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Mathematics · 2025 · 3 Apr · Shift 1

25 questions from this JEE Main paper

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2025 · 3 Apr · Shift 1
Mathematics

Mathematics · 2025 · 3 Apr · Shift 1

25 questions from this JEE Main paper

Functions1 questions Sequences and Series2 questions Trigonometric Functions and Equations1 questions Sets and Relations1 questions Parabola1 questions Indefinite Integrals1 questions Definite Integration1 questions Quadratic Equation and Inequalities1 questions 3D Geometry2 questions Limits Continuity and Differentiability1 questions Ellipse1 questions Differential Equations1 questions Binomial Theorem2 questions Complex Numbers1 questions Differentiation1 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants1 questions Permutations and Combinations2 questions Vector Algebra1 questions Hyperbola1 questions Area Under the Curves1 questions

Q26. $If the domain of the function f (x) = lo g_{e} (\frac{2 x - 3}{5 + 4 x}) + sin^{- 1} (\frac{4 + 3 x}{2 - x}) is [α, β), then α^{2} + 4 β is equal to$
Mathematics · Functions · MCQ
Q27.Let $a_{1}, a_{2}, a_{3}, \dots$ . be a G.P. of increasing positive numbers. If $a_{3} a_{5} = 729$ and $a_{2} + a_{4} = \frac{111}{4}$ , then $24 (a_{1} + a_{2} + a_{3})$ is equal to
Mathematics · Sequences and Series · MCQ
Q28.The sum $1 + 3 + 11 + 25 + 45 + 71 + \dots$ upto 20 terms, is equal to
Mathematics · Sequences and Series · MCQ
Q29. $The number of solutions of the equation 2 x + 3 tan x = π, x \in [- 2 π, 2 π] - {\pm \frac{π}{2}, \pm \frac{3 π}{2}} is:$
Mathematics · Trigonometric Functions and Equations · MCQ
Q30.Let $A = {- 3, - 2, - 1, 0, 1, 2, 3}$ . Let R be a relation on A defined by $x R y$ if and only if $0 \leq x^{2} + 2 y \leq 4$ . Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R…
Mathematics · Sets and Relations · MCQ
Q31.The radius of the smallest circle which touches the parabolas $y = x^{2} + 2$ and $x = y^{2} + 2$ is
Mathematics · Parabola · MCQ
Q32. $Let f (x) = \int x^{3} 3 - x^{2} d x . If 5 f (2) = - 4, then f (1) is equal to$
Mathematics · Indefinite Integrals · MCQ
Q33.Let the domain of the function $f (x) = lo g_{2} lo g_{4} lo g_{6} (3 + 4 x - x^{2})$ be $(a, b)$ . If $\int_{0}^{b - a} [x^{2}] d x = p - q - r, p, q, r \in N, gcd (p, q, r) = 1$ , where $[\cdot]$ is the…
Mathematics · Definite Integration · MCQ
Q34.Let $α$ and $β$ be the roots of $x^{2} + 3 x - 16 = 0$ , and $γ$ and $δ$ be the roots of $x^{2} + 3 x - 1 = 0$ . If $P_{n} = α^{n} + β^{n}$ and $Q_{n} = γ^{n} + \overset{o}{^}^{n}$ , then $\frac{P _{25} + 3 P _{24}}{2 P _{23}} + \frac{Q _{25} - Q _{23}}{Q _{24}}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q35.Let a line passing through the point $(4, 1, 0)$ intersect the line $L_{1} : \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ at the point $A (α, β, γ)$ and the line $L_{2} : x - 6 = y = - z + 4$ at the point $B (a, b, c)$ . Then $1 α a 0 β b 1 γ c$ …
Mathematics · 3D Geometry · MCQ
Q36.Let $f (x) = {(1 + a x)^{1/ x}, x 0$ be continuous at $x = 0$ . Then $e^{a} b c$ is equal to:
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.A line passing through the point $P (5, 5)$ intersects the ellipse $\frac{x ^{2}}{36} + \frac{y ^{2}}{25} = 1$ at $A$ and $B$ such that $(P A) \cdot (P B)$ is maximum. Then $5 (P A^{2} + P B^{2})$ is equal to :
Mathematics · Ellipse · MCQ
Q38.Line $L_{1}$ passes through the point $(1, 2, 3)$ and is parallel to $z$ -axis. Line $L_{2}$ passes through the point $(λ, 5, 6)$ and is parallel to $y$ -axis. Let for $λ = λ_{1}, λ_{2}, λ_{2} < λ_{1}$ , the shortest…
Mathematics · 3D Geometry · MCQ
Q39.Let $g$ be a differentiable function such that $\int_{0}^{x} g (t) d t = x - \int_{0}^{x} tg (t) d t, x \geq 0$ and let $y = y (x)$ satisfy the differential equation $\frac{d y}{d x} - y tan x = 2 (x + 1) sec xg (x), x \in [0, \frac{π}{2})$ …
Mathematics · Differential Equations · MCQ
Q40.The sum of all rational terms in the expansion of $(2 + 3)^{8}$ is :
Mathematics · Binomial Theorem · MCQ
Q41.If $r = 1 \sum 9 (\frac{r + 3}{2 ^{r}}) \cdot^{9} C_{r} = α (\frac{3}{2})^{9} - β, α, β \in N$ , then $(α + β)^{2}$ is equal to
Mathematics · Binomial Theorem · MCQ
Q42.Let $z \in C$ be such that $\frac{z ^{2} + 3 i}{z - 2 + i} = 2 + 3 i$ . Then the sum of all possible values of $z^{2}$ is :
Mathematics · Complex Numbers · MCQ
Q43. $If y (x) = sin x 271 cos x 281 sin x + cos x + 1 271, x \in R, then \frac{d ^{2} y}{d x ^{2}} + y is equal to$
Mathematics · Differentiation · MCQ
Q44.A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_{1} : 2 x + y + 6 = 0$ and $L_{2} : 4 x + 2 y - p = 0, p > 0$ , at the points A and B , respectively. If $A B = \frac{9}{2}$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q45.Let $A$ be a matrix of order $3 \times 3$ and $∣ A ∣ = 5$ . If $∣2 adj (3 A adj (2 A)) ∣ = 2^{α} \cdot 3^{β} \cdot 5^{γ}, α, β, γ \in N$ , then $α + β + γ$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q46.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 $P (W_{n})$ …
Mathematics · Permutations and Combinations · Numerical
Q47.Let $a = \hat{i} + \hat{j} + \hat{k}, b = 3 \hat{i} + 2 \hat{j} - \hat{k}, c = λ \hat{j} + μ \hat{k}$ and $\hat{d}$ be a unit vector such that $a \times \hat{d} = b \times \hat{d}$ and $c \cdot \hat{d} = 1$ . If $c$ …
Mathematics · Vector Algebra · Numerical
Q48.Let the product of the focal distances of the point $P (4, 23)$ 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 $q$ …
Mathematics · Hyperbola · Numerical
Q49.The area of the region bounded by the curve $y = max {∣ x ∣, x ∣ x - 2∣}$ , the $x$ -axis and the lines $x = - 2$ and $x = 4$ is equal to
Mathematics · Area Under the Curves · Numerical
Q50.If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 1 0^{n}; m, n \in {1, 2, 3, \dots, 9}$ , then $m + n$ is equal to
Mathematics · Permutations and Combinations · Numerical