JEE MAINS 2025 28 Jan

Question 1

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is

Accepted Answer

4607

Answer

4608

Answer

5720

Answer

5719

Question 2

Let ABCD be a trapezium whose vertices lie on the parabola $y^2 = 4x$. Let the sides AD and BC of the trapezium be parallel to y-axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point (1, 0), then the area of ABCD is :

Accepted Answer

$\frac{75}{4}$

Answer

$\frac{25}{2}$

Answer

$\frac{125}{8}$

Answer

$\frac{75}{8}$

Question 3

Two number $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1} + i^{k_2}$ , $(i = \sqrt{-1})$ is non-zero, equals

Accepted Answer

$\frac{3}{4}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{4}$

Answer

$\frac{2}{3}$

Question 4

If $f(x) = \frac{2^x}{2^x + \sqrt{2}}$, $x \in R$, then $\sum_{k=1}^{81} f \left( \frac{k}{82} \right)$ is equal to :

Accepted Answer

$\frac{81}{2}$

Answer

41

Answer

82

Answer

$81\sqrt{2}$

Question 5

Let $f : R 	o R$ be a function defined by $f(x) = (2 + 3a)x^2 + \left( \frac{a+2}{a-1} ight) x + b$, $a 
e 1$. If $f(x + y) = f(x) + f(y) + 1 - \frac{2}{7} xy$, then the value of $\sum_{i=1}^{5} 28 | f(i) |$ is:

Accepted Answer

675

Answer

715

Answer

735

Answer

545

Question 6

Let A(x, y, z) be a point in xy-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1).
Let B = (1, 4, –1) and C = (2, 0, –2). Then among the statements
($S_1$) : $\Delta$ABC is an isosceles right angled triangle
and
($S_2$) : the area of $\Delta$ABC is $\frac{9\sqrt{2}}{2}$.

Accepted Answer

only ($S_1$) is true

Answer

both are true

Answer

only ($S_2$) is true

Answer

both are false

Question 7

The relation $R = \{(x, y) : x, y \in Z 	ext{ and } x + y 	ext{ is even}\}$ is :

Accepted Answer

an equivalence relation

Answer

reflexive and transitive but not symmetric

Answer

reflexive and symmetric but not transitive

Answer

symmetric and transitive but not reflexive

Question 8

Let the equation of the circle, which touches x-axis at the point (a, 0), $a > 0$ and cuts off an intercept of length b on y-axis be $x^2 + y^2 - \alpha x + \beta y + \gamma = 0$. If the circle lies below x-axis, then the ordered pair $(2a, b^2)$ is equal to :

Accepted Answer

$(\alpha, \beta^2 - 4\gamma)$

Answer

$(\alpha, \beta^2 + 4\gamma)$

Answer

$(\gamma, \beta^2 - 4\alpha)$

Answer

$(\gamma, \beta^2 + 4\alpha)$

Question 9

Let $<a_n>$ be a sequence such that $a_0 = 0$, $a_1 = \frac{1}{2}$ and $2a_{n+2} = 5a_{n+1} - 3a_n$, $n = 0, 1, 2, 3, \dots$ Then $\sum_{k=1}^{100} a_k$ is equal to :

Accepted Answer

$3a_{100} - 100$

Answer

$3a_{99} - 100$

Answer

$3a_{100} + 100$

Answer

$3a_{99} + 100$

Question 10

$\cos^{-1} \left( \sin^{-1} \frac{3}{5} + \sin^{-1} \frac{5}{13} + \sin^{-1} \frac{33}{65} \right)$ is equal to :

Accepted Answer

0

Answer

1

Answer

$\frac{33}{65}$

Answer

$\frac{32}{65}$

Question 11

Let $T_r$ be the $r^{th}$ term of an A.P. If for some $m$, $T_m = \frac{1}{25}$, $T_{25} = \frac{1}{20}$ and $20\sum_{r=1}^{25} T_r = 13$, then $5m\sum_{r=m}^{2m} T_r$ is equal to :

Accepted Answer

126

Answer

112

Answer

98

Answer

142

Question 12

If the image of the point (4, 4, 3) in the line $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-1}{3}$ is $(\alpha, \beta, \gamma)$, then $\alpha + \beta + \gamma$ is equal to

