Sample QuestionsJEE Main 4-April-2025 Paper - Shift 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Let the mean and the standard deviation of the observation $2,3,3,4,5,7$, a, b be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is :
- ✓
- B
$\frac{3}{4}$
- C
- D
$\frac{1}{2}$
Answer: A.
View full solution →Let A be the point of intersection of the lines $L_1: \frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1}$ and $L_2: \frac{x-1}{3}=\frac{y+3}{4}=\frac{z+7}{5}$. Let B and C be the point on the lines $L _1$ and $L _2$ respectively such that $AB = AC =\sqrt{15}$. Then the square of the area of the triangle ABC is :
View full solution →Let $f(x)+2 f\left(\frac{1}{x}\right)=x^2+5$ and $2 g(x)-3 g\left(\frac{1}{2}\right)=x, x>0$. If $\alpha=\int_1^2 f(x) d x$, and $\beta=\int_1^2 g(x) d x$, then the value of $9 \alpha+\beta$ is :
Answer: D.
View full solution →The centre of a circle $C$ is at the centre of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$. Let $C$ pass through the foci $F_1$ and $F_2$ of $E$ such that the circle $C$ and the ellipse $E$ intersect at four points. Let P be one of these four points. If the area of the triangle $PF _1 F_2$ is 30 and the length of the major axis of E is 17 , then the distance between the foci of $E$ is :
View full solution →If a curve $y=y(x)$ passes through the point $\left(1, \frac{\pi}{2}\right)$ and satisfies the differential equation $\left(7 x^4 \cot y-e^x \operatorname{cosec} y\right) \frac{d x}{d y}=x^5, x \geq 1$, then at $x=2$, the value of cosy is:
- A
$\frac{2 e^2-e}{64}$
- B
$\frac{2 e^2+e}{64}$
- ✓
$\frac{2 e ^2- e }{128}$
- D
$\frac{2 e^2+e}{128}$
Answer: C.
View full solution →Let the three sides of a triangle $A B C$ be given by the vectors $2 \hat{i}-\hat{j}+\hat{k}, \quad \hat{i}-3 \hat{j}-5 \hat{k}$ and $3 \hat{i}-4 \hat{j}-4 \hat{k}$. Let $G$ be the centroid of the triangle ABC . Then $6\left(|\overrightarrow{ AG }|^2+|\overrightarrow{ BG }|^2+|\overrightarrow{ CG }|^2\right)$ is equal to __________
View full solution →Let m and $n ,( m < n )$ be two 2-digit numbers. Then the total numbers of pairs $(m, n)$, such that $\operatorname{gcd}(m, n)=6$, is $\qquad$
View full solution →A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\frac{11}{50}$, the n is equal to
View full solution →$
\begin{array}{l}
\text { If } \int \frac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^9} d x= \\
\frac{1}{m}\left(\left(\sqrt{1+x^2}+x\right)^n\left(n \sqrt{1+x^2}-x\right)\right)+C \text { where } C
\end{array}
$
is the constant of integration and $m , n \in N$, then $m + n$ is equal to
View full solution →If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\sum_{ k =1}^{ n }\left(\alpha^{ k }+\frac{1}{\alpha^{ k }}\right)^2=20$, then n is equal to _________
View full solution →In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $\left[ M ^{ P } L ^{ Q } T ^{ R } A ^{ S }\right]$. The value of P and Q are :
- A
$-1,0$
- B
$-1,1$
- C
$1,-1$
- ✓
$0,-1$
Answer: D.
View full solution →A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :
Answer: B.
View full solution →Displacement of a wave is expressed as $x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) m$. The wavelength of the wave when its velocity is $300 m / s$ is :
Answer: B.
View full solution →Match List-I with List-II.| List-I | List-II |
| (A) Isobaric | (I) $\Delta Q =\Delta W$ |
| (B) Isochoric | (II) $\Delta Q=\Delta U$ |
| (C) Adiabatic | (III) $\Delta Q=$ zero |
| (D) Isothermal | (IV) $\Delta Q =\Delta U + P \Delta V$ |
$\Delta Q =$ Heat supplied
$\Delta W =$ Work done by the system
$\Delta U =$ Change in internal energy
$P =$ Pressure of the system
$\Delta V =$ Change in volume of the system
Choose the correct answer from the options given below : - A
(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
- B
(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
- ✓
(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
- D
(A)-(II), (B)-(IV), (C)-(III), (D)-(I)
Answer: C.
View full solution →Consider a n-type semiconductor in which $n _{ e }$ and $n _{ h }$ are number of electrons and holes, respectively.
