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Mathematics · 2025 · 22 Jan · Shift 2

25 questions from this JEE Main paper

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2025 · 22 Jan · Shift 2
Mathematics

Mathematics · 2025 · 22 Jan · Shift 2

25 questions from this JEE Main paper

Quadratic Equation and Inequalities1 questions 3D Geometry2 questions Matrices and Determinants2 questions Trigonometric Functions and Equations1 questions Binomial Theorem2 questions Differential Equations2 questions Probability1 questions Indefinite Integrals1 questions Vector Algebra1 questions Area Under the Curves1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability1 questions Application of Derivatives1 questions Functions1 questions Complex Numbers1 questions Sequences and Series1 questions Parabola1 questions Ellipse1 questions Properties of Triangle1 questions Straight Lines and Pair of Straight Lines1 questions Sets and Relations1 questions

Q26.Let $α_{θ}$ and $β_{θ}$ be the distinct roots of $2 x^{2} + (cos θ) x - 1 = 0, θ \in (0, 2 π)$ . If m and M are the minimum and the maximum values of $α_{θ}^{4} + β_{θ}^{4}$ , then $16 (M + m)$ equals :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.Let a line pass through two distinct points $P (- 2, - 1, 3)$ and $Q$ , and be parallel to the vector $3 \hat{i} + 2 \hat{j} + 2 \hat{k}$ . If the distance of the point Q from the point $R (1, 3, 3)$ is 5 , then the square of the area of $△ P QR$ …
Mathematics · 3D Geometry · MCQ
Q28.If the system of linear equations : $x + y + 2 z = 6 2 x + 3 y + az = a + 1 - x - 3 y + b z = 2 b$ where $a, b \in R$ , has infinitely many solutions, then $7 a + 3 b$ …
Mathematics · Matrices and Determinants · MCQ
Q29.The sum of all values of $θ \in [0, 2 π]$ satisfying $2 sin^{2} θ = cos 2 θ$ and $2 cos^{2} θ = 3 sin θ$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q30.Let $α, β, γ$ and $δ$ be the coefficients of $x^{7}, x^{5}, x^{3}$ and $x$ respectively in the expansion of $(x + x^{3} - 1)^{5} + (x - x^{3} - 1)^{5}, x > 1 . If u and v satisfy the equations α u + β v = 18, γ u + δ v = 20,$ …
Mathematics · Binomial Theorem · MCQ
Q31.The perpendicular distance, of the line $\frac{x - 1}{2} = \frac{y + 2}{- 1} = \frac{z + 3}{2}$ from the point $P (2, - 10, 1)$ , is :
Mathematics · 3D Geometry · MCQ
Q32.If $x = f (y)$ is the solution of the differential equation $(1 + y^{2}) + (x - 2 e^{t a n^{- 1} y}) \frac{d y}{d x} = 0, y \in (- \frac{π}{2}, \frac{π}{2})$ with $f (0) = 1$ , then $f (\frac{1}{3})$ …
Mathematics · Differential Equations · MCQ
Q33.If $A$ and $B$ are two events such that $P (A \cap B) = 0.1$ , and $P (A ∣ B)$ and $P (B ∣ A)$ are the roots of the equation $12 x^{2} - 7 x + 1 = 0$ , then the value of $\frac{P ( A ˉ \cup B ˉ )}{P ( A ˉ \cap B ˉ )}$ is :
Mathematics · Probability · MCQ
Q34.For a $3 \times 3$ matrix $M$ , let trace $(M)$ denote the sum of all the diagonal elements of $M$ . Let $A$ be a $3 \times 3$ matrix such that $∣ A ∣ = \frac{1}{2}$ and trace $(A) = 3$ . If $B = adj (adj (2 A))$ , then the…
Mathematics · Matrices and Determinants · MCQ
Q35.If $\int e^{x} (\frac{x s i n ^{- 1} x}{1 - x ^{2}} + \frac{s i n ^{- 1} x}{( 1 - x ^{2} ) ^{3/2}} + \frac{x}{1 - x ^{2}}) d x = g (x) + C$ , where C is the constant of integration, then $g (\frac{1}{2})$ …