Accepted Answer

9

Answer

12

Answer

8

Answer

7

Question 13

If $\int_{-\pi/2}^{\pi/2} \frac{96 x^2 \cos^2 x}{1 + e^x} dx = \pi(\alpha \pi^2 + \beta)$, $\alpha, \beta \in Z$, then $(\alpha + \beta)^2$ equals :

Accepted Answer

100

Answer

144

Answer

196

Answer

64

Question 14

The sum of all local minimum values of the function
$f(x) = \begin{cases} 1 - 2x, & x < -1 \ \frac{1}{3} (7 - 2|x|), & -1 \le x \le 2 \ \frac{11}{18} (x-4)(x-5), & x > 2 \end{cases}$ is

Accepted Answer

$\frac{157}{72}$

Answer

$\frac{171}{72}$

Answer

$\frac{131}{72}$

Answer

$\frac{167}{72}$

Question 15

The sum, of the squares of all the roots of the equation $x^2 + |2x - 3| - 4 = 0$, is :

Accepted Answer

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

Answer

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

Answer

$6(3 - \sqrt{2})$

Answer

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

Question 16

Let for some function $y = f(x)$, $\int_{0}^{x} t f(t)dt = x^2 f(x)$, $x > 0$ and $f(2) = 3$. Then $f(6)$ is equal to :

Accepted Answer

1

Answer

2

Answer

6

Answer

3

Question 17

Let ${^n C_{r-1}} = 28$, ${^n C_r} = 56$ and ${^n C_{r+1}} = 70$. Let $A(4\cos t, 4\sin t)$, $B(2\sin t, -2\cos t)$ and $C(3r - n, r^2 - n - 1)$ be the vertices of a triangle ABC, where $t$ is a parameter. If $(3x - 1)^2 + (3y)^2 = \alpha$, is the locus of the centroid of triangle ABC, then $\alpha$ equals :

Accepted Answer

20

Answer

8

Answer

6

Answer

18

Question 18

Let $O$ be the origin, the point $A$ be
$z_1 = \sqrt{3} + 2\sqrt{2}i$,
the point $B(z_2)$ be such that
$\sqrt{3} |z_2| = |z_1|$ and $\arg(z_2) = \arg(z_1) + \frac{\pi}{6}$.
Then

Accepted Answer

ABO is an obtuse angled isosceles triangle

Answer

area of triangle ABO is $\frac{11}{3}$

Answer

ABO is a scalene triangle

Answer

area of triangle ABO is $\frac{11}{4}$

Question 19

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denote the number of defective oranges, then the variance of x is :

Accepted Answer

$\frac{28}{75}$

Answer

$\frac{14}{25}$

Answer

$\frac{26}{75}$

Answer

$\frac{18}{25}$

Question 20

The area (in sq. units) of the region $\{(x, y): 0 \le y \le 2|x| + 1, 0 \le y \le x^2 + 1, |x| \le 3\}$ is

Accepted Answer

$\frac{64}{3}$

Answer

$\frac{80}{3}$

Answer

$\frac{17}{3}$

Answer

$\frac{32}{3}$

Question 21

Let M denote the set of all real matrices of order $3 	imes 3$ and let $S = \{-3, -2, -1, 1, 2\}$. Let
$S_1 = \{A = [a_{ij}] \in M : A = A^T 	ext{ and } a_{ij} \in S, \forall i, j\}$
$S_2 = \{A = [a_{ij}] \in M : A = -A^T 	ext{ and } a_{ij} \in S, \forall i, j\}$
$S_3 = \{A = [a_{ij}] \in M : a_{11} + a_{22} + a_{33} = 0 	ext{ and } a_{ij} \in S, \forall i, j\}$
If $n(S_1 \cup S_2 \cup S_3) = 125\alpha$, then $\alpha$ equals.

