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Mathematics · 2025 · 24 Jan · Shift 2

25 questions from this JEE Main paper

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2025 · 24 Jan · Shift 2
Mathematics

Mathematics · 2025 · 24 Jan · Shift 2

25 questions from this JEE Main paper

Sequences and Series2 questions Probability1 questions Application of Derivatives1 questions Sets and Relations1 questions Area Under the Curves1 questions Matrices and Determinants2 questions Inverse Trigonometric Functions1 questions Binomial Theorem1 questions Vector Algebra2 questions Parabola1 questions Ellipse1 questions Straight Lines and Pair of Straight Lines1 questions Permutations and Combinations2 questions Limits Continuity and Differentiability1 questions Quadratic Equation and Inequalities1 questions Differentiation1 questions Functions1 questions 3D Geometry1 questions Indefinite Integrals1 questions Differential Equations1 questions Hyperbola1 questions

Q26.In an arithmetic progression, if $S_{40} = 1030$ and $S_{12} = 57$ , then $S_{30} - S_{10}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q27.Let $A = [a_{ij}]$ be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability $P (E)$ is :
Mathematics · Probability · MCQ
Q28.Let $(2, 3)$ be the largest open interval in which the function $f (x) = 2 lo g_{e} (x - 2) - x^{2} + a x + 1$ is strictly increasing and (b, c) be the largest open interval, in which the function $g (x) = (x - 1)^{3} (x + 2 - a)^{2}$ is…
Mathematics · Application of Derivatives · MCQ
Q29.Let $A = {x \in (0, π) - {\frac{π}{2}} : lo g_{(2/ π)} ∣ sin x ∣ + lo g_{(2/ π)} ∣ cos x ∣ = 2}$ and $B = {x ⩾ 0 : x (x - 4) - 3∣ x - 2∣ + 6 = 0}$ . Then $n (A \cup B)$ …
Mathematics · Sets and Relations · MCQ
Q30.The area of the region enclosed by the curves $y = e^{x}, y = ∣ e^{x} - 1 ∣$ and $y$ -axis is :
Mathematics · Area Under the Curves · MCQ
Q31.For some $a, b,$ let $f (x) = a + \frac{s i n x}{x} a a 1 1 + \frac{s i n x}{x} 1 b b b + \frac{s i n x}{x}, x e q 0, x \to 0 lim f (x) = λ + μ a + u b .$ …
Mathematics · Matrices and Determinants · MCQ
Q32.If $α > β > γ > 0$ , then the expression $cot^{- 1} {β + \frac{( 1 + β ^{2} )}{( α - β )}} + cot^{- 1} {γ + \frac{( 1 + γ ^{2} )}{( β - γ )}} + cot^{- 1} {α + \frac{( 1 + α ^{2} )}{( γ - α )}}$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q33.If the system of equations $x + 2 y - 3 z = 2 2 x + λ y + 5 z = 5 14 x + 3 y + μ z = 33$ has infinitely many solutions, then $λ + μ$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q34.Suppose $A$ and $B$ are the coefficients of $3 0^{th}$ and $1 2^{th}$ terms respectively in the binomial expansion of $(1 + x)^{2 n - 1}$ . If $2 A = 5 B$ , then n is equal to:
Mathematics · Binomial Theorem · MCQ
Q35.Let the position vectors of three vertices of a triangle be $4 p + q - 3 r, - 5 p + q + 2 r$ and $2 p - q + 2 r$ . If the position vectors of the orthocenter and the circumcenter of the triangle are $\frac{p + q + r}{4}$ …
Mathematics · Vector Algebra · MCQ
Q36.If $7 = 5 + \frac{1}{7} (5 + α) + \frac{1}{7 ^{2}} (5 + 2 α) + \frac{1}{7 ^{3}} (5 + 3 α) + \dots\dots\dots\dots \infty$ , then the value of $α$ is :
Mathematics · Sequences and Series · MCQ
Q37.If the equation of the parabola with vertex $V (\frac{3}{2}, 3)$ and the directrix $x + 2 y = 0$ is $α x^{2} + β y^{2} - γ x y - 30 x - 60 y + 225 = 0$ , then $α + β + γ$ is equal to :
Mathematics · Parabola · MCQ
Q38.Let $a = 3 \hat{i} - \hat{j} + 2 \hat{k}, b = a \times (\hat{i} - 2 \hat{k})$ and $c = b \times \hat{k}$ . Then the…
Mathematics · Vector Algebra · MCQ
Q39.The equation of the chord, of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ , whose mid-point is $(3, 1)$ is :
Mathematics · Ellipse · MCQ
Q40.Let the points $(\frac{11}{2}, α)$ lie on or inside the triangle with sides $x + y = 11, x + 2 y = 16$ and $2 x + 3 y = 29$ . Then the product of the smallest and the largest values of $α$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$ , is equal to :
Mathematics · Permutations and Combinations · MCQ
Q42.Let $[x]$ denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f (x) = [x] + ∣ x - 2∣, - 2 < x < 3$ , is not continuous and not differentiable. Then $m + n$ is equal to…
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.The number of real solution(s) of the equation $x^{2} + 3 x + 2 = min {∣ x - 3∣, ∣ x + 2∣}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q44.Let $f : (0, \infty) \to R$ be a function which is differentiable at all points of its domain and satisfies the condition $x^{2} f^{'} (x) = 2 x f (x) + 3$ , with $f (1) = 4$ . Then $2 f (2)$ is equal to :
Mathematics · Differentiation · MCQ
Q45.The function $f : (- \infty, \infty) \to (- \infty, 1)$ , defined by $f (x) = \frac{2 ^{x} - 2 ^{- x}}{2 ^{x} + 2 ^{- x}}$ is :
Mathematics · Functions · MCQ
Q46.Let P be the image of the point $Q (7, - 2, 5)$ in the line $L : \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z}{4}$ and $R (5, p, q)$ be a point on $L$ . Then the square of the area of $△ P QR$ is …
Mathematics · 3D Geometry · Numerical
Q47.If $\int \frac{2 x ^{2} + 5 x + 9}{x ^{2} + x + 1} d x = x x^{2} + x + 1 + α x^{2} + x + 1 + β lo g_{e} x + \frac{1}{2} + x^{2} + x + 1 + C$ , where $C$ is the constant of integration, then $α + 2 β$ …
Mathematics · Indefinite Integrals · Numerical
Q48.Let $y = y (x)$ be the solution of the differential equation $2 cos x \frac{d y}{d x} = sin 2 x - 4 y sin x, x \in (0, \frac{π}{2})$ . If $y (\frac{π}{3}) = 0$ , then $y^{'} (\frac{π}{4}) + y (\frac{π}{4})$ …
Mathematics · Differential Equations · Numerical
Q49.Number of functions $f : {1, 2, \dots, 100} \to {0, 1}$ , that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to .
Mathematics · Permutations and Combinations · Numerical
Q50.Let $H_{1} : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ and $H_{2} : - \frac{x ^{2}}{A ^{2}} + \frac{y ^{2}}{B ^{2}} = 1$ be two hyperbolas having length of latus rectums $152$ and $125$ …
Mathematics · Hyperbola · Numerical