Mathematics · Indefinite Integrals · MCQ
Q36.Let $a$ and $b$ be two unit vectors such that the angle between them is $\frac{π}{3}$ . If $λ a + 2 b$ and $3 a - λ b$ are perpendicular to each other, then the number of values of $λ$ in $[- 1, 3]$ …
Mathematics · Vector Algebra · MCQ
Q37.The area of the region enclosed by the curves $y = x^{2} - 4 x + 4$ and $y^{2} = 16 - 8 x$ is :
Mathematics · Area Under the Curves · MCQ
Q38.In a group of 3 girls and 4 boys, there are two boys $B_{1}$ and $B_{2}$ . The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B_{1}$ and $B_{2}$ are not…
Mathematics · Permutations and Combinations · MCQ
Q39.If $lim_{x \to \infty} ((\frac{e}{1 - e}) (\frac{1}{e} - \frac{x}{1 + x}))^{x} = α$ , then the value of $\frac{l o g _{e} α}{1 + l o g _{e} α}$ equals :
Mathematics · Limits Continuity and Differentiability · MCQ
Q40.Let $f (x) = \int_{0}^{x^{2}} \frac{t ^{2} - 8 t + 15}{e ^{t}} dt, x \in R$ . Then the numbers of local maximum and local minimum points of $f$ , respectively, are :
Mathematics · Application of Derivatives · MCQ
Q41.Let $A = {1, 2, 3, 4}$ and $B = {1, 4, 9, 16}$ . Then the number of many-one functions $f : A \to B$ such that $1 \in f (A)$ is equal to :
Mathematics · Functions · MCQ
Q42.Let the curve $z (1 + i) + \overset{z}{ˉ} (1 - i) = 4, z \in C$ , divide the region $∣ z - 3∣ \leq 1$ into two parts of areas $α$ and $β$ . Then $∣ α - β ∣$ equals :
Mathematics · Complex Numbers · MCQ
Q43.Suppose that the number of terms in an A.P. is $2 k, k \in N$ . If the sum of all odd terms of the A.P. is 40 , the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27 , then k is equal to:
Mathematics · Sequences and Series · MCQ
Q44.Let $P (4, 43)$ be a point on the parabola $y^{2} = 4 a x$ and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the…
Mathematics · Parabola · MCQ
Q45.Let $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ and $H : \frac{x ^{2}}{A ^{2}} - \frac{y ^{2}}{B ^{2}} = 1$ . Let the distance between the foci of E and the foci of $H$ be $23$ …
Mathematics · Ellipse · MCQ
Q46.Let $A (6, 8), B (10 cos α, - 10 sin α)$ and $C (- 10 sin α, 10 cos α)$ , be the vertices of a triangle. If $L (a, 9)$ and $G (h, k)$ be its orthocenter and centroid respectively, then $(5 a - 3 h + 6 k + 100 sin 2 α)$ …
Mathematics · Properties of Triangle · Numerical
Q47.Let $y = f (x)$ be the solution of the differential equation $\frac{d y}{d x} + \frac{x y}{x ^{2} - 1} = \frac{x ^{6} + 4 x}{1 - x ^{2}}, - 1 < x < 1$ such that $f (0) = 0$ . If $6 \int_{- 1/2}^{1/2} f (x) d x = 2 π - α$ then…
Mathematics · Differential Equations · Numerical
Q48.If $\sum_{r = 1}^{30} \frac{r ^{2} ( ^{30} C _{r} ) ^{2}}{^{30} C _{r - 1}} = α \times 2^{29}$ , then $α$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q49.Let the distance between two parallel lines be 5 units and a point $P$ lie between the lines at a unit distance from one of them. An equilateral triangle $P QR$ is formed such that $Q$ lies on one of the parallel lines, while R lies on…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q50.Let $A = {1, 2, 3}$ . The number of relations on $A$ , containing $(1, 2)$ and $(2, 3)$ , which are reflexive and transitive but not symmetric, is .
Mathematics · Sets and Relations · Numerical