Question 22

If $\alpha = 1 + \sum_{r=1}^{6} (-3)^{r-1}  {^{12} C_{2r-1}}$, then the distance of the point $(12, \sqrt{3})$ form the line $\alpha x - \sqrt{3} y + 1 = 0$ is ………

Question 23

Let $\mathbf{a} = \hat{i} + \hat{j} + \hat{k}$, $\mathbf{b} = 2\hat{i} + 2\hat{j} + \hat{k}$ and $\mathbf{d} = \mathbf{a} 	imes \mathbf{b}$. If $\mathbf{c}$ is a vector such that $\mathbf{a} \cdot \mathbf{c} = |\mathbf{c}|$, $|\mathbf{c} - 2\mathbf{a}| = 8$ and the angle between $\mathbf{d}$ and $\mathbf{c}$ is $\frac{\pi}{4}$, then $|10 - 3\mathbf{b} \cdot \mathbf{c}| + |\mathbf{d} 	imes \mathbf{c}|^2$ is equal to …..

Question 24

Let
$f(x) = \begin{cases} 3x, & x < 0 \ \min\{1 + x - [x], x + 2[x]\}, & 0 \le x \le 2 \ 5, & x > 2 \end{cases}$
where [.] denotes greatest integer function. If $\alpha$ and $\beta$ are the number of points, where $f$ is not continuous and is not differentiable, respectively, then $\alpha + \beta$ equals…….

Question 25

Let $E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1$ be an ellipse. Ellipses $E_i$'s are constructed such that their centres and eccentricities are same as that of $E_1$, and the length of minor axis of $E_i$ is the length of major axis of $E_{i+1}$ ($i \ge 1$). If $A_i$ is the area of the ellipse $E_i$, then $\frac{5}{\pi} \sum_{i=1}^{\infty} A_i$, is equal to ……

Question 26

Two capacitors $C_1$ and $C_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_1$ and $U_2$, respectively. Which of the given statements is true ?

Accepted Answer

$C_2 > C_1, U_2 > U_1$

Answer

$C_1 > C_2, U_1 > U_2$

Answer

$C_2 > C_1, U_2 < U_1$

Answer

$C_1 > C_2, U_1 < U_2$

Question 27

In the experiment for measurement of viscosity ‘$\eta$’ of given liquid with a ball having radius R, consider following statements.
A. Graph between terminal velocity V and R will be a parabola
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of $\eta$ will change.
Choose the correct answer from the options given below:

Accepted Answer

A, C and D only

Answer

B, D and E only

Answer

C, D and E only

Answer

A, B and E only

Question 28

Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases.
D. The onset of turbulence is determined by Reynold’s number.
E. In a steady flow two stream lines never intersect.
Choose the correct answer from the options given below :

Accepted Answer

C, D, E only

Answer

A, D, E only

Answer

B, C, D only

Answer

A, B, C only

Question 29

Three infinitely long wires with linear charge density $\lambda$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface ?

Accepted Answer

$(x^2 + y^2) (y^2 + z^2) (z^2 + x^2) = 	ext{constant}$

Answer

$xy + yz + zx = 	ext{constant}$

Answer

$(x + y) (y + z) (z + x) = 	ext{constant}$

Answer

$xyz = 	ext{constant}$

Question 30

A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is______.

Accepted Answer

$\sqrt{2}$

Answer

$\sqrt{3}$

Answer

$\frac{3}{2}$

Answer

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

Question 31

Consider a long thin conducting wire carrying a uniform current I. A particle having mass “M” and charge “q” is released at a distance “a" from the wire with a speed $v_o$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [$\mu_0$ is vacuum permeability]

Accepted Answer

$a e^{-\frac{4 \pi m v_o}{q I \mu_0}}$

Answer

$a \left[ 1 - \frac{m v_o^2}{2q I} \right]$

Answer

$\frac{a}{2}$

Answer

$a \left[ 1 - \frac{m v_o}{q I} \right]$

Question 32

A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines – engine $E_1$ works between 473K to 373K and engine $E_2$ works between 373K to 273K. If $\eta_{12}$, $\eta_1$ and $\eta_2$ are the efficiencies of the engines $E, E_1$ and $E_2$, respectively, then

Accepted Answer

$\eta_{12} < \eta_1 + \eta_2$

Answer

$\eta_{12} = \eta_1 \eta_2$

Answer

$\eta_{12} = \eta_1 + \eta_2$

Answer

$\eta_{12} \ge \eta_1 + \eta_2$

Question 33

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

A is true but R is false.

