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Mathematics · 2025 · 4 Apr · Shift 1

25 questions from this JEE Main paper

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2025 · 4 Apr · Shift 1
Mathematics

Mathematics · 2025 · 4 Apr · Shift 1

25 questions from this JEE Main paper

Limits Continuity and Differentiability3 questions 3D Geometry2 questions Sequences and Series2 questions Ellipse1 questions Quadratic Equation and Inequalities1 questions Sets and Relations1 questions Trigonometric Ratio and Identites1 questions Definite Integration1 questions Area Under the Curves2 questions Probability2 questions Vector Algebra1 questions Binomial Theorem2 questions Functions1 questions Straight Lines and Pair of Straight Lines1 questions Inverse Trigonometric Functions1 questions Circle1 questions Matrices and Determinants1 questions Complex Numbers1 questions

Q26.Let $f : R \to R$ be a continuous function satisfying $f (0) = 1$ and $f (2 x) - f (x) = x$ for all $x \in R$ . If $lim_{n \to \infty} {f (x) - f (\frac{x}{2 ^{n}})} = G (x)$ , then $\sum_{r = 1}^{10} G (r^{2})$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let the shortest distance between the lines $\frac{x - 3}{3} = \frac{y - α}{- 1} = \frac{z - 3}{1}$ and $\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - β}{4}$ be $330$ . Then the positive value of $5 α + β$ is
Mathematics · 3D Geometry · MCQ
Q28.Let $A = {1, 6, 11, 16, \dots}$ and $B = {9, 16, 23, 30, \dots}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n (A \cup B)$ is
Mathematics · Sequences and Series · MCQ
Q29.The length of the latus-rectum of the ellipse, whose foci are $(2, 5)$ and $(2, - 3)$ and eccentricity is $\frac{4}{5}$ , is
Mathematics · Ellipse · MCQ
Q30.Consider the equation $x^{2} + 4 x - n = 0$ , where $n \in [20, 100]$ is a natural number. Then the number of all distinct values of $n$ , for which the given equation has integral roots, is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.Consider the sets $A = {(x, y) \in R \times R : x^{2} + y^{2} = 25}, B = {(x, y) \in R \times R : x^{2} + 9 y^{2} = 144}$ , $C = {(x, y) \in Z \times Z : x^{2} + y^{2} \leq 4}$ …
Mathematics · Sets and Relations · MCQ
Q32. $1 + 3 + 5^{2} + 7 + 9^{2} + \dots$ upto 40 terms is equal to
Mathematics · Sequences and Series · MCQ
Q33.If $10 sin^{4} θ + 15 cos^{4} θ = 6$ , then the value of $\frac{27 cosec ^{6} θ + 8 s e c ^{6} θ}{16 s e c ^{8} θ}$ is
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.The value of $\int_{- 1}^{1} \frac{( 1 + ∣ x ∣ - x ) e ^{x} + ( ∣ x ∣ - x ) e ^{- x}}{e ^{x} + e ^{- x}} d x$ is equal to
Mathematics · Definite Integration · MCQ
Q35.Let $f : [0, \infty) \to R$ be a differentiable function such that $f (x) = 1 - 2 x + \int_{0}^{x} e^{x - t} f (t) d t$ for all $x \in [0, \infty)$ . Then the area of the region bounded by $y = f (x)$ and the coordinate axes is
Mathematics · Area Under the Curves · MCQ
Q36.The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is
Mathematics · Probability · MCQ
Q37.A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is
Mathematics · Probability · MCQ
Q38.Consider two vectors $u = 3 \hat{i} - \hat{j}$ and $v = 2 \hat{i} + \hat{j} - λ \hat{k}, λ > 0$ . The angle between them is given by $cos^{- 1} (\frac{5}{2 7})$ . Let $v = v_{1} + v_{2}$ …
Mathematics · Vector Algebra · MCQ
Q39.For an integer $n \geq 2$ , if the arithmetic mean of all coefficients in the binomial expansion of $(x + y)^{2 n - 3}$ is 16 , then the distance of the point $P (2 n - 1, n^{2} - 4 n)$ from the line $x + y = 8$ is
Mathematics · Binomial Theorem · MCQ
Q40.Let $A$ and $B$ be two distinct points on the line $L : \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ . Both $A$ and $B$ are at a distance $217$ from the foot of perpendicular drawn from the point $(1, 2, 3)$ on the line $L$ . If $O$ is…
Mathematics · 3D Geometry · MCQ
Q41.Let $f, g : (1, \infty) \to R$ be defined as $f (x) = \frac{2 x + 3}{5 x + 2}$ and $g (x) = \frac{2 - 3 x}{1 - x}$ . If the range of the function fog: $[2, 4] \to R$ is $[α, β]$ , then $\frac{1}{β - α}$ is…
Mathematics · Functions · MCQ
Q42.If $lim_{x \to 1^{+}} \frac{( x - 1 ) ( 6 + λ c o s ( x - 1 )) + μ s i n ( 1 - x )}{( x - 1 ) ^{3}} = - 1$ , where $λ, μ \in R$ , then $λ + μ$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let the three sides of a triangle are on the lines $4 x - 7 y + 10 = 0, x + y = 5$ and $7 x + 4 y = 15$ . Then the distance of its orthocentre from the orthocentre of the tringle formed by the lines $x = 0, y = 0$ and $x + y = 1$ is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.In the expansion of $(32 + \frac{1}{3 3})^{n}, n \in N$ , if the ratio of $1 5^{th}$ term from the beginning to the $1 5^{th}$ term from the end is $\frac{1}{6}$ , then the value of $^{n} C_{3}$ …
Mathematics · Binomial Theorem · MCQ
Q45.Considering the principal values of the inverse trigonometric functions, $sin^{- 1} (\frac{3}{2} x + \frac{1}{2} 1 - x^{2}), - \frac{1}{2} < x < \frac{1}{2}$ , is equal to
Mathematics · Inverse Trigonometric Functions · MCQ
Q46.Let $C$ be the circle $x^{2} + (y - 1)^{2} = 2, E_{1}$ and $E_{2}$ be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line $x + y = 3$ touch the curves $C, E_{1}$ and $E_{2}$ at $P (x_{1}, y_{1}), Q (x_{2}, y_{2})$ …
Mathematics · Circle · Numerical
Q47.Let $m$ and $n$ be the number of points at which the function $f (x) = max {x, x^{3}, x^{5}, \dots x^{21}}, x \in R$ , is not differentiable and not continuous, respectively. Then $m + n$ is equal to…
Mathematics · Limits Continuity and Differentiability · Numerical
Q48.Let $A = cos θ 0 sin θ 010 - sin θ 0 cos θ$ . If for some $θ \in (0, π), A^{2} = A^{T}$ , then the sum of the diagonal elements of the…
Mathematics · Matrices and Determinants · Numerical
Q49.If the area of the region ${(x, y) : ∣ x - 5∣ \leq y \leq 4 x}$ is $A$ , then $3 A$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q50.Let $A = {z \in C : ∣ z - 2 - i ∣ = 3}, B = {z \in C : Re (z - i z) = 2}$ and $S = A \cap B$ . Then $\sum_{z \in S} ∣ z ∣^{2}$ is equal to .
Mathematics · Complex Numbers · Numerical