(A) Holes are minority carriers
(B) The dopant is a pentavalent atom
(C) $n _{ c } n _{ h } \neq n _{ i }^2$
(where $n_i$ is number of electrons or holes in semiconductor when it is intrinsic form)
(D) $n _{ e } n _{ h } \geq n _{ i }^2$
(E) The holes are not generated due to the donors
Choose the correct answer from the options given below :
Answer: C.
View full solution →An inductor of self inductance 1 H connected in series with a resistor of $100 \pi$ ohm and an ac supply of $100 \pi$ volt, 50 Hz. Maximum current flowing in the circuit is ____________ A.
View full solution →In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the centre maximum of the single slit diffraction pattern, then the width of each slit is $x \times 10^{-3} cm$, where x-value is ___________ .
View full solution →If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by ____________ times.
$
\begin{array}{l}
\left(\mu_0=4 \pi \times 10^{-7} H / m, \quad \in_0=8.85 \times 10^{-12} F / m\right. \quad \left.c=3 \times 10^8 m / s\right)
\end{array}
$
View full solution →A solid sphere with uniform density and radius R is rotating initially with constant angular velocity $\left(\omega_1\right)$ about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $R / 2$ is $x \omega_1$. The value of $x$ is __________ .
View full solution →A particle of charge $1.6$ $\mu C$ and mass $16$ $\mu g$ is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is __________ s.$(\pi=3.14)$
View full solution →Half life of zero order reaction $A \rightarrow$ product is 1 hour, when initial concentration of reaction is $2.0$ $mol$ $L ^{-1}$. The time required to decrease concentration of A from $0.50$ to $0.25$ $mol$ $L ^{-1}$ is:
Answer: C.
View full solution →- A
Statement I is incorrect but Statement II is correct.
- ✓
Statement I is correct but Statement II is incorrect.
- C
Both Statement I and Statement II are correct.
- D
Both Statement I and Statement II are incorrect.
Answer: B.
View full solution →Consider the following molecule (X).
The structure of X is
The elements of Group 13 with highest and lowest first ionisation enthalpies are respectively:
Answer: D.
View full solution →'$X$' is the number of electrons in $t_{2 g}$ orbitals of the most stable complex ion among $\left[ Fe \left( NH _3\right)_6\right]^{3+}$, $\left[ Fe \left( Cl _6\right)\right]^{3-}$, $\left[ Fe \left( C _2 O _4\right)_3\right]^{3-}$ and $\left[ Fe \left( H _2 O \right)_6\right]^{3+}$. The nature of oxide of vanadium of the type $V _2 O _{ X }$ is:
Answer: D.
View full solution →$x~mg$ of $Mg ( OH )_2$ (molar mass $=58$) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is __________ mg. (Nearest integer)
(Given : $Mg ( OH )_2$ is assumed to dissociate completely in $H _2 O$)
View full solution →The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185$ $S$ $cm ^2$ $mol^{-1}$ and the ionic conductance of hydroxyl and chloride ions are $170$ and $70$ $S$ $cm ^2$ $mol^{-}$ ${ }^1$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is $85.5$ $S$ $cm ^2$ $mol^{-1}$, its degree of dissociation is given by $x \times 10^{-1}$. The value of $x$ is ___________ . (Nearest integer)
View full solution →A metal complex with a formula $MC \ell_4 \cdot 3 NH _3$ is involved in $sp ^3 d^2$ hybridisation. It upon reaction with excess of $AgNO _3$ solution gives 'x' moles of AgCl. Consider 'x' is equal to the number of lone pairs of electron present in central atom of $BrF _5$. Then the number of geometrical isomers exhibited by the complex is ____________ .
View full solution →The amount of calcium oxide produced on heating 150 kg limestone ($75 \%$ pure) is ___________ kg. (Nearest integer)
Given : Molar mass (in $g~mol ^{-1}$) of Ca-40, O-16, C-12
View full solution →Sea water, which can be considered as a 6 molar $(6 M )$ solution of NaCl, has a density of $2$ $g$ $mL ^{-1}$. The concentration of dissolved oxygen $\left( O _2\right)$ in sea water is 5.8 ppm. Then the concentration of dissolved oxygen $\left( O _2\right)$ in sea water, is $x \times 10^{-4} m$. $x =$ ________ . (Nearest integer)
Given: Molar mass of NaCl is $58.5$ $g$ $mol ^{-1}$
Molar mass of $O _2$ is $32$ $g$ $mol ^{-1}$
View full solution →
all three possible structures may be drawn as follows.