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JEE-MAIN EXAMINATION – JANUARY 2025

JEE-MAIN TEST PAPER WITH SOLUTION

Held on Tuesday 28th January 2025, Time: 3:00 PM to 6:00 PM

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JEE Main
Mathematics, Physics, Chemistry
Evening Session
3 hours

Paper Overview

75
Total Questions
0
Correct
0
Incorrect
75
N/A
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Complete Solutions

Q#ExplanationQuestionCorrectSolutionStatus
1Explain
Bag B1\mathrm{B}_{1} contains 6 white and 4 blue balls, Bag B2\mathrm{B}_{2} contains 4 white and 6 blue balls, and Bag B3\mathrm{B}_{3} contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from BagB2\mathrm{Bag} \mathrm{B}_{2}, is :
(A) 13\frac{1}{3}
(B) 415\frac{4}{15}
(C) 23\frac{2}{3}
(D) 25\frac{2}{5}
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2Explain
Let A,B,C\mathrm{A}, \mathrm{B}, \mathrm{C} be three points in xy-plane, whose position vector are given by 3i^+j^,i^+3j^\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j} and ai+(1−a)j^\mathrm{ai}+(1-\mathrm{a}) \hat{\mathrm{j}} respectively with respect to the origin O . If the distance of the point C from the line bisecting the angle between the vectors OA→\overrightarrow{\mathrm{OA}} and OB→\overrightarrow{\mathrm{OB}} is 92\frac{9}{\sqrt{2}}, then the sum of all the possible values of aa is :
(A) 1
(B) 9/29 / 2
(C) 0
(D) 2
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3Explain
If the components of a⃗=αi^+βj^+γk^\vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} along and perpendicular to b⃗=3i^+j^−k^\vec{b}=3 \hat{i}+\hat{j}-\hat{k} respectively, are 1611(3i^+j^−k^)\frac{16}{11}(3 \hat{i}+\hat{j}-\hat{k}) and 111(−4i^−5j^−17k^)\frac{1}{11}(-4 \hat{i}-5 \hat{j}-17 \hat{k}), then α2+β2+γ2\alpha^{2}+\beta^{2}+\gamma^{2} is equal to :
(A) 23
(B) 18
(C) 16
(D) 26
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4Explain
If α+iβ\alpha+\mathrm{i} \beta and γ+iδ\gamma+\mathrm{i} \delta are the roots of x2−(3−2i)x−(2i−2)=0,i=−1\mathrm{x}^{2}-(3-2 \mathrm{i}) \mathrm{x}-(2 \mathrm{i}-2)=0, \mathrm{i}=\sqrt{-1}, then αγ+βδ\alpha \gamma+\beta \delta is equal to :
(A) 6
(B) 2
(C) -2
(D) -6
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5Explain
If the midpoint of a chord of the ellipse x29+y24=1\frac{x^{2}}{9}+\frac{y^{2}}{4}=1 is (2,4/3)(\sqrt{2}, 4 / 3), and the length of the chord is 2α3\frac{2 \sqrt{\alpha}}{3}, then α\alpha is :
(A) 18
(B) 22
(C) 26
(D) 20
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6Explain
Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S , one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is :
(A) 14\frac{1}{4}
(B) 23\frac{2}{3}
(C) 13\frac{1}{3}
(D) 12\frac{1}{2}
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7Explain
Let ff be a real valued continuous function defined on the positive real axis such that g(x)=∫0xtf(t)dt\mathrm{g}(\mathrm{x})=\int_{0}^{\mathrm{x}} \mathrm{t} f(\mathrm{t}) \mathrm{dt}. If g(x3)=x6+x7\mathrm{g}\left(\mathrm{x}^{3}\right)=\mathrm{x}^{6}+\mathrm{x}^{7}, then value of ∑r=115f(r3)\sum_{\mathrm{r}=1}^{15} f\left(\mathrm{r}^{3}\right) is :
