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Mathematics · 2025 · 28 Jan · Shift 2

25 questions from this JEE Main paper

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2025 · 28 Jan · Shift 2
Mathematics

Mathematics · 2025 · 28 Jan · Shift 2

25 questions from this JEE Main paper

Area Under the Curves1 questions Probability2 questions Definite Integration2 questions Ellipse1 questions 3D Geometry1 questions Straight Lines and Pair of Straight Lines2 questions Binomial Theorem1 questions Vector Algebra2 questions Quadratic Equation and Inequalities1 questions Inverse Trigonometric Functions1 questions Complex Numbers1 questions Trigonometric Ratio and Identites1 questions Indefinite Integrals1 questions Matrices and Determinants1 questions Functions1 questions Sequences and Series2 questions Limits Continuity and Differentiability1 questions Parabola1 questions Differential Equations1 questions Permutations and Combinations1 questions

Q26.The area of the region bounded by the curves $x (1 + y^{2}) = 1$ and $y^{2} = 2 x$ is:
Mathematics · Area Under the Curves · MCQ
Q27.Bag $B_{1}$ contains 6 white and 4 blue balls, Bag $B_{2}$ contains 4 white and 6 blue balls, and Bag $B_{3}$ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the…
Mathematics · Probability · MCQ
Q28.Let $f : R \to R$ be a twice differentiable function such that $f (2) = 1$ . If $F (x) = x f (x)$ for all $x \in R$ , $0 \int 2 x F^{'} (x) d x = 6$ …
Mathematics · Definite Integration · MCQ
Q29.If the midpoint of a chord of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ is $(2, 4/3)$ , and the length of the chord is $\frac{2 α}{3}$ , then $α$ is :
Mathematics · Ellipse · MCQ
Q30.The square of the distance of the point $(\frac{15}{7}, \frac{32}{7}, 7)$ from the line $\frac{x + 1}{3} = \frac{y + 3}{5} = \frac{z + 5}{7}$ in the direction of the vector $\hat{i} + 4 \hat{j} + 7 \hat{k}$ is:
Mathematics · 3D Geometry · MCQ
Q31.Two equal sides of an isosceles triangle are along $- x + 2 y = 4$ and $x + y = 4$ . If $m$ is the slope of its third side, then the sum, of all possible distinct values of $m$ , is:
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q32.Let the coefficients of three consecutive terms $T_{r}$ , $T_{r + 1}$ and $T_{r + 2}$ in the binomial expansion of $(a + b)^{12}$ be in a G.P. and let $p$ be the number of all possible values of $r$ . Let $q$ be the sum of all rational terms in…
Mathematics · Binomial Theorem · MCQ
Q33.If the components of $a = α \hat{i} + β \hat{j} + γ \hat{k}$ along and perpendicular to $b = 3 \hat{i} + \hat{j} - \hat{k}$ respectively, are $\frac{16}{11} (3 \hat{i} + \hat{j} - \hat{k})$ and $\frac{1}{11} (- 4 \hat{i} - 5 \hat{j} - 17 \hat{k})$ …
Mathematics · Vector Algebra · MCQ
Q34.Let $f : R - {0} \to (- \infty, 1)$ be a polynomial of degree 2 , satisfying $f (x) f (\frac{1}{x}) = f (x) + f (\frac{1}{x})$ . If $f (K) = - 2 K$ , then the sum of squares of all possible values…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q35.Let [x] denote the greatest integer less than or equal to x. Then the domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is:
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:
Mathematics · Probability · MCQ
Q37.If A and B are the points of intersection of the circle $x^{2} + y^{2} - 8 x = 0$ and the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ and a point P moves on the line $2 x - 3 y + 4 = 0$ , then the centroid of $Δ P A B$ lies on the line :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q38.Let $A, B, C$ be three points in xy-plane, whose position vector are given by $3 \hat{i} + \hat{j}, \hat{i} + 3 \hat{j}$ and $a \hat{i} + (1 - a) \hat{j}$ respectively with respect to the origin O . If the distance of the point C…
Mathematics · Vector Algebra · MCQ
Q39.If $α + i β$ and $γ + i δ$ are the roots of $x^{2} - (3 - 2 i) x - (2 i - 2) = 0$ , $i = - 1$ , then $α γ + β δ$ is equal to:
Mathematics · Complex Numbers · MCQ
Q40.If $r = 1 \sum 13 {\frac{1}{s i n ( \frac{π}{4} + ( r - 1 ) \frac{π}{6} ) s i n ( \frac{π}{4} + \frac{r π}{6} )}} = a 3 + b, a, b \in Z$ , then $a^{2} + b^{2}$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q41.If $f (x) = \int \frac{1}{x ^{1/4} ( 1 + x ^{1/4} )} d x, f (0) = - 6$ , then $f (1)$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q42.Let $A = [\frac{1}{2} 0 - 2 1]$ and $P = [cos θ sin θ - sin θ cos θ], θ > 0$ . If $B = PAP^{⊤}, C = P^{⊤} B^{10} P$ …
Mathematics · Matrices and Determinants · MCQ
Q43.Let $f$ be a real valued continuous function defined on the positive real axis such that $g (x) = 0 \int x t f (t) d t$ . If $g (x^{3}) = x^{6} + x^{7}$ , then value of $r = 1 \sum 15 f (r^{3})$ is :
Mathematics · Definite Integration · MCQ
Q44.Let $f : [0, 3] \to$ A be defined by $f (x) = 2 x^{3} - 15 x^{2} + 36 x + 7$ and $g : [0, \infty) \to B$ be defined by $g (x) = \frac{x ^{2025}}{x ^{2025} + 1}$ , If both the functions are onto and $S = {x \in Z; x \in A$ or $x \in B}$ , then $n (S)$ …
Mathematics · Functions · MCQ
Q45.For positive integers $n$ , if $4 a_{n} = (n^{2} + 5 n + 6)$ and $S_{n} = k = 1 \sum n (\frac{1}{a _{k}})$ , then the value of $507 S_{2025}$ is :
Mathematics · Sequences and Series · MCQ
Q46.Let $f (x) = n \to \infty lim r = 0 \sum n (\frac{t a n ( x / 2 ^{r + 1} ) + t a n ^{3} ( x / 2 ^{r + 1} )}{1 - t a n ^{2} ( x / 2 ^{r + 1} )})$ Then $x \to 0 lim \frac{e ^{x} - e ^{f (x)}}{( x - f ( x ))}$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q47.Let $A$ and $B$ be the two points of intersection of the line $y + 5 = 0$ and the mirror image of the parabola $y^{2} = 4 x$ with respect to the line $x + y + 4 = 0$ . If $d$ denotes the distance between $A$ and $B$ , and a denotes the area of $△ S A B$ …
Mathematics · Parabola · Numerical
Q48.If $y = y (x)$ is the solution of the differential equation, $4 - x^{2} \frac{d y}{d x} = ((sin^{- 1} (\frac{x}{2}))^{2} - y) sin^{- 1} (\frac{x}{2}), - 2 \leq x \leq 2, y (2) = \frac{π ^{2} - 8}{4}$ …
Mathematics · Differential Equations · Numerical
Q49.The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the polygon is 219°, then n is equal to .
Mathematics · Sequences and Series · Numerical
Q50.The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .
Mathematics · Permutations and Combinations · Numerical