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Mathematics · 2025 · 8 Apr · Shift 2

25 questions from this JEE Main paper

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2025 · 8 Apr · Shift 2
Mathematics

Mathematics · 2025 · 8 Apr · Shift 2

25 questions from this JEE Main paper

3D Geometry2 questions Differential Equations1 questions Sequences and Series1 questions Straight Lines and Pair of Straight Lines2 questions Matrices and Determinants2 questions Ellipse1 questions Quadratic Equation and Inequalities1 questions Inverse Trigonometric Functions1 questions Complex Numbers1 questions Limits Continuity and Differentiability1 questions Definite Integration2 questions Sets and Relations1 questions Permutations and Combinations1 questions Probability1 questions Vector Algebra1 questions Application of Derivatives1 questions Binomial Theorem2 questions Area Under the Curves1 questions Parabola1 questions Functions1 questions

Q26.Let the values of $λ$ for which the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - λ}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ is $\frac{1}{6}$ be $λ_{1}$ and $λ_{2}$ .…
Mathematics · 3D Geometry · MCQ
Q27.Let $f (x) = x - 1$ and $g (x) = e^{x}$ for $x \in R$ . If $\frac{d y}{d x} = (e^{- 2 x} g (f (f (x))) - \frac{y}{x})$ , $y (0) = 0$ , then $y (1)$ is
Mathematics · Differential Equations · MCQ
Q28.If $\frac{1}{1 ^{4}} + \frac{1}{2 ^{4}} + \frac{1}{3 ^{4}} + \dots \infty = \frac{π ^{4}}{90}$ , $\frac{1}{1 ^{4}} + \frac{1}{3 ^{4}} + \frac{1}{5 ^{4}} + \dots \infty = α$ , $\frac{1}{2 ^{4}} + \frac{1}{4 ^{4}} + \frac{1}{6 ^{4}} + \dots \infty = β$ , then $\frac{α}{β}$ …
Mathematics · Sequences and Series · MCQ
Q29.Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle $α$ with the positive x-axis and the equations of its diagonals are $(3 + 1) x + (3 - 1) y = 0$ and $(3 - 1) x - (3 + 1) y + 83 = 0$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.A line passing through the point P( $a$ , 0) makes an acute angle $α$ with the positive x-axis. Let this line be rotated about the point P through an angle $\frac{α}{2}$ in the clockwise direction. If in the new position, the slope…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.Let α be a solution of $x^{2} + x + 1 = 0$ , and for some a and b in $R, [4 a b] 1 - 1 - 2 16 - 1 - 14 132 - 8 = [000]$ …
Mathematics · Matrices and Determinants · MCQ
Q32.Let the ellipse $3 x^{2} + p y^{2} = 4$ pass through the centre $C$ of the circle $x^{2} + y^{2} - 2 x - 4 y - 11 = 0$ of radius $r$ . Let $f_{1}, f_{2}$ be the focal distances of the point $C$ on the ellipse. Then $6 f_{1} f_{2} - r$ is equal to
Mathematics · Ellipse · MCQ
Q33.The sum of the squares of the roots of $∣ x - 2 ∣^{2} + ∣ x - 2∣ - 2 = 0$ and the squares of the roots of $x^{2} - 2∣ x - 3∣ - 5 = 0$ , is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.The value of $cot^{- 1} (\frac{1 + t a n ^{2} ( 2 ) - 1}{t a n ( 2 )}) - cot^{- 1} (\frac{1 + t a n ^{2} ( \frac{1}{2} ) + 1}{t a n ( \frac{1}{2} )})$ is equal to
Mathematics · Inverse Trigonometric Functions · MCQ