(A) 320
(B) 340
(C) 270
(D) 310
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8Explain
The square of the distance of the point (157,327,7)\left(\frac{15}{7}, \frac{32}{7}, 7\right) from the line x+13=y+35=z+57\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7} in the direction of the vector i^+4j^+7k^\hat{i}+4 \hat{j}+7 \hat{k} is :
(A) 54
(B) 41
(C) 66
(D) 44
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9Explain
The area of the region bounded by the curves x(1+y2)=1\mathrm{x}\left(1+\mathrm{y}^{2}\right)=1 and y2=2x\mathrm{y}^{2}=2 \mathrm{x} is :
(A) 2(π2−13)2\left(\frac{\pi}{2}-\frac{1}{3}\right)
(B) π4−13\frac{\pi}{4}-\frac{1}{3}
(C) π2−13\frac{\pi}{2}-\frac{1}{3}
(D) 12(π2−13)\frac{1}{2}\left(\frac{\pi}{2}-\frac{1}{3}\right)
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10Explain
Let A=[12−201]\mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{array}\right] and P=[cos⁡θ−sin⁡θsin⁡θcos⁡θ],θ>0\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right], \theta>0. If B=PAPT,C=PTB10PB=P A P^{T}, C=P^{T} B^{10} P and the sum of the diagonal elements of C is mn\frac{\mathrm{m}}{\mathrm{n}}, where gcd⁡(m,n)=\operatorname{gcd}(\mathrm{m}, \mathrm{n})= 1 , then m+n\mathrm{m}+\mathrm{n} is :
(A) 65
(B) 127
(C) 258
(D) 2049
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11Explain
If f(x)=∫1x1/4(1+x1/4)dx,f(0)=−6f(\mathrm{x})=\int \frac{1}{\mathrm{x}^{1 / 4}\left(1+\mathrm{x}^{1 / 4}\right)} \mathrm{dx}, f(0)=-6, then f(1)f(1) is equal to :
(A) log⁡e2+2\log _{\mathrm{e}} 2+2
(B) 4(log⁡e2−2)4\left(\log _{\mathrm{e}} 2-2\right)
(C) 2−log⁡e22-\log _{\mathrm{e}} 2
(D) 4(log⁡e2+2)4\left(\log _{\mathrm{e}} 2+2\right)
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12Explain
Let f:R→R\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} be a twice differentiable function such that f(2)=1f(2)=1. If F(x)=xf(x)\mathrm{F}(\mathrm{x})=\mathrm{x} f(\mathrm{x}) for all x∈R\mathrm{x} \in \mathrm{R}, ∫02xF′(x)dx=6\int_{0}^{2} x F^{\prime}(x) d x=6 and ∫02x2F′′(x)dx=40\int_{0}^{2} x^{2} F^{\prime \prime}(x) d x=40, then F′(2)+∫02 F(x)dx\mathrm{F}^{\prime}(2)+\int_{0}^{2} \mathrm{~F}(\mathrm{x}) \mathrm{dx} is equal to :
(A) 11
(B) 15
(C) 9
(D) 13
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13Explain
For positive integers nn, if 4an=(n2+5n+6)4 a_{n}=\left(n^{2}+5 n+6\right) and Sn=∑k=1n(1ak)\mathrm{S}_{\mathrm{n}}=\sum_{\mathrm{k}=1}^{\mathrm{n}}\left(\frac{1}{\mathrm{a}_{\mathrm{k}}}\right), then the value of 507 S2025507 \mathrm{~S}_{2025} is :
(A) 540
(B) 1350
(C) 675
(D) 135
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14Explain
Let f:[0,3]→Af:[0,3] \rightarrow \mathrm{A} be defined by f(x)=2x3−15x2+36x+7f(\mathrm{x})=2 \mathrm{x}^{3}-15 \mathrm{x}^{2}+36 \mathrm{x}+7 and g:[0,∞)→B\mathrm{g}:[0, \infty) \rightarrow \mathrm{B} be defined by g(x)=x2025x2025+1g(x)=\frac{x^{2025}}{x^{2025}+1}. If both the functions are onto and S={x∈Z:x∈AS=\{x \in \mathbf{Z}: x \in A or x∈B}x \in B\}, then n(S)n(S) is equal to :
(A) 30
(B) 36
(C) 29
(D) 31
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15Explain
