Sample QuestionsJEE Main 2-April-2025 Paper - Shift 1 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Let the focal chord PQ of the parabola $y^2=4 x$ make an angle of $60^{\circ}$ with the positive x -axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the $y$-axis at the point $(0, \alpha)$, then $5 \alpha^2$ is equal to :
Answer: A.
View full solution →Let $a \in R$ and $A$ be a matrix of order $3 \times 3$ such that $\operatorname{det}(A)=-4$ and $A+I=\left[\begin{array}{lll}1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2\end{array}\right]$, where $I$ is the identity matrix of order $3 \times 3$.
If $\operatorname{det}((a+1) \operatorname{adj}((a-1) A))$ is $2^{ m } 3^{ n }, m , n \in$ $\{0,1,2, \ldots \ldots 20\}$, then $m + n$ is equal to :
Answer: D.
View full solution →Let $A B C D$ be a tetrahedron such that the edges $AB , AC$ and AD are mutually perpendicular. Let the areas of the triangles $ABC , ACD$ and ADB be 5,6 and 7 square units respectively. Then the area (in square units) of the $\triangle BCD$ is equal to :
- A
$\sqrt{340}$
- ✓
- C
$\sqrt{110}$
- D
$7 \sqrt{3}$
Answer: B.
View full solution →Let the vertices $Q$ and $R$ of the triangle $P Q R$ lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, Q R=5$ and the coordinates of the point P be $(0,2,3)$. If the area of the triangle PQR is $\frac{ m }{ n }$ then :
- A
$m -5 \sqrt{21} n =0$
- ✓
$2 m-5 \sqrt{21} n =0$
- C
$5 m-2 \sqrt{21} n =0$
- D
$5 m-21 \sqrt{2} n=0$
Answer: B.
View full solution →If $S$ and $S^{\prime}$ are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and $P$ be a point on the ellipse, then $\min \left(S P . S^{\prime} P\right)+$ $\max \left( SP ^{\prime} . S ^{\prime} P \right)$ is equal to :
- A
$3(1+\sqrt{2})$
- B
$3(6+\sqrt{2})$
- C
- ✓
Answer: D.
View full solution →The absolute difference between the squares of the radii of the two circles passing through the point $(-9,4)$ and touching the lines $x+y=3$ and $x-y=3$, is equal to __________.
View full solution →Three distinct numbers are selected randomly from the set $\{1,2,3, \ldots \ldots, 40\}$. If the probability, that the selected numbers are in an increasing G.P. is $\frac{ m }{ n }$, $\operatorname{gcd}( m , n )=1$, then $m + n$ is equal to __________.
View full solution →If the area of the region
$\left\{(x, y):\left|4-x^2\right| \leq y \leq x^2, y \leq 4, x \geq 0\right\}$is $\left(\frac{80 \sqrt{2}}{\alpha}-\beta\right), \alpha, \beta \in N$, then $\alpha+\beta$ is equal to __________.
View full solution →Let $f: R \rightarrow R$ be a thrice differentiable odd function satisfying $f^{\prime}( x ) \geq 0, f^{\prime}( x )=f( x ), f(0)=0, f^{\prime}(0)=3$. Then $9 f\left(\log _{ c } 3\right)$ is equal to __________.
View full solution →Let [•] denote the greatest integer function. If $\int_0^{ e ^3}\left[\frac{1}{ e ^{ x -1}}\right] dx =\alpha-\log _{ e } 2$, then $\alpha^3$ is equal to __________.
View full solution →A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is:
(Given: The magnitude of charge of an electron is e and mass is m, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)
- A
$\sqrt{2 m\left(\frac{ hc }{\lambda}-\phi\right)} / eB$
- B
$\sqrt{ m \left(\frac{ hc }{\lambda}-\phi\right)} / eB$
- ✓
$\sqrt{8 m\left(\frac{ hc }{\lambda}-\phi\right)} / eB$
- D
$2 \sqrt{m\left(\frac{ hc }{\lambda}-\phi\right)} / eB$
Answer: C.
View full solution →A small bob of mass 100 mg and charge $+10 \mu C$ is connected to an insulating string of length 1 m . It is brought near to an infinitely long nonconducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends an angle of $45^{\circ}$ with the sheet at equilibrium the charge density of sheet will be :
(Given, $\varepsilon_0=8.85 \times 10^{-12} \frac{F}{ m }$ and acceleration due to gravity, $g =10 m / s ^2$ )
- A
$0.885 nC / m ^2$
- B
$17.7 nC / m ^2$
- C
$885 nC / m ^2$
- ✓
$1.77 nC / m ^2$
Answer: D.
View full solution →| List-I | List-II |
| (A) Coefficient of viscosity | (I) $\left[ ML ^0 T^{-3}\right]$ |
| (B) Intensity of wave | (II) $\left[ ML ^{-2} T^{-2}\right]$ |
| (C) Pressure gradient | (III) $\left[ M ^{-1} LT ^2\right]$ |
| (D) Compressibility | (IV) $\left[ ML ^{-1} T^{-1}\right]$ |
Choose the correct answer from the options given below:- A
(A)-(1), (B)-(IV), (C)-(III), (D)-(II)
- ✓
(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
- C
(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
- D
(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
Answer: B.