Answer

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

Answer

A is false but R is true

Answer

Both A and R are true but R is NOT the correct explanation of A

Question 34

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature ?

Accepted Answer

1

Answer

2

Answer

3

Answer

4

Question 35

A bead of mass ‘m’ slides without friction on the wall of a vertical circular hoop of radius ‘R’ as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ‘R’. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ‘R’, would be (spring constant is ‘k’, g is acceleration due to gravity)

Accepted Answer

$\sqrt{\frac{kR^2}{m} + 3gR}$

Answer

$\sqrt{\frac{2kR^2}{m} + 2gR}$

Answer

$\sqrt{\frac{4kR^2}{m} + 2gR}$

Answer

$\sqrt{\frac{kR^2}{m} + 2gR}$

Question 36

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In a central force field, the work done is independent of the path chosen
Reason R: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements, choose the most appropriate answer from the options given below

Accepted Answer

Both A and R are true but R is NOT the correct explanation of A

Answer

A is true but R is false

Answer

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

Answer

A is false but R is true

Question 37

Choose the correct nuclear process from the below options [p: proton, n: neutron, $e^-$: electron, $e^+$: positron, $
u$: neutrino, $\bar{
u}$: antineutrino]

Accepted Answer

$n 	o p + e^- + \bar{
u}$

Answer

$n 	o p + e^- + 
u$

Answer

$n 	o p + e^+ + 
u$

Answer

$n 	o p + e^+ + \bar{
u}$

Question 38

Which of the following circuits has the same output as that of the given circuit? (The given circuit simplifies to Y = A)

Accepted Answer

Output Y = A

Answer

Output Y = A $\cdot$ B

Answer

Output Y = A + B

Answer

Output Y = B

Question 39

Find the equivalent resistance between two ends of the following circuit. (The circuit shows three resistors of resistance $r/3$ connected in parallel)

Accepted Answer

$\frac{r}{9}$

Answer

$r$

Answer

$\frac{r}{6}$

Answer

$\frac{r}{3}$

Question 40

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

Accepted Answer

32/27

Answer

9/8

Answer

8/9

Answer

27/32

Question 41

Due to presence of an em-wave whose electric component is given by $E = 100 \sin(\omega t - kx)$ $	ext{NC}^{-1}$, a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Accepted Answer

$200 \sin(\omega t - kx)$ $	ext{NC}^{-1}$

Answer

$25 \sin(\omega t - kx)$ $	ext{NC}^{-1}$

Answer

$400 \sin(\omega t - kx)$ $	ext{NC}^{-1}$

Answer

$50 \sin(\omega t - kx)$ $	ext{NC}^{-1}$

Question 42

A particle of mass ‘$m$’ and charge ‘$q$’ is fastened to one end ‘$A$’ of a massless string having equilibrium length $l$, whose other end is fixed at point ‘$O$’. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is

Accepted Answer

$\sqrt{\frac{qE\ell}{m}}$

Answer

$\sqrt{\frac{2qE\ell}{m}}$

Answer

$\sqrt{\frac{qE\ell}{4m}}$

Answer

$\sqrt{\frac{qE\ell}{2m}}$

Question 43

A proton of mass ‘$m_p$’ has same energy as that of a photon of wavelength ‘$\lambda$’. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

Accepted Answer

$\frac{1}{c} \sqrt{\frac{E}{2m_p}}$

Answer

$\frac{1}{c} \sqrt{\frac{2E}{m_p}}$

Answer

$\frac{1}{c} \sqrt{\frac{E}{m_p}}$

Answer

$\frac{1}{2c} \sqrt{\frac{E}{m_p}}$

Question 44

The centre of mass of a thin rectangular plate (fig - x) with sides of length a and b, whose mass per unit area ($\sigma$) varies as $\sigma = \sigma_0 \frac{x}{ab}$ (where $\sigma_0$ is a constant), would be______

Accepted Answer

$\left( \frac{2a}{3}, \frac{b}{2} \right)$

Answer

$\left( \frac{2a}{3}, \frac{2b}{3} \right)$

Answer

$\left( \frac{a}{2}, \frac{b}{2} \right)$

Answer

$\left( \frac{a}{3}, \frac{b}{2} \right)$

Question 45

A thin prism $P_1$ with angle $4^{\circ}$ made of glass having refractive index 1.54, is combined with another thin prism $P_2$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $P_2$ in degrees is

Accepted Answer

3

Answer

4

Answer

16/3

Answer

1.5

Question 46

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ is______

Question 47

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, $n = \_\_\_\_\_\_\_$.
Consider all the bodies have equal masses.