Let [x][x] denote the greatest integer less than or equal to x . Then domain of f(x)=sec⁡−1(2[x]+1)f(\mathrm{x})=\sec ^{-1}(2[\mathrm{x}]+1) is :
(A) (−∞,−1]∪[0,∞)(-\infty,-1] \cup[0, \infty)
(B) (−∞,−∞)(-\infty,-\infty)
(C) (−∞,−1]∪[1,∞)(-\infty,-1] \cup[1, \infty)
(D) (−∞,∞]−{0}(-\infty, \infty]-\{0\}
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16Explain
If ∑r=113{1sin⁡(π4+(r−1)π6)sin⁡(π4+rπ6)}=a3+b\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a,b∈Z\mathrm{a}, \mathrm{b} \in \mathbf{Z}, then a2+b2\mathrm{a}^{2}+\mathrm{b}^{2} is equal to :
(A) 10
(B) 2
(C) 8
(D) 4
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17Explain
Two equal sides of an isosceles triangle are along −x+2y=4-x+2 y=4 and x+y=4x+y=4. If mm is the slope of its third side, then the sum, of all possible distinct values of m , is :
(A) -6
(B) 12
(C) 6
(D) −210-2 \sqrt{10}
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18Explain
Let the coefficients of three consecutive terms Tr\mathrm{T}_{\mathrm{r}}, Tr+1\mathrm{T}_{\mathrm{r}+1} and Tr+2\mathrm{T}_{\mathrm{r}+2} in the binomial expansion of (a+b)12(\mathrm{a}+\mathrm{b})^{12} be in a G.P. and let pp be the number of all possible values of r . Let q be the sum of all rational terms in the binomial expansion of (34+43)12(\sqrt[4]{3}+\sqrt[3]{4})^{12}. Then p+qp+q is equal to :
(A) 283
(B) 295
(C) 287
(D) 299
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19Explain
If A and B are the points of intersection of the circle x2+y2−8x=0x^{2}+y^{2}-8 x=0 and the hyperbola x29−y24=1\frac{x^{2}}{9}-\frac{y^{2}}{4}=1 and a point PP moves on the line 2x−3y+4=02 x-3 y+4=0, then the centroid of △PAB\triangle \mathrm{PAB} lies on the line :
(A) 4x−9y=124 x-9 y=12
(B) x+9y=36x+9 y=36
(C) 9x−9y=329 x-9 y=32
(D) 6x−9y=206 x-9 y=20
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20Explain
Let f:R−{0}→(−∞,1)f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1) be a polynomial of degree 2 , satisfying f(x)f(1x)=f(x)+f(1x)f(\mathrm{x}) f\left(\frac{1}{\mathrm{x}}\right)=f(\mathrm{x})+f\left(\frac{1}{\mathrm{x}}\right). If f( K)=−2 Kf(\mathrm{~K})=-2 \mathrm{~K}, then the sum of squares of all possible values of KK is :
(A) 1
(B) 6
(C) 7
(D) 9
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21Explain
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15 , is ____\_\_\_\_ .
(64)
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22Explain
Let f(x)=lim⁡n→∞∑r=0n(tan⁡(x/2r+1)+tan⁡3(x/2r+1)1−tan⁡2(x/2r+1))f(\mathrm{x})=\lim _{\mathrm{n} \rightarrow \infty} \sum_{\mathrm{r}=0}^{\mathrm{n}}\left(\frac{\tan \left(\mathrm{x} / 2^{\mathrm{r}+1}\right)+\tan ^{3}\left(\mathrm{x} / 2^{\mathrm{r}+1}\right)}{1-\tan ^{2}\left(\mathrm{x} / 2^{\mathrm{r}+1}\right)}\right). Then lim⁡x→0ex−ef(x)(x−f(x))\lim _{\mathrm{x} \rightarrow 0} \frac{\mathrm{e}^{\mathrm{x}}-\mathrm{e}^{f(\mathrm{x})}}{(\mathrm{x}-f(\mathrm{x}))} is equal to ____\_\_\_\_ .
(1)
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23Explain
The interior angles of a polygon with nn sides, are in an A.P. with common difference 6∘6^{\circ}. If the largest interior angle of the polygon is 219∘219^{\circ}, then n is equal to ____\_\_\_\_ .