Q35.Let $A = {θ \in [0, 2 π] : 1 + 10 Re (\frac{2 c o s θ + i s i n θ}{c o s θ - 3 i s i n θ}) = 0}$ . Then $θ \in A \sum θ^{2}$ is equal to
Mathematics · Complex Numbers · MCQ
Q36.Given below are two statements: Statement I: $x \to 0 lim (\frac{t a n ^{- 1} x + l o g _{e} \frac{1 + x}{1 - x} - 2 x}{x ^{5}}) = \frac{2}{5}$ Statement II: $x \to 1 lim (x^{\frac{2}{1 - x}}) = \frac{1}{e ^{2}}$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.The integral $- 1 \int \frac{3}{2} (∣ π^{2} x sin (π x)) d x$ is equal to:
Mathematics · Definite Integration · MCQ
Q38.Let $A = 246 2 + p 6 + 2 p 12 + 3 p 2 + p + q 8 + 3 p + 2 q 20 + 6 p + 3 q$ . If $det (adj (adj (3 A))) = 2^{m} \cdot 3^{n}$ , $m, n \in N$ , then $m + n$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q39.Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive…
Mathematics · Sets and Relations · MCQ
Q40.Let f(x) be a positive function and $I_{1} = - \frac{1}{2} \int 1 2 x f (2 x (1 - 2 x)) d x$ and $I_{2} = - 1 \int 2 f (x (1 - x)) d x$ . Then the value of $\frac{I _{2}}{I _{1}}$ is equal to
Mathematics · Definite Integration · MCQ
Q41.There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is
Mathematics · Permutations and Combinations · MCQ
Q42.If A and B are two events such that $P (A) = 0.7$ , $P (B) = 0.4$ and $P (A \cap \overline{B}) = 0.5$ , where $\overline{B}$ denotes the complement of B, then $P (B ∣ (A \cup \overline{B}))$ is equal to
Mathematics · Probability · MCQ
Q43.Let $a = \hat{i} + 2 \hat{j} + \hat{k}$ and $b = 2 \hat{i} + \hat{j} - \hat{k}$ . Let $\overset{c}{^}$ be a unit vector in the plane of the vectors $a$ and $b$ and be perpendicular to $a$ . Then such a vector $\overset{c}{^}$ …
Mathematics · Vector Algebra · MCQ
Q44.Let the function $f (x) = \frac{x}{3} + \frac{3}{x} + 3, x e q 0$ be strictly increasing in $(- \infty, α_{1}) \cup (α_{2}, \infty)$ and strictly decreasing in $(α_{3}, α_{4}) \cup (α_{4}, α_{5})$ . Then $i = 1 \sum 5 α_{i}^{2}$ …
Mathematics · Application of Derivatives · MCQ
Q45.The number of integral terms in the expansion of $(5^{\frac{1}{2}} + 7^{\frac{1}{8}})^{1016}$ is:
Mathematics · Binomial Theorem · MCQ
Q46.The product of the last two digits of $(1919)^{1919}$ is
Mathematics · Binomial Theorem · Numerical
Q47.Let the area of the bounded region ${(x, y) : 0 \leq 9 x \leq y^{2}, y \geq 3 x - 6}$ be $A$ . Then $6 A$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q48.Let $r$ be the radius of the circle, which touches $x$ - axis at point $(a, 0), a < 0$ and the parabola $y^{2} = 9 x$ at the point $(4, 6)$ . Then $r$ is equal to .
Mathematics · Parabola · Numerical
Q49.Let the area of the triangle formed by the lines $x + 2 = y - 1 = z, \frac{x - 3}{5} = \frac{y}{- 1} = \frac{z - 1}{1}$ and $\frac{x}{- 3} = \frac{y - 3}{3} = \frac{z - 2}{1}$ be $A$ . Then $A^{2}$ is equal to .
Mathematics · 3D Geometry · Numerical
Q50.Let the domain of the function $f (x) = cos^{- 1} (\frac{4 x + 5}{3 x - 7})$ be $[α, β]$ and the domain of $g (x) = lo g_{2} (2 - 6 lo g_{27} (2 x + 5))$ be $(γ, δ)$ . Then $∣7 (α + β) + 4 (γ + δ) ∣$ is…
Mathematics · Functions · Numerical