Question 48

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $[M^a L^b T^c]$. If $b = 3$, the value of $c$ is_____

Question 49

Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of intertia $I_1$ and $I_2$, respectively. For $R_2 = 2R_1$, the ratio of $I_1$ and $I_2$ would be $1/x$, where $x = \_\_\_\_\_\_\_$

Question 50

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with $10^{th}$ bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same $10^{th}$ bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be_____mm.

Question 51

The incorrect decreasing order of atomic radii is :

Accepted Answer

$	ext{Be} > 	ext{Mg} > 	ext{Al} > 	ext{Si}$

Answer

$	ext{Mg} > 	ext{Al} > 	ext{C} > 	ext{O}$

Answer

$	ext{Al} > 	ext{B} > 	ext{N} > 	ext{F}$

Answer

$	ext{Si} > 	ext{P} > 	ext{Cl} > 	ext{F}$

Question 52

Given below are two statements :
Statement I : In the oxalic acid vs $	ext{KMnO}_4$ (in the presence of dil $	ext{H}_2	ext{SO}_4$) titration the solution needs to be heated initially to $60^{\circ}	ext{C}$, but no heating is required in Ferrous ammonium sulphate (FAS) vs $	ext{KMnO}_4$ titration (in the presence of dil $	ext{H}_2	ext{SO}_4$)
Statement II : In oxalic acid vs $	ext{KMnO}_4$ titration, the initial formation of $	ext{MnSO}_4$ takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs $	ext{KMnO}_4$, heating oxidizes $	ext{Fe}^{2+}$ into $	ext{Fe}^{3-}$ by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

Both Statement I and Statement II are true

Answer

Statement I is false but Statement II is true

Answer

Statement I is true but Statement II is false

Answer

Both Statement I and Statement II are false

Question 53

Match the List-I with List-II
| List-I (Redox Reaction) | List-II (Type of Redox Reaction) |
| :--- | :--- |
| A. $	ext{CH}_4(	ext{g}) + 2	ext{O}_2(	ext{g}) \xrightarrow{\Delta} 	ext{CO}_2(	ext{g}) + 2	ext{H}_2	ext{O}(l)$ | (I) Disproportionation reaction |
| B. $2	ext{NaH}(	ext{s}) \xrightarrow{\Delta} 2	ext{Na}(	ext{s}) + 	ext{H}_2(	ext{g})$ | (II) Combination reaction |
| C. $	ext{V}_2	ext{O}_5(	ext{s}) + 5	ext{Ca}(	ext{s}) \xrightarrow{\Delta} 2	ext{V}(	ext{s}) + 5	ext{CaO}(	ext{s})$ | (III) Decomposition reaction |
| D. $2	ext{H}_2	ext{O}_2(	ext{aq}) \xrightarrow{\Delta} 2	ext{H}_2	ext{O}(l) + 	ext{O}_2(	ext{g})$ | (IV) Displacement reaction |
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 54

Given below are two statements :
Statement I : $	ext{Et} \atop 	ext{Et} 	ext{N Cl}$ will undergo alkaline hydrolysis at a faster rate than $	ext{Et} \atop 	ext{Et} 	ext{CH Cl}$
Statement II : $	ext{Et} \atop 	ext{Et} 	ext{N Cl}$, intramolecular substitution takes place first by involving lone pair of electrons on nitrogen.
In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

Both Statement I and Statement II are correct

Answer

Both Statement I and Statement II are incorrect

Answer

Statement I is incorrect but statement II is correct

Answer

Statement I is correct but Statement II is incorrect

Question 55

A weak acid HA has degree of dissociation x. Which option gives the correct expression of $	ext{pH} - 	ext{p}K_a$ ?

