.05 M aqueous solution of diethyl amine is 10 . The value of equilibrium constant is

$4 \times 10^{- 7}$

Incorrect

$2 \times 10^{- 7}$

Incorrect

$2 \times 10^{- 3}$

Incorrect

$4 \times 10^{- 3}$

Incorrect

Q 143ChemistrySection A • MCQsolutions

+1 / -0

The observed molar mass determined for ${Na}_{2} {SO}_{4}$ by freezing point depression method is $50.0 g / mol$ . The molecular weight of ${Na}_{2} {SO}_{4}$ is 142 . What will be the degree of dissociation $𝛼$ for ${Na}_{2} {SO}_{4}$ in water?

0.23

Incorrect

0.18

Incorrect

0.78

Incorrect

0.92

Incorrect

Q 144ChemistrySection A • MCQelectrochemistry

+1 / -0

Copper is to be electrodeposited on a nickel block of $(20 \times 5) {cm}^{2}$ area by using ${CuSO}_{4}$ as electrolyte. How much quantity of electricity is needed to deposit a 3.6 $𝜇 m$ layer of copper?

[Atomic weight of $Cu = 63.5 {mol}^{- 1}$ Density of ${CuSO}_{4} = 8.9 g / cc$ ]

974 Coulombs

Incorrect

580 Coulombs

Incorrect

1080 Coulombs

Incorrect

365 Coulombs

Incorrect

Q 145ChemistrySection A • MCQchemical kinetics

+1 / -0

The half-life of a first order reaction varies with temperature according to

$\ln (𝑡_{1 / 2}) \propto \frac{1}{𝑇}$

Incorrect

$In (𝑡_{1 / 2}) \propto 𝑇$

Incorrect

$(𝑡_{1 / 2}) \propto \frac{1}{𝑇^{2}}$

Incorrect

$(𝑡_{1 / 2}) \propto 𝑇^{2}$

Incorrect

Q 146ChemistrySection A • MCQsurface chemistry

+1 / -0

The charge of " ${SnO}_{2} - {sol}^{'}$ in alkaline and acidic medium are respectively

(Hint ${SnO}_{2}$ is amphoteric oxide)

positive and positive

Incorrect

negative and negative

Incorrect

positive and negative

Incorrect

negative and positive

Incorrect

Q 147ChemistrySection A • MCQmetallurgy

+1 / -0

Which one of the following statements is true about the froth flotation method?

Ores possessing magnetic properties can be concentrated in this process

Incorrect

The mineral particles become wet by water

Incorrect

The mineral particles become wet by oil

Incorrect

It is not possible to separate a mixture of two sulphide ores by adjusting proportion of oil to water

Incorrect

Q 148ChemistrySection A • MCQp block elements

+1 / -0

When cold and dilute NaOH reacts with ${Cl}_{2}$ , which of the following is formed?

NaOCl

Incorrect

${NaClO}_{2}$

Incorrect

${NaClO}_{3}$

Incorrect

${NaClO}_{4}$

Incorrect

Q 149ChemistrySection A • MCQchemical bonding and molecular structure

+1 / -0

The hybridisation of Xe in ${XeO}_{3}$ is

$𝑠 𝑝^{3}$

Incorrect

$𝑠 𝑝^{3} 𝑑$

Incorrect

$𝑠 𝑝^{3} 𝑑^{3}$

Incorrect

$𝑑 𝑠 𝑝^{2}$

Incorrect

Q 150ChemistrySection A • MCQd and f block elements

+1 / -0

Which of the following is a diamagnetic ion?

${Co}^{2 +}$

Incorrect

${Cu}^{2 +}$

Incorrect

${Mn}^{2 +}$

Incorrect

${Sc}^{3 +}$

Incorrect

Q 151ChemistrySection A • MCQcoordination compounds

+1 / -0

Among the following Cr(III) complexes, which one will have the highest octahedral crystal field splitting?

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

Incorrect

${[Cr {(H_{2} O)}_{6}]}^{3 +}$

Incorrect

${[Cr {({NH}_{3})}_{6}]}^{3 +}$

Incorrect

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

Incorrect

Q 152ChemistrySection A • MCQpolymers

+1 / -0

Which one among the following is a semi-synthetic polymer?

Cellulose acetate

Incorrect

Starch

Incorrect

Rubber

Incorrect

Nylon-6, 6

Incorrect

Q 153ChemistrySection A • MCQbiomolecules

+1 / -0

Considering the facts that

I. sucrose forms glycosidic linkage between $C_{1}$ of glucose and $C_{2}$ fructose, while

II. lactose forms glycosidic linkage between $C_{1}$ of galactose and $C_{4}$ of glucose.

Choose the correct statement.

Both sucrose and lactose are reducing sugars.

Incorrect

Both sucrose the lactose are non-reducing sugars.

Incorrect

Sucrose is reducing sugar and lactose is non-reducing sugar.

Incorrect

Lactose is reducing sugar and sucrose is non-reducing sugar.

Incorrect

Q 154ChemistrySection A • MCQchemistry in everyday life

+1 / -0

$Match the following :$

$\begin{matrix} List-I & List-II \\ A. & Codeine & I. & Antiseptic \\ B. & Dettol & II. & Antibiotic \\ C. & Tetracycline & III. & Narcotic analgesics \end{matrix}$

$The correct match is$

A	B	C
I	II	III

Incorrect

A	B	C
II	III	I

Incorrect

A	B	C
III	I	II

Incorrect

A	B	C
III	II	I

Incorrect

Q 155ChemistrySection A • MCQaldehyde and ketone

+1 / -0

The major product in the following reaction sequence is

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

Incorrect

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

Incorrect

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

Incorrect

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

Incorrect

Q 156ChemistrySection A • MCQalcohols phenols and ethers

+1 / -0

$Match the following$

$\begin{matrix} \begin{matrix} List-I \\ (Reaction) \end{matrix} & \begin{matrix} List-II \\ (Product) \end{matrix} \\ A. & Ketone + {NaBH}_{4} & I. & 1^{\circ} - alcohol \\ B. & Ester + {LiAlH}_{4} & II. & 3^{\circ} - alcohol \\ C. & 𝑅 Mg 𝑋 + Ketone & III. & 2^{\circ} - alcohol \\ IV. & Alkane \end{matrix}$