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 1

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 1
Mathematics

Mathematics · 2025 · 2 Apr · Shift 1

25 questions from this JEE Main paper

Matrices and Determinants3 questions 3D Geometry2 questions Trigonometric Functions and Equations1 questions Ellipse1 questions Parabola1 questions Application of Derivatives1 questions Complex Numbers1 questions Hyperbola1 questions Binomial Theorem2 questions Quadratic Equation and Inequalities1 questions Vector Algebra1 questions Differentiation2 questions Sets and Relations1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability1 questions Sequences and Series1 questions Probability1 questions Area Under the Curves1 questions Circle1 questions Definite Integration1 questions

Q26.Let $A = [α 6 - 1 β], α > 0$ , such that $det (A) = 0$ and $α + β = 1$ . If I denotes $2 \times 2$ identity matrix, then the matrix…
Mathematics · Matrices and Determinants · MCQ
Q27.Let the vertices Q and R of the triangle PQR lie on the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}, QR = 5$ and the coordinates of the point $P$ be $(0, 2, 3)$ . If the area of the triangle $P QR$ is $\frac{m}{n}$ then :
Mathematics · 3D Geometry · MCQ
Q28.Let $a \in R$ and $A$ be a matrix of order $3 \times 3$ such that $det (A) = - 4$ and $A + I = 12 a a 11 102$ , where $I$ is the identity matrix…
Mathematics · Matrices and Determinants · MCQ
Q29.If $θ \in [- 2 π, 2 π]$ , then the number of solutions of $22 cos^{2} θ + (2 - 6) cos θ - 3 = 0$ , is equal to:
Mathematics · Trigonometric Functions and Equations · MCQ
Q30.If $S$ and $S^{'}$ are the foci of the ellipse $\frac{x ^{2}}{18} + \frac{y ^{2}}{9} = 1$ and P be a point on the ellipse, then $min (S P \cdot S^{'} P) + max (S P \cdot S^{'} P)$ is equal to :
Mathematics · Ellipse · MCQ
Q31.Let the focal chord PQ of the parabola $y^{2} = 4 x$ make an angle of $6 0^{\circ}$ 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…
Mathematics · Parabola · MCQ
Q32.If the function $f (x) = 2 x^{3} - 9 a x^{2} + 12 a^{2} x + 1$ , where $a > 0$ , attains its local maximum and local minimum values at p and q , respectively, such that $p^{2} = q$ , then $f (3)$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q33.Let $A B C D$ be a tetrahedron such that the edges $A B, A C$ and $A D$ 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)…
Mathematics · 3D Geometry · MCQ
Q34.Let $z$ be a complex number such that $∣ z ∣ = 1$ . If $\frac{2 + k ^{2} z}{k + z ˉ} = k z, k \in R$ , then the maximum distance of $k + i k^{2}$ from the circle $∣ z - (1 + 2 i) ∣ = 1$ is :
Mathematics · Complex Numbers · MCQ
Q35.Let one focus of the hyperbola $H : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ be at $(10, 0)$ and the corresponding directrix be $x = \frac{9}{10}$ . If $e$ and $l$ respectively are the eccentricity and the…
Mathematics · Hyperbola · MCQ
Q36.The largest $n \in N$ such that $3^{n}$ divides 50 ! is :
Mathematics · Binomial Theorem · MCQ
Q37.Let $P_{n} = α^{n} + β^{n}, n \in N$ . If $P_{10} = 123, P_{9} = 76, P_{8} = 47$ and $P_{1} = 1$ , then the quadratic equation having roots $\frac{1}{α}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.If $a$ is a nonzero vector such that its projections on the vectors $2 \hat{i} - \hat{j} + 2 \hat{k}, \hat{i} + 2 \hat{j} - 2 \hat{k}$ and $\hat{k}$ are equal, then a unit vector along $a$ is :
Mathematics · Vector Algebra · MCQ
Q39.If the system of linear equations $3 x + y + β z = 3 2 x + α y - z = - 3 x + 2 y + z = 4$ has infinitely many solutions, then the value of $22 β - 9 α$ is :
Mathematics · Matrices and Determinants · MCQ
Q40.Let $f : R \to R$ be a twice differentiable function such that $(sin x cos y) (f (2 x + 2 y) - f (2 x - 2 y)) = (cos x sin y) (f (2 x + 2 y) + f (2 x - 2 y))$ , for all $x, y \in R$ . If $f^{'} (0) = \frac{1}{2}$ , then…
Mathematics · Differentiation · MCQ
Q41.Let A be the set of all functions $f : Z \to Z$ and R be a relation on A such that $R = {(f, g) : f (0) = g (1)$ and $f (1) = g (0)}$ . Then R is :
Mathematics · Sets and Relations · MCQ
Q42.The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to :
Mathematics · Permutations and Combinations · MCQ
Q43.For $α, β, γ \in R$ , if $lim_{x \to 0} \frac{x ^{2} s i n α x + ( γ - 1 ) e ^{x^{2}}}{s i n 2 x - β x} = 3$ , then $β + γ - α$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q44.The term independent of $x$ in the expansion of $(\frac{( x + 1 )}{( x ^{2/3} + 1 - x ^{1/3} )} - \frac{( x - 1 )}{( x - x ^{1/2} )})^{10}, x > 1$ , is :
Mathematics · Binomial Theorem · MCQ
Q45.Let $a_{1}, a_{2}, a_{3}, \dots$ be in an A.P. such that $\sum_{k = 1}^{12} a_{2 k - 1} = - \frac{72}{5} a_{1}, a_{1} e q 0$ . If $\sum_{k = 1}^{n} a_{k} = 0$ , then $n$ is :
Mathematics · Sequences and Series · MCQ
Q46.Three distinct numbers are selected randomly from the set ${1, 2, 3, \dots, 40}$ . If the probability, that the selected numbers are in an increasing G.P., is $\frac{m}{n}, gcd (m, n) = 1$ , then $m + n$ is equal to …
Mathematics · Probability · Numerical
Q47.Let $f : R \to R$ be a thrice differentiable odd function satisfying $f^{'} (x) \geq 0, f^{'} (x) = f (x), f (0) = 0, f^{'} (0) = 3$ . Then $9 f (lo g_{e} 3)$ is equal to .
Mathematics · Differentiation · Numerical
Q48.If the area of the region ${(x, y) : 4 - x^{2} \leq y \leq x^{2}, y \leq 4, x \geq 0}$ is $(\frac{80 2}{α} - β), α, β \in N$ , then $α + β$ is equal to …
Mathematics · Area Under the Curves · Numerical
Q49.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 .
Mathematics · Circle · Numerical
Q50.Let [.] denote the greatest integer function. If $0 \int e^{3} [\frac{1}{e ^{x - 1}}] d x = α - lo g_{e} 2$ , then $α^{3}$ is equal to .
Mathematics · Definite Integration · Numerical