New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2025 · 2 Apr · Shift 2

25 questions from this JEE Main paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2025 · 2 Apr · Shift 2
Mathematics

Mathematics · 2025 · 2 Apr · Shift 2

25 questions from this JEE Main paper

Statistics1 questions Definite Integration3 questions Permutations and Combinations1 questions Parabola1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability1 questions 3D Geometry2 questions Trigonometric Functions and Equations1 questions Sets and Relations1 questions Functions1 questions Straight Lines and Pair of Straight Lines1 questions Sequences and Series2 questions Ellipse1 questions Binomial Theorem1 questions Vector Algebra1 questions Probability1 questions Inverse Trigonometric Functions1 questions Quadratic Equation and Inequalities1 questions Differential Equations1 questions Application of Derivatives1 questions

Q26.If the mean and the variance of $6, 4, a, 8, b, 12, 10, 13$ are 9 and 9.25 respectively, then $a + b + ab$ is equal to :
Mathematics · Statistics · MCQ
Q27.Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10 \int_{1}^{1} f (t) dt = 5 x f (x) - x^{5} - 9$ for all $x ⩾ 1$ , then the value of $f (3)$ is :
Mathematics · Definite Integration · MCQ
Q28.The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : Includes diagram
Mathematics · Permutations and Combinations · MCQ
Q29.Let the point P of the focal chord PQ of the parabola $y^{2} = 16 x$ be $(1, - 4)$ . If the focus of the parabola divides the chord $P Q$ in the ratio $m : n, gcd (m, n) = 1$ , then $m^{2} + n^{2}$ is equal to :
Mathematics · Parabola · MCQ
Q30.If the system of equations $2 x + λ y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + μ z = 9$ has infinitely many solutions, then $(λ^{2} + μ^{2})$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q31.Let $A$ be a $3 \times 3$ real matrix such that $A^{2} (A - 2 I) - 4 (A - I) = O$ , where $I$ and $O$ are the identity and null matrices, respectively. If $A^{5} = α A^{2} + β A + γ I$ , where $γ$ , and $γ$ are real constants, then $α + β + γ$ …
Mathematics · Matrices and Determinants · MCQ
Q32. $I f x \to 0 lim \frac{c o s ( 2 x ) + a c o s ( 4 x ) - b}{x ^{4}} i s f ini t e, t h e n (a + b) i s e q u a l t o :$
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.If the image of the point $P (1, 0, 3)$ in the line joining the points $A (4, 7, 1)$ and $B (3, 5, 3)$ is $Q (α, β, γ)$ , then $α + β + γ$ is equal to :
Mathematics · 3D Geometry · MCQ
Q34.If $θ ϵ [- \frac{7 π}{6}, \frac{4 π}{3}]$ , then the number of solutions of $3 cosec^{2} θ - 2 (3 - 1) cosec θ - 4 = 0$ , is equal to :
Mathematics · Trigonometric Functions and Equations · MCQ
Q35.Let $A = {1, 2, 3, \dots ., 100}$ and $R$ be a relation on $A$ such that $R = {(a, b) : a = 2 b + 1}$ . Let $(a_{1}$ , $a_{2}), (a_{2}, a_{3}), (a_{3}, a_{4}), \dots ., (a_{k}, a_{k + 1})$ be a sequence of…
Mathematics · Sets and Relations · MCQ
Q36.If the domain of the function $f (x) = \frac{1}{10 + 3 x - x ^{2}} + \frac{1}{x + ∣ x ∣}$ is $(a, b)$ , then $(1 + a)^{2} + b^{2}$ is equal to :
Mathematics · Functions · MCQ
Q37.Let the area of the triangle formed by a straight line $L : x + b y + c = 0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of $4 5^{\circ}$ with the…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.The line $L_{1}$ is parallel to the vector $a = - 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and passes through the point $(7, 6, 2)$ and the line $L_{2}$ is parallel to the vector $b = 2 \hat{i} + \hat{j} + 3 \hat{k}$ …
Mathematics · 3D Geometry · MCQ
Q39.The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$ . Then the number of terms which are integers in the A.P. is :
Mathematics · Sequences and Series · MCQ
Q40.Let $(a, b)$ be the point of intersection of the curve $x^{2} = 2 y$ and the straight line $y - 2 x - 6 = 0$ in the second quadrant. Then the integral $I = \int_{a}^{b} \frac{9 x ^{2}}{1 + 5 ^{x}} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q41.If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :
Mathematics · Ellipse · MCQ
Q42. $I f r = 0 \sum 10 (\frac{10 ^{r + 1} - 1}{10 ^{r}}) .^{11} C_{r + 1} = \frac{_{α} 11 - 11 ^{11}}{10 ^{10}}, t h e n α i s e q u a l t o :$
Mathematics · Binomial Theorem · MCQ
Q43. $4 \int_{0}^{1} (\frac{1}{3 + x ^{2} + 1 + x ^{2}}) d x - 3 lo g_{e} (3)$ is equal to :
Mathematics · Definite Integration · MCQ
Q44.Let $a = 2 \hat{i} - 3 \hat{j} + \hat{k}, b = 3 \hat{i} + 2 \hat{j} + 5 \hat{k}$ and a vector $c$ be such that $(a - c) \times b = - 18 \hat{i} - 3 \hat{j} + 12 \hat{k}$ …
Mathematics · Vector Algebra · MCQ
Q45. $Given three indentical bags each containing 10 balls, whose colours are as follows : Bag I Bag II Bag III Red 345 Blue 231 Green 534$ …
Mathematics · Probability · MCQ
Q46. $If y = cos (\frac{π}{3} + cos^{- 1} \frac{x}{2}), then (x - y)^{2} + 3 y^{2} is equal to$
Mathematics · Inverse Trigonometric Functions · Numerical
Q47.If the set of all $a \in R - {1}$ , for which the roots of the equation $(1 - a) x^{2} + 2 (a - 3) x + 9 = 0$ are positive is $(- \infty, - α] \cup [β, γ)$ , then $2 α + β + γ$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q48.If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1 + 4 \cdot 1 ^{4}} + \frac{4 \cdot 2}{1 + 4 \cdot 2 ^{4}} + \frac{4 \cdot 3}{1 + 4 \cdot 3 ^{4}} + \dots .$ . is $\frac{m}{n}$ , where $gcd (m, n) = 1$ …
Mathematics · Sequences and Series · Numerical
Q49.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + 2 y sec^{2} x = 2 sec^{2} x + 3 tan x \cdot sec^{2} x$ such that $y (0) = \frac{5}{4}$ . Then $12 (y (\frac{π}{4}) - e^{- 2})$ …
Mathematics · Differential Equations · Numerical
Q50.Let $A (4, - 2), B (1, 1)$ and $C (9, - 3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and $A B$ of the triangle $A B C$ …
Mathematics · Application of Derivatives · Numerical