(20)
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24Explain
Let A and B be the two points of intersection of the line y+5=0y+5=0 and the mirror image of the parabola y2=4xy^{2}=4 x with respect to the line x+y+4=0x+y+4=0. If dd denotes the distance between A and B , and a denotes the area of △SAB\triangle \mathrm{SAB}, where S is the focus of the parabola y2=4xy^{2}=4 x, then the vlaue of (a+d)(a+d) is ____\_\_\_\_ .
(14)
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25Explain
If y=y(x)y=y(x) is the solution of the differential equation, 4−x2dydx=((sin⁡−1(x2))2−y)sin⁡−1(x2)\sqrt{4-x^{2}} \frac{d y}{d x}=\left(\left(\sin ^{-1}\left(\frac{x}{2}\right)\right)^{2}-y\right) \sin ^{-1}\left(\frac{x}{2}\right), −2≤x≤2,y(2)=(π2−84)-2 \leq x \leq 2, y(2)=\left(\frac{\pi^{2}-8}{4}\right), then y2(0)y^{2}(0) is equal to ____\_\_\_\_
(4)
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26Explain
A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10πrads−110 \pi \mathrm{rad} \mathrm{s}^{-1} about an axis through its centre and perpendicular to the disc. What is the protential difference developed between the axis of the disc and the rim ? ( π=3.14\pi=3.14 )
(A) 0.0628 V
(B) 0.5024 V
(C) 0.2512 V
(D) 0.1256 V
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27Explain
A parallel plate capacitor of capacitance 1μ F1 \mu \mathrm{~F} is charged to a potential difference of 20 V . The distance between plates is 1μ m1 \mu \mathrm{~m}. The energy density between plates of capacitor is :
(A) 1.8×103 J/m31.8 \times 10^{3} \mathrm{~J} / \mathrm{m}^{3}
(B) 2×10−4 J/m32 \times 10^{-4} \mathrm{~J} / \mathrm{m}^{3}
(C) 2×102 J/m32 \times 10^{2} \mathrm{~J} / \mathrm{m}^{3}
(D) 1.8×105 J/m31.8 \times 10^{5} \mathrm{~J} / \mathrm{m}^{3}
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28Explain
Match List-I with List-II Choose the correct answer from the options given below:
(A) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
(B) (A)-(I), (B)-(III), (C)-(IV), (D)-(II)
(C) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
(D) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
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29Explain
The ratio of vapour densities of two gases at the same temperature is 425\frac{4}{25}, then the ratio of r.m.s. velocities will be :
(A) 254\frac{25}{4}
(B) 25\frac{2}{5}
(C) 52\frac{5}{2}
(D) 425\frac{4}{25}
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30Explain
The kinetic energy of translation of the molecules in 50 g of CO2\mathrm{CO}_{2} gas at 17∘C17^{\circ} \mathrm{C} is :
(A) 3986.3 J
(B) 4102.8 J
(C) 4205.5 J
(D) 3582.7 J
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31Explain
In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A . If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ' -2 ' then the radius of curvature of meniscus is :
(A) 1 cm
(B) 13 cm\frac{1}{3} \mathrm{~cm}
(C) 23 cm\frac{2}{3} \mathrm{~cm}
(D) 43 cm\frac{4}{3} \mathrm{~cm}
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32Explain
The frequency of revolution of the electron in Bohr's orbit varies with n , the principal quantum number as
(A) 1n\frac{1}{n}
(B) 1n3\frac{1}{\mathrm{n}^{3}}
(C) 1n4\frac{1}{\mathrm{n}^{4}}
(D) 1n2\frac{1}{\mathrm{n}^{2}}
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33Explain
Which of the following phenomena can not be explained by wave theory of light?
(A) Reflection of light
(B) Diffraction of light
(C) Refraction of light
(D) Compton effect
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34Explain
The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between t=0t=0 to t=4 s\mathrm{t}=4 \mathrm{~s} ?
