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 · 4 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 · 4 Apr · Shift 2
Mathematics

Mathematics · 2025 · 4 Apr · Shift 2

25 questions from this JEE Main paper

Sets and Relations1 questions Functions1 questions Statistics1 questions Hyperbola1 questions Application of Derivatives1 questions Matrices and Determinants1 questions Differential Equations1 questions Sequences and Series2 questions Ellipse2 questions Parabola2 questions Complex Numbers2 questions Binomial Theorem1 questions 3D Geometry2 questions Inverse Trigonometric Functions1 questions Definite Integration1 questions Limits Continuity and Differentiability1 questions Indefinite Integrals1 questions Probability1 questions Vector Algebra1 questions Permutations and Combinations1 questions

Q26.Let $A = {- 3, - 2, - 1, 0, 1, 2, 3}$ and R be a relation on A defined by $x R y$ if and only if $2 x - y \in {0, 1}$ . Let $l$ be the number of elements in $R$ . Let $m$ and $n$ be the minimum number of elements required to be added…
Mathematics · Sets and Relations · MCQ
Q27.Let the domains of the functions $f (x) = lo g_{4} lo g_{3} lo g_{7} (8 - lo g_{2} (x^{2} + 4 x + 5))$ and $g (x) = sin^{- 1} (\frac{7 x + 10}{x - 2})$ be $(α, β)$ and $[γ, δ]$ , respectively. Then $α^{2} + β^{2} + γ^{2} + δ^{2}$ …
Mathematics · Functions · MCQ
Q28.Let the mean and the standard deviation of the observation $2, 3, 3, 4, 5, 7, a, b$ be 4 and $2$ respectively. Then the mean deviation about the mode of these observations is :
Mathematics · Statistics · MCQ
Q29.Let the sum of the focal distances of the point $P (4, 3)$ on the hyperbola $H : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ be $8 \frac{5}{3}$ . If for H , the length of the latus rectum is $l$ and the…
Mathematics · Hyperbola · MCQ
Q30.Let $a > 0$ . If the function $f (x) = 6 x^{3} - 45 a x^{2} + 108 a^{2} x + 1$ attains its local maximum and minimum values at the points $x_{1}$ and $x_{2}$ respectively such that $x_{1} x_{2} = 54$ , then $a + x_{1} + x_{2}$ is equal…
Mathematics · Application of Derivatives · MCQ
Q31.Let the matrix $A = 110001010$ satisfy $A^{n} = A^{n - 2} + A^{2} - I$ for $n ⩾ 3$ . Then the sum of all the elements of $A^{50}$ is :
Mathematics · Matrices and Determinants · MCQ
Q32.If a curve $y = y (x)$ passes through the point $(1, \frac{π}{2})$ and satisfies the differential equation $(7 x^{4} cot y - e^{x} cosec y) \frac{d x}{d y} = x^{5}, x \geq 1$ , then at $x = 2$ …
Mathematics · Differential Equations · MCQ
Q33.If the sum of the first 20 terms of the series $\frac{4 \cdot 1}{4 + 3 \cdot 1 ^{2} + 1 ^{4}} + \frac{4 \cdot 2}{4 + 3 \cdot 2 ^{2} + 2 ^{4}} + \frac{4 \cdot 3}{4 + 3 \cdot 3 ^{2} + 3 ^{4}} + \frac{4 \cdot 4}{4 + 3 \cdot 4 ^{2} + 4 ^{4}} + \dots \cdot$ is…
Mathematics · Sequences and Series · MCQ
Q34.Let for two distinct values of p the lines $y = x + p$ touch the ellipse $E : \frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1$ at the points A and B . Let the line $y = x$ intersect E at the points C and D . Then the area of the quadrilateral…
Mathematics · Ellipse · MCQ
Q35.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…
Mathematics · Ellipse · MCQ
