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Mathematics · 2025 · 24 Jan · Shift 1

25 questions from this JEE Main paper

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2025 · 24 Jan · Shift 1
Mathematics

Mathematics · 2025 · 24 Jan · Shift 1

25 questions from this JEE Main paper

Limits Continuity and Differentiability2 questions Quadratic Equation and Inequalities1 questions Binomial Theorem1 questions Functions1 questions Definite Integration1 questions Complex Numbers1 questions Ellipse1 questions Differential Equations2 questions 3D Geometry2 questions Probability1 questions Vector Algebra1 questions Application of Derivatives1 questions Area Under the Curves1 questions Sequences and Series1 questions Statistics1 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants2 questions Circle1 questions Sets and Relations1 questions Inverse Trigonometric Functions1 questions Permutations and Combinations1 questions

Q26. $lim_{x \to 0} cosec x (2 cos^{2} x + 3 cos x - cos^{2} x + sin x + 4)$ is:
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.Let $f : R - {0} \to R$ be a function such that $f (x) - 6 f (\frac{1}{x}) = \frac{35}{3 x} - \frac{5}{2}$ . If the $x \to 0 lim (\frac{1}{α x} + f (x)) = β; α, β \in R$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.The product of all the rational roots of the equation $(x^{2} - 9 x + 11)^{2} - (x - 4) (x - 5) = 3$ , is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.For some $n e q 10$ , let the coefficients of the 5 th, 6 th and 7 th terms in the binomial expansion of $(1 + x)^{n + 4}$ be in A.P. Then the largest coefficient in the expansion of $(1 + x)^{n + 4}$ is:
Mathematics · Binomial Theorem · MCQ
Q30.Let $f (x) = \frac{2 ^{x + 2} + 16}{2 ^{2 x + 1} + 2 ^{x + 4} + 32}$ . Then the value of $8 (f (\frac{1}{15}) + f (\frac{2}{15}) + \dots + f (\frac{59}{15}))$ is equal to
Mathematics · Functions · MCQ
Q31.If $I (m, n) = \int_{0}^{1} x^{m - 1} (1 - x)^{n - 1} d x, m, n > 0$ , then $I (9, 14) + I (10, 13)$ is
Mathematics · Definite Integration · MCQ
Q32.If $α$ and $β$ are the roots of the equation $2 z^{2} - 3 z - 2 i = 0$ , where $i = - 1$ , then $16 \cdot Re (\frac{α ^{19} + β ^{19} + α ^{11} + β ^{11}}{α ^{15} + β ^{15}}) \cdot lm (\frac{α ^{19} + β ^{19} + α ^{11} + β ^{11}}{α ^{15} + β ^{15}})$ …
Mathematics · Complex Numbers · MCQ
Q33.Let the product of the focal distances of the point $(3, \frac{1}{2})$ on the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, (a > b)$ , be $\frac{7}{4}$ . Then the absolute difference of the eccentricities of two such ellipses…
Mathematics · Ellipse · MCQ
Q34.Let $y = y (x)$ be the solution of the differential equation $(x y - 5 x^{2} 1 + x^{2}) d x + (1 + x^{2}) d y = 0, y (0) = 0$ . Then $y (3)$ is equal to
Mathematics · Differential Equations · MCQ
Q35.Let in a $△ A B C$ , the length of the side $A C$ be 6 , the vertex $B$ be $(1, 2, 3)$ and the vertices $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ lie on the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ . Then the area (in sq. units) of $△ A B C$ is:
Mathematics · 3D Geometry · MCQ
Q36.Let the line passing through the points $(- 1, 2, 1)$ and parallel to the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z}{4}$ intersect the line $\frac{x + 2}{3} = \frac{y - 3}{2} = \frac{z - 4}{1}$ at the point $P$ . Then the distance of $P$ from the point $Q (4, - 5, 1)$ …
Mathematics · 3D Geometry · MCQ
Q37. $A$ and $B$ alternately throw a pair of dice. A wins if he throws a sum of 5 before $B$ throws a sum of 8 , and $B$ wins if he throws a sum of 8 before $A$ throws a sum of 5 . The probability, that A wins if A makes the first throw, is
Mathematics · Probability · MCQ
Q38.Let $a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = 3 \hat{i} + \hat{j} - \hat{k}$ and $c$ be three vectors such that $c$ is coplanar with $a$ and $b$ . If the vector $C$ is perpendicular to $b$ and $a \cdot c = 5$ …
Mathematics · Vector Algebra · MCQ
Q39.Consider the region $R = {(x, y) : x \leq y \leq 9 - \frac{11}{3} x^{2}, x \geq 0}$ . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:
Mathematics · Application of Derivatives · MCQ
Q40.The area of the region ${(x, y) : x^{2} + 4 x + 2 \leq y \leq ∣ x + 2∣}$ is equal to
Mathematics · Area Under the Curves · MCQ
Q41.Let $S_{n} = \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \dots$ upto $n$ terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is $2026 S_{2025}$ , then the absolute difference…
Mathematics · Sequences and Series · MCQ
Q42.For a statistical data $x_{1}, x_{2}, \dots, x_{10}$ of 10 values, a student obtained the mean as 5.5 and $\sum_{i = 1}^{10} x_{i}^{2} = 371$ . He later found that he had noted two values in the data incorrectly as 4 and 5 ,…
Mathematics · Statistics · MCQ
Q43.Let the lines $3 x - 4 y - α = 0, 8 x - 11 y - 33 = 0$ , and $2 x - 3 y + λ = 0$ be concurrent. If the image of the point $(1, 2)$ in the line $2 x - 3 y + λ = 0$ is $(\frac{57}{13}, \frac{- 40}{13})$ , then $∣ α λ ∣$ is equal to
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q44.If the system of equations $2 x - y + z = 4 5 x + λ y + 3 z = 12 100 x - 47 y + μ z = 212$ has infinitely many solutions, then $μ - 2 λ$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q45.Let circle $C$ be the image of $x^{2} + y^{2} - 2 x + 4 y - 4 = 0$ in the line $2 x - 3 y + 5 = 0$ and $A$ be the point on $C$ such that $O A$ is parallel to $x$ -axis and $A$ lies on the right hand side of the centre $O$ of $C$ . If $B (α, β)$ , with $β < 4$ …
Mathematics · Circle · MCQ
Q46.Let A be a $3 \times 3$ matrix such that $X^{T} AX = O$ for all nonzero $3 \times 1$ matrices $X = x y z$ . If $A 111 = 14 - 5, A 121 = 04 - 8$ …
Mathematics · Matrices and Determinants · Numerical
Q47.Let $f$ be a differentiable function such that $2 (x + 2)^{2} f (x) - 3 (x + 2)^{2} = 10 \int_{0}^{x} (t + 2) f (t) d t, x \geq 0$ . Then $f (2)$ is equal to .
Mathematics · Differential Equations · Numerical
Q48.Let $S = {p_{1}, p_{2} \dots, p_{10}}$ be the set of first ten prime numbers. Let $A = S \cup P$ , where $P$ is the set of all possible products of distinct elements of $S$ . Then the number of all ordered pairs $(x, y), x \in S$ , $y \in A$ …
Mathematics · Sets and Relations · Numerical
Q49.If for some $α, β; α \leq β