(A) 30 m
(B) 10 m
(C) 13 m
(D) 11 m
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35Explain
A bar magnet has total length 2l=202 l=20 units and the field point P is at a distance d=10\mathrm{d}=10 units from the centre of the magnet. If the relative uncertainty of length measurement is 1%1 \%, then uncertainty of the magnetic field at point P is :
(A) 10%10 \%
(B) 4%4 \%
(C) 3%3 \%
(D) 5%5 \%
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36Explain
Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s\mathrm{km} / \mathrm{s}, the escape velocity in km/s\mathrm{km} / \mathrm{s} from the planet will be :
(A) 11.2
(B) 5.6
(C) 2.8
(D) 8.4
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37Explain
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position x0\mathrm{x}_{0} and initial momentum p0\mathrm{p}_{0} is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency ω\omega. Reason (R) : The amplitude and phase can be expressed in terms of x0x_{0} an p0p_{0}. In the light of the above statements, choose the correct answer from the options given below:
(A) Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
(B) (A) is false but (R) is true
(C) (A) is true but (R) is false
(D) Both (A) and (R) are true and (R) is the correct explanation of (A)
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38Explain
A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is :
(A) 3.75 cm
(B) 30 cm
(C) 7.5 cm
(D) 15 cm
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39Explain
A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4)m(3,4) \mathrm{m}. Under the action of force F→=(2i^+3j^)N\overrightarrow{\mathrm{F}}=(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \mathrm{N}, it moves to a new point Q having coordinates (6,10)m(6,10) \mathrm{m} in 4 sec . The average power and instantaneous power at the end of 4 sec are in the ratio of :
(A) 13:613: 6
(B) 6:136: 13
(C) 1:21: 2
(D) 4:34: 3
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40Explain
In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage VAB\mathrm{V}_{\mathrm{AB}} is correctly represented by :
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41Explain
An infinite wire has a circular bend of radius a, and carrying a current II as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by :
(A) μ04πIa[π2+1]\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+1\right]
(B) μ04πIa[3π2+1]\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+1\right]
(C) μ02πIa[π2+2]\frac{\mu_{0}}{2 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+2\right]
(D) μ04πIa[3π2+2]\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+2\right]
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42Explain
A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is
(A) 300 g
(B) 190 g
(C) 200 g
(D) 290 g
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43Explain
a 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given : density of water =1000 kg m−3=1000 \mathrm{~kg} \mathrm{~m}^{-3} )
(A) 1400 cm31400 \mathrm{~cm}^{3}
(B) 4000 cm34000 \mathrm{~cm}^{3}
(C) 400 cm3400 \mathrm{~cm}^{3}
(D) 600 cm3600 \mathrm{~cm}^{3}
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44Explain
The magnetic field of an E.M. wave is given by B→=(32i^+12j^)30sin⁡[ω(t−zc)]\overrightarrow{\mathrm{B}}=\left(\frac{\sqrt{3}}{2} \hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}\right) 30 \sin \left[\omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)\right] (S.I. Units) The corresponding electric field in S.I. units is :
(A) E→=(12i^−32j^)30csin⁡[ω(t−zc)]\overrightarrow{\mathrm{E}}=\left(\frac{1}{2} \hat{\mathrm{i}}-\frac{\sqrt{3}}{2} \hat{\mathrm{j}}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right)\right]
(B) E⃗=(34i^+14j^)30ccos⁡[ω(t−zc)]\vec{E}=\left(\frac{3}{4} \hat{i}+\frac{1}{4} \hat{j}\right) 30 c \cos \left[\omega\left(t-\frac{z}{c}\right)\right]
(C) E→=(12i^+32j^)30csin⁡[ω(t+zc)]\overrightarrow{\mathrm{E}}=\left(\frac{1}{2} \hat{\mathrm{i}}+\frac{\sqrt{3}}{2} \hat{\mathrm{j}}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}+\frac{\mathrm{z}}{\mathrm{c}}\right)\right]
(D) E→=(32i^−12j^)30csin⁡[ω(t+zc)]\overrightarrow{\mathrm{E}}=\left(\frac{\sqrt{3}}{2} \hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}\right) 30 \mathrm{c} \sin \left[\omega\left(\mathrm{t}+\frac{\mathrm{z}}{\mathrm{c}}\right)\right]
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45Explain
A balloon and its content having mass MM is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' 3 a ' will be : (Take ' g ' as acceleration due to gravity)
(A) 3Ma2a−g\frac{3 \mathrm{Ma}}{2 \mathrm{a}-\mathrm{g}}
(B) 3Ma2a+g\frac{3 \mathrm{Ma}}{2 \mathrm{a}+\mathrm{g}}
(C) 2Ma3a+g\frac{2 \mathrm{Ma}}{3 \mathrm{a}+\mathrm{g}}
(D) 2Ma3a−g\frac{2 M a}{3 a-g}
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46Explain
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field BB exists into the page. The bar starts to move from the vertex at time t=0\mathrm{t}=0 with a constant velocity. If the induced EMF is E∝tn\mathrm{E} \propto \mathrm{t}^{\mathrm{n}}, then value of n is ____\_\_\_\_ .