Accepted Answer

$\log \left( \frac{x}{1-x} \right)$

Answer

$\log (1 + 2x)$

Answer

$-\log \left( \frac{1+x}{x} \right)$

Answer

0

Question 56

Consider ‘n’ is the number of lone pair of electrons present in the equatorial position of the most stable structure of $	ext{ClF}_3$. The ions from the following with ‘n’ number of unpaired electrons are :
A. $	ext{V}^{3+}$
B. $	ext{Ti}^{3+}$
C. $	ext{Cu}^{2+}$
D. $	ext{Ni}^{2+}$
E. $	ext{Ti}^{2+}$
Choose the correct answer from the options given below :

Accepted Answer

A, D and E only

Answer

A and C only

Answer

B and C only

Answer

B and D only

Question 57

For a given reaction $R 	o P$, $t_{1/2}$ is related to $[A]_0$ as given in table :
| $\mathbf{t}_{1/2} / \mathbf{min}$ | $\mathbf{[A]_0} / \mathbf{molL^{-1}}$ |
| :---: | :---: |
| 200 | 0.100 |
| 100 | 0.025 |
Given : $\log 2 = 0.30$
Which of the following is true ?
A. The order of the reaction is $\frac{1}{2}$.
B. If $[A]_0$ is 1M, then $t_{1/2}$ is $200 \sqrt{10}$ min
C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M.
D. $t_{1/2}$ is 800 min for $[A]_0 = 1.6$ M
Choose the correct answer from the options given below :

Accepted Answer

A, B and D only

Answer

A and C only

Answer

A and B only

Answer

C and D only

Question 58

A molecule ("P") on treatment with acid undergoes rearrangement and gives ("Q") ("Q") on ozonolysis followed by reflux under alkaline condition gives ("R"). The structure of ("R") is given below :
The structure of ("P") is

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 59

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K. If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following :

Accepted Answer

The solid phase (ice) disappears completely.

Answer

Volume of system increases.

Answer

Liquid phase disappears completely.

Answer

The amount of ice decreases.

Question 60

The molecules having square pyramidal geometry are

Accepted Answer

$	ext{BrF}_5$ & $	ext{XeOF}_4$

Answer

$	ext{SbF}_5$ & $	ext{XeOF}_4$

Answer

$	ext{SbF}_5$ & $	ext{PCl}_5$

Answer

$	ext{BrF}_5$ & $	ext{PCl}_5$

Question 61

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet colour in non-luminous flame under hot condition in borax bead test is

Accepted Answer

$	ext{Ni}^{2+}$

Answer

$	ext{Ti}^{3+}$

Answer

$	ext{Mn}^{2+}$

Answer

$	ext{Cr}^{3+}$

Question 62

Both acetaldehyde and acetone (individually) undergo which of the following reactions?
A. Iodoform Reaction
B. Cannizaro Reaction
C. Aldol condensation
D. Tollen's Test
E. Clemmensen Reduction
Choose the correct answer from the options given below :

Accepted Answer

A, C and E only

Answer

A, B and D only

Answer

C and E only

Answer

B, C and D only

Question 63

In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?
A. $n = 1, l = 0, m_l = 0$
B. $n = 2, l = 0, m_l = 0$
C. $n = 2, l = 1, m_l = 1$
D. $n = 3, l = 2, m_l = 1$
E. $n = 3, l = 2, m_l = 0$
Choose the correct answer from the options given below :

Accepted Answer

D and E only

Answer

A and B only

Answer

B and C only

Answer

C and D only

Question 64

The products A and B in the following reactions, respectively are
$\mathrm{CH_3-CH_2-CH_2-Br \xrightarrow{	ext{AgNO}_2} A}$
$\mathrm{CH_3-CH_2-CH_2-Br \xrightarrow{	ext{AgCN}} B}$

Accepted Answer

$	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{NO}_2$, $	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{NC}$

Answer

$	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{ONO}$, $	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{NC}$

Answer

$	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{ONO}$, $	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{CN}$

Answer

$	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{NO}_2$, $	ext{CH}_3 - 	ext{CH}_2 - 	ext{CH}_2 - 	ext{CN}$

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