View full solution →
A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ', is :
( C is the center of curvature of the spherical surface and $R$ is the radius of curvature)- A
0.24 m right to the spherical surface
- ✓
0.4 m left to the spherical surface
- C
0.24 m left to the spherical surface
- D
0.4 m right to the spherical surface
Answer: B.
View full solution →Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' $\alpha$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :
- A
$\alpha$
- ✓
$\alpha / 4$
- C
$\alpha / 8$
- D
$\alpha / 2$
Answer: B.
View full solution →A person travelling on a straight line moves with a uniform velocity $v _1$ for a distance x and with a uniform velocity $v _2$ for the next $\frac{3}{2} x$ distance. The average velocity in this motion is $\frac{50}{7} m / s$. If $v _1$ is $5 m / s$ then $v _2=$ __________ $m / s$.
View full solution →$\gamma_{ A }$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_{ B }$ is the specific heat ratio of polyatomic gas $B$ having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{\gamma_{ A }}{\gamma_{ B }}=\left(1+\frac{1}{ n }\right)$, then the value of n is __________.
View full solution →If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is $30^{\circ}$ in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is __________ $\mu m$.
View full solution →A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11} Nm ^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is __________ $\times 10^5$ (in SI units)
View full solution →A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $100 cm^2$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5 \times 10^3 kg / m ^3$. What force one needs to apply on the hinged door so that it does not get opened ?
(Acceleration due to gravity $=10 m / s ^2$ )
View full solution →A molecule with the formula AX4Y has all it's elements from p-block. Element A is rarest, monoatomic, non-radioactive from its group and has the lowest ionization enthalpy value among A, X and Y. Elements X and Y have first and second highest electronegativity values respectively among all the known elements. The shape of the molecule is :
Consider the following molecules :
The correct order of rate of hydrolysis is :
Answer: D.
View full solution →Consider the following compound (X)
The most stable and least stable carbon radicals, respectively, produced by homolytic cleavage of corresponding C - H bond are :
Answer: D.
View full solution →On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $CO _2$ and 0.567 g of $H _2 O$. The empirical formula mass of compound ( X ) is __________ g.
(Given molar mass in $g mol ^{-1} C : 12, H : 1, O : 16$ )
Answer: A.
View full solution →Choose the correct tests with respective observations.
(A) $CuSO _4$ (acidified with acetic acid) + $K _4\left[ Fe ( CN )_6\right] \rightarrow$ Chocolate brown precipitate.
(B) $FeCl _3+ K _4\left[ Fe ( CN )_6\right] \rightarrow$ Prussian blue precipitate.
(C) $ZnCl _2+ K _4\left[ Fe ( CN )_6\right]$, neutralised with $NH _4 OH$ $\rightarrow$ White or bluish white precipitate.
(D) $MgCl _2+ K _4\left[ Fe ( CN )_6\right] \rightarrow$ Blue precipitate.
(E) $BaCl _2+ K _4\left[ Fe ( CN )_6\right]$, neutralised with NaOH $\rightarrow$ White precipitate.
Choose the correct answer from the options given below:
Answer: C.
View full solution →For the reaction $A \rightarrow$ products.
The concentration of A at 10 minutes is __________ $\times 10^{-3} mol L ^{-1}$ (nearest integer).
The reaction was started with $2.5 mol L ^{-1}$ of A. View full solution →Consider the following equilibrium,
$CO(g)+2 H_2(g) \rightleftharpoons CH_3 OH(g)$
0.1 mol of CO along with a catalyst is present in a $2 dm ^3$ flask maintained at 500 K . Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of $CH _3 OH$ is formed. The $K _{ p }^0$ is __________ $\times 10^{-3}$ (nearest integer).
Given : $R =0.08 dm ^3$ bar $K ^{-1} mol^{-1}$
Assume only methanol is formed as the product and the system follows ideal gas behaviour.
View full solution →0.1 mol of the following given antiviral compound $( P )$ will weigh __________ $\times 10^{-1} g$
(Given: molar mass in g mol-1 H: 1, C : 12, N : 14, O: 16, F: 19, I: 127) View full solution →Consider the following electrochemical cell at standard condition.
$\begin{array}{l}Au(s)\left|QH_2, Q\right| NH_4 X(0.01 M)| | Ag^{+}(1 M) \mid Ag(s) \\
E_{\text {cell }}=+0.4 V\end{array}$
The couple $QH _2 / Q$ represents quinhydrone electrode, the half cell reaction is given below
$\left[\right.$ Given : $E _{ Ag ^{+} / Ag }^{ o }=+0.8 V$ and $\left.\frac{2.303 RT }{ F }=0.06 V\right]$
The $pK _{ b }$ value of the ammonium halide salt $\left( NH _4 X \right)$ used here is __________. (nearest integer) View full solution →A transition metal (M) among $Mn , Cr , Co$ and Fe has the highest standard electrode potential $\left( M ^{3+} / M ^{2+}\right)$. It forms a metal complex of the type $\left[ M ( CN )_6\right]^4$. The number of electrons present in the $e _{ g }$ orbital of the complex is __________ .
View full solution →