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47Explain
An electric dipole of dipole moment 6×10−6Cm6 \times 10^{-6} \mathrm{Cm} is placed in uniform electric field of magnitude 106 V/m10^{6} \mathrm{~V} / \mathrm{m}. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____\_\_\_\_ J.
(12)
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48Explain
The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7×106 Pa7 \times 10^{6} \mathrm{~Pa}, would be ____\_\_\_\_ mm3\mathrm{mm}^{3}. (Given bulk modulus of copper =1.4×1011Nm−2=1.4 \times 10^{11} \mathrm{Nm}^{-2} )
(50)
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49Explain
The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B , will be ____\_\_\_\_ A.
(2)
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50Explain
A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ____\_\_\_\_ π×10−13 m3/s\pi \times 10^{-13} \mathrm{~m}^{3} / \mathrm{s}.
(54)
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51Explain
consider the elementary reaction A(g)+B(g)→C(g)+D(g)\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g}) If the volume of reaction mixture is suddenly reduced to 13\frac{1}{3} of its initial volume, the reaction rate will become ' xx ' times of the original reaction rate. The value of xx is :
(A) 19\frac{1}{9}
(B) 9
(C) 13\frac{1}{3}
(D) 3
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52Explain
The amphoteric oxide among V2O3, V2O4\mathrm{V}_{2} \mathrm{O}_{3}, \mathrm{~V}_{2} \mathrm{O}_{4} and V2O5\mathrm{V}_{2} \mathrm{O}_{5} upon reaction with alkali leads to formation of an oxide anion. The oxidation state of V in the oxide anion is :
(A) +3
(B) +7
(C) +5
(D) +4
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53Explain
Match List-I with List-II. Choose the correct answer from the options given below:
(A) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
(B) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
(C) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
(D) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
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54Explain
Identify product [A],[B][\mathrm{A}],[\mathrm{B}] and [C][\mathrm{C}] in the following reaction sequence :
(A) [A]:CH3−CH=CH2,[ B]:CH3CHO[\mathrm{A}]: \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2},[\mathrm{~B}]: \mathrm{CH}_{3} \mathrm{CHO}, [C] : HCHO
(B) [A]:CH2=CH2,[ B][\mathrm{A}]: \mathrm{CH}_{2}=\mathrm{CH}_{2},[\mathrm{~B}]: HCHO
(C) [A]:CH3−CH=CH2,[ B]:CH3CHO[\mathrm{A}]: \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2},[\mathrm{~B}]: \mathrm{CH}_{3} \mathrm{CHO}, [C]:CH3CH2OH[\mathrm{C}]: \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}
(D) [A]:CH3CH2CH3,[ B]:CH3CHO,[C]:HCHO[\mathrm{A}]: \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3},[\mathrm{~B}]: \mathrm{CH}_{3} \mathrm{CHO},[\mathrm{C}]: \mathrm{HCHO}
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55Explain
Arrange the following in increasing order of solubility product : Ca(OH)2,AgBr,PbS,HgS\mathrm{Ca}(\mathrm{OH})_{2}, \mathrm{AgBr}, \mathrm{PbS}, \mathrm{HgS}
(A) PbS<HgS<Ca(OH)2<AgBr\mathrm{PbS}<\mathrm{HgS}<\mathrm{Ca}(\mathrm{OH})_{2}<\mathrm{AgBr}
(B) HgS<PbS<AgBr<Ca(OH)2\mathrm{HgS}<\mathrm{PbS}<\mathrm{AgBr}<\mathrm{Ca}(\mathrm{OH})_{2}
(C) Ca(OH)2<AgBr<HgS<PbS\mathrm{Ca}(\mathrm{OH})_{2}<\mathrm{AgBr}<\mathrm{HgS}<\mathrm{PbS}
(D) HgS<AgBr<PbS<Ca(OH)2\mathrm{HgS}<\mathrm{AgBr}<\mathrm{PbS}<\mathrm{Ca}(\mathrm{OH})_{2}
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56Explain
The purification method based on the following physical transformation is :
(A) Sublimation
(B) Distillation
(C) Crystallization
(D) Extraction
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57Explain
Identify correct conversion during acidic hydrolysis from the following : (A) starch gives galactose. (B) cane sugar gives equal amount of glucose and fructose. (C) milk sugar gives glucose and galactose. (D) amylopectin gives glucose and fructose. (E) amylose gives only glucose. Choose the correct answer from the options given below :
(A) (C), (D) and (E) only
(B) (A), (B) and (C) only
(C) (B), (C) and (E) only
(D) (B), (C) and (D) only
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58Explain
An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A→B→C→D→A\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D} \rightarrow \mathrm{A} as shown in the three cases above. Choose the correct option regarding ΔU\Delta \mathrm{U}.
