Sample QuestionsJEE Main 3-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.
Line $L_1$ passes through the point $(1,2,3)$ and is parallel to z-axis. Line $L_2$ passes through the point $(\lambda, 5,6)$ and is parallel to $y$ -axis. Let for $\lambda=\lambda_1, \lambda_2, \lambda_2<\lambda_1$, the shortest distance between the two lines be 3 . Then the square of the distance of the point $\left(\lambda_1, \lambda_2, 7\right)$ from the line $L_1$ is
Answer: C.
View full solution →Let $f( x )=\left\{\begin{array}{lll}(1+ ax )^{1 / x } & , & x < 0 \\ 1+ b & , & x =0 \\ \frac{( x +4)^{1 / 2}-2}{( x + c )^{1 / 3}-2} & , & x >0\end{array}\right.$
be continuous at $x=0$. Then $e^u$ bc is equal to
Answer: C.
View full solution →The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is
- A
$\frac{7 \sqrt{2}}{2}$
- B
$\frac{7 \sqrt{2}}{16}$
- C
$\frac{7 \sqrt{2}}{4}$
- D
$\frac{7 \sqrt{2}}{8}$
View full solution →Let the domain of the function $f(x)=\log _2 \log _4 \log _6\left(3+4 x-x^2\right)$ be $(a, b)$. If $\int_0^{b-a}\left[x^2\right] d x=p-\sqrt{q}-\sqrt{r}, p, q, r \in N, \operatorname{gcd}(p, q, r)=1$, where [ $\cdot]$ is the greatest integer function, then $p + q + r$ is equal to
View full solution →Let $a_1, a_2, a_3, \ldots$ be a G. P. of increasing positive numbers. If $a_3 a_5=729$ and $a_2+a_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to
View full solution →The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, then $x$-axis and the lines $x=-2$ and $x=4$ is equal to __________.
View full solution →If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^{ n }$; $m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to __________.
View full solution →Let $\overrightarrow{ a }=\hat{ i }+\hat{ j }+\hat{ k }, \overrightarrow{ b }=3 \hat{ i }+2 \hat{ j }-\hat{ k }, \overrightarrow{ c }=\lambda \hat{ j }+\mu \hat{ k }$ and $\hat{ d }$ be a unit vector such that $\overrightarrow{ a } \times \hat{ d }=\overrightarrow{ b } \times \hat{ d }$ and $\overrightarrow{ c } . \hat{ d }=1$, If $\vec{c}$ is perpendicular to $\vec{a}$, then $|3 \lambda \hat{d}+\mu \overrightarrow{ c }|^2$ is equal to __________.
View full solution →Let the product of the focal distances of the point $P (4,2 \sqrt{3})$ on the hyperbola $H : \frac{ x ^2}{ a ^2}-\frac{ y ^2}{b^2}=1$ be 32. Let the length of the conjugate axis of H be p and the length of its latus rectum be $q$. Then $p^2+q^2$ is equal to __________.
View full solution →All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $W _{ n }$. Let the probability $P \left( W _{ n }\right)$ of choosing the word $W _{ n }$ satisfy $P \left( W _{ n }\right)=2 P \left( W _{ n -1}\right), n >1$.
If $P ( CDBEA )=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in N$, then $\alpha+\beta$ is equal to : __________.
View full solution →Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below.
Answer: A.
View full solution →View full solution →The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is
Answer: C.
View full solution →A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
- A
$\frac{ S }{2}, \sqrt{\frac{3 gS }{2}}$Q
- B
$\frac{ S }{2}, \frac{3 gS }{2}$
- C
$\frac{ S }{4}, \frac{3 gS }{2}$
- ✓
$\frac{ S }{4}, \sqrt{\frac{3 gS }{2}}$
Answer: D.
View full solution →View full solution →View full solution →Two coherent monochromatic light beams of intensities 4 I and 9 I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of $x$ is __________.
View full solution →A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T . The magnetic force on the wire is __________ mN.
Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time $T =4$ seconds. If the sides of the triangle are increased to length $2 a$ and also the masses of the spheres are made 2 m , then they will collide after __________ seconds.
View full solution →Correct order of limiting molar conductivity for cations in water at 298 K is :
- A
$H ^{+}> Na ^{+}> K ^{+}> Ca ^{2+}> Mg ^{2+}$
- ✓
$H ^{+}> Ca ^{2+}> Mg ^{2+}> K ^{+}> Na ^{+}$
- C
$Mg ^{2+}> H ^{+}> Ca ^{2+}> K ^{+}> Na ^{+}$
- D
$H ^{+}> Na ^{+}> Ca ^{2+}> Mg ^{2+}> K ^{+}$
Answer: B.
View full solution →View full solution →Match the LIST-I with LIST-II
LIST - I
(Molecules/ion) | LIST - II
(Hybridisation of central atom) |
| A. | PF_(5) | I | dsp^(2) |
| B. | SF_(6) | II. | sp^(3)d |
| C. | Ni(CO)_(4) | III. | sp^(3)d^(2) |
| D. | [PtCl_(4)]^(2-) | IV. | sp^(3) |
Choose the correct answer from the options given below :
Which compound would give 3-methyl-6oxoheptanal upon ozonolysis ?
Answer: B.
View full solution →2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is :
(Given : Ebullioscopic constant of water $=0.52 K kg mol ^{-1}$)
Answer: B.
View full solution →View full solution →View full solution →The number of optical isomers exhibited by the iron complex (A) obtained from the following reaction is __________
$
FeCl_3+KOH+H_2 C_2 O_4 \rightarrow A
$
View full solution →0.5 g of an organic compound on combustion gave 1.46 g of $CO _2$ and 0.9 g of $H _2 O$. The percentage of carbon in the compound is __________. (Nearest integer)
[Given : Molar mass (in $g mol ^{-1}$ ) $C : 12, H : 1$, O : 16]
View full solution →View full solution →