Q36.A line passing through the point $A (- 2, 0)$ , touches the parabola $P : y^{2} = x - 2$ at the point $B$ in the first quadrant. The area, of the region bounded by the line $A B$ , parabola $P$ and the $x$ -axis, is :
Mathematics · Parabola · MCQ
Q37.Let the product of $ω_{1} = (8 + i) sin θ + (7 + 4 i) cos θ$ and $ω_{2} = (1 + 8 i) sin θ + (4 + 7 i) cos θ$ be $α + i β$ , $i = - 1$ . Let p and q be the maximum and the minimum values of $α + β$ …
Mathematics · Complex Numbers · MCQ
Q38.If $1^{2} \cdot (^{15} C_{1}) + 2^{2} \cdot (^{15} C_{2}) + 3^{2} \cdot (^{15} C_{3}) + \dots + 1 5^{2} \cdot (^{15} C_{15}) = 2^{m} \cdot 3^{n} \cdot 5^{k}$ , where $m, n, k \in N$ , then $m + n + k$ …
Mathematics · Binomial Theorem · MCQ
Q39.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 points on the lines $L_{1}$ and $L_{2}$ …
Mathematics · 3D Geometry · MCQ
Q40.The sum of the infinite series $cot^{- 1} (\frac{7}{4}) + cot^{- 1} (\frac{19}{4}) + cot^{- 1} (\frac{39}{4}) + cot^{- 1} (\frac{67}{4}) + \dots$ . is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q41.The axis of a parabola is the line $y = x$ and its vertex and focus are in the first quadrant at distances $2$ and $22$ units from the origin, respectively. If the point $(1, k)$ lies on the parabola, then a possible value of…
Mathematics · Parabola · MCQ
Q42.Let $f (x) + 2 f (\frac{1}{x}) = x^{2} + 5$ and $2 g (x) - 3 g (\frac{1}{2}) = x, x > 0$ . If $α = \int_{1}^{2} f (x) d x$ , and $β = \int_{1}^{2} g (x) d x$ , then the value of $9 α + β$ is :
Mathematics · Definite Integration · MCQ
Q43.Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and $q$ respectively. Let d and D be the…
Mathematics · Sequences and Series · MCQ
Q44.Let the values of p , for which the shortest distance between the lines $\frac{x + 1}{3} = \frac{y}{4} = \frac{z}{5}$ and $r = (p \hat{i} + 2 \hat{j} + \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k})$ is $\frac{1}{6}$ …
Mathematics · 3D Geometry · MCQ
Q45.Let $f$ be a differentiable function on $R$ such that $f (2) = 1, f^{'} (2) = 4$ . Let $x \to 0 lim (f (2 + x))^{3/ x} = e^{α}$ . Then the number of times the curve $y = 4 x^{3} - 4 x^{2} - 4 (α - 7) x - α$ meets…
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.If $\int \frac{( 1 + x ^{2} + x ) ^{10}}{( 1 + x ^{2} - x ) ^{9}} d x = \frac{1}{m} ((1 + x^{2} + x)^{n} (n 1 + x^{2} - x)) + C$ where C is the…
Mathematics · Indefinite Integrals · Numerical
Q47.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 $\frac{11}{50}$ , then n is equal to .
Mathematics · Probability · Numerical
Q48.Let the three sides of a triangle ABC be given by the vectors $2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k}$ and $3 \hat{i} - 4 \hat{j} - 4 \hat{k}$ . Let $G$ be the centroid of the triangle $A B C$ . Then $6 (∣ AG ∣^{2} + ∣ BG ∣^{2} + ∣ CG ∣^{2})$ …
Mathematics · Vector Algebra · Numerical
Q49.If $α$ is a root of the equation $x^{2} + x + 1 = 0$ and $\sum_{k = 1}^{n} (α^{k} + \frac{1}{α ^{k}})^{2} = 20$ , then n is equal to .
Mathematics · Complex Numbers · Numerical
Q50.Let m and $n, (m < n)$ , be two 2-digit numbers. Then the total numbers of pairs $(m, n)$ , such that $gcd (m, n) = 6$ , is .
Mathematics · Permutations and Combinations · Numerical