(A) ΔU(\Delta \mathrm{U}( Case-III )>ΔU()>\Delta \mathrm{U}( Case-II )>ΔU()>\Delta \mathrm{U}( Case-I ))
(B) ΔU(\Delta \mathrm{U}( Case-I )>ΔU()>\Delta \mathrm{U}( Case-II )>ΔU()>\Delta \mathrm{U}( Case-III ))
(C) ΔU(\Delta \mathrm{U}( Case-I )>ΔU()>\Delta \mathrm{U}( Case-III )>ΔU()>\Delta \mathrm{U}( Case-II ))
(D) ΔU(\Delta \mathrm{U}( Case-I )=ΔU()=\Delta \mathrm{U}( Case-II )=ΔU()=\Delta \mathrm{U}( Case-III ))
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59Explain
The product B formed in the following reaction sequence is :
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60Explain
Concentrated nitric acid is labelled as 75%75 \% by mass. The volume in mL of the solution which contains 30 g of nitric acid is ____\_\_\_\_. Given : Density of nitric acid solution is (1.25 g/mL)(1.25 \mathrm{~g} / \mathrm{mL})
(A) 45
(B) 55
(C) 32
(D) 40
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61Explain
Match List-I with List-II. Choose the correct answer from the options given below:
(A) (A)-(I), (B)-(IV), (C)-(III), (D)-(II)
(B) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
(C) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(D) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
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62Explain
The total number of compounds from below when treated with hot KMnO4\mathrm{KMnO}_{4} giving benzoic acid is :
(A) 3
(B) 4
(C) 6
(D) 5
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63Explain
The major product of the following reaction is :
(A) 6-Phenylhepta-2,4-diene
(B) 2-Phenylhepta-2,5-diene
(C) 6-Phenylhepta-3,5-diene
(D) 2-Phenylhepta-2,4-diene
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64Explain
Given below are two statements : Statement (I) : According to the Law of Octaves, the elements were arranged in the increasing order of their atomic number. Statement (II) : Meyer observed a periodically repeated pattern upon plotting physical properties of certain elements against their respective atomic numbers. In the light of the above statements, choose the correct answer from the options given below :
(A) Statement I is false but Statement II is true
(B) Both Statement I and Statement II are true
(C) Statement I is true but Statement II is false
(D) Both Statement I and Statement II are false
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65Explain
For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth ?
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66Explain
Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom? (A) (1 s<2p<3 d<4 s)(1 \mathrm{~s}<2 \mathrm{p}<3 \mathrm{~d}<4 \mathrm{~s}) (B) (1 s<2 s=2p<3 s=3p)(1 \mathrm{~s}<2 \mathrm{~s}=2 \mathrm{p}<3 \mathrm{~s}=3 \mathrm{p}) (C) (1 s<2 s<2p<3 s<3p)(1 \mathrm{~s}<2 \mathrm{~s}<2 \mathrm{p}<3 \mathrm{~s}<3 \mathrm{p}) (D) (1 s<2 s<4 s<3 d)(1 \mathrm{~s}<2 \mathrm{~s}<4 \mathrm{~s}<3 \mathrm{~d}) Choose the correct answer from the options given below :
(A) (B) and (D) only
(B) (A) and (C) only
(C) (C) and (D) only
(D) (A) and (B) only
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67Explain
Assume a living cell with (0.9%(ω/ω))(0.9 \%(\omega / \omega)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data upto first decimal place only) The cell will :
(A) shrink since solution is (0.5%(ω/ω))(0.5 \%(\omega / \omega))
(B) shrink since solution is (0.45%(ω/ω))(0.45 \%(\omega / \omega)) as a result of association of glucose molecules (due to hydrogen bonding)
(C) swell up since solution is (1%(ω/ω))(1 \%(\omega / \omega))
(D) Show no change in volume since solution is (0.9%(ω/ω))(0.9 \%(\omega / \omega))
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68Explain
Identify correct statements : (A) Primary amines do not give diazonium salts when treated with (NaNO2)(\mathrm{NaNO}_{2}) in acidic condition. (B) Aliphatic and aromatic primary amines on heating with (CHCl3)(\mathrm{CHCl}_{3}) and ethanolic KOH form carbylamines. (C) Secondary and tertiary amines also give carbylamine test. (D) Benzenesulfonyl chloride is known as Hinsberg's reagent. (E) Tertiary amines reacts with benzenesulfonyl chloride very easily. Choose the correct answer from the options given below :
(A) (B) and (D) only
(B) (A) and (B) only
(C) (D) and (E) only
(D) (B) and (C) only
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69Explain
Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :
(A) Both Statement I and Statement II are false
(B) Both Statement I and Statement II are true
(C) Statement I is true but Statement II is false
(D) Statement I is false but Statement II is true
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70Explain
Identify the inorganic sulphides that are yellow in colour : (A) ((NH4)2 S)(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}) (B) PbS (C) CuS (D) (As2 S3)(\mathrm{As}_{2} \mathrm{~S}_{3}) (E) (As2 S5)(\mathrm{As}_{2} \mathrm{~S}_{5}) Choose the correct answer from the options given below :
(A) (A) and (C) only
(B) (A), (D) and (E) only
(C) (A) and (B) only
(D) (D) and (E) only
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71Explain
The spin only magnetic moment ( μ\mu ) value (B.M.) of the compound with strongest oxidising power among Mn2O3\mathrm{Mn}_{2} \mathrm{O}_{3}, TiO and VO is ____\_\_\_\_ B.M. (Nearest integer).
(5)
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72Explain
Consider the following data : Heat of formation of CO2( g)=−393.5 kJ mol−1\mathrm{CO}_{2}(\mathrm{~g})=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1} Heat of formation of H2O(l)=−286.0 kJ mol−1\mathrm{H}_{2} \mathrm{O}(\mathrm{l})=-286.0 \mathrm{~kJ} \mathrm{~mol}^{-1} Heat of combustion of benzene =−3267.0 kJ mol−1=-3267.0 \mathrm{~kJ} \mathrm{~mol}^{-1} The heat of formation of benzene is ____\_\_\_\_ kJmol−1\mathrm{kJ} \mathrm{mol}^{-1}. (Nearest integer)
(48)
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73Explain
Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12 . The current in Amperes used for the given electrolysis is ____\_\_\_\_ . (Nearest integer).
(2)
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74Explain
A group 15 element forms dπ−dπ\mathrm{d} \pi-\mathrm{d} \pi bond with transition metals. It also forms hydride, which is a strongest base among the hydrides of other group members that form dπ−dπ\mathrm{d} \pi-\mathrm{d} \pi bond. The atomic number of the element is ____\_\_\_\_ .
(15)
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75Explain
Total number of molecules/species from following which will be paramagnetic is ____\_\_\_\_ . O2,O2+,O2−,NO,NO2,CO,K2[NiCl4]\mathrm{O}_{2}, \mathrm{O}_{2}^{+}, \mathrm{O}_{2}^{-}, \mathrm{NO}, \mathrm{NO}_{2}, \mathrm{CO}, \mathrm{K}_{2}\left[\mathrm{NiCl}_{4}\right], [Co(NH3)6]Cl3, K2[Ni(CN)4]\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}, \mathrm{~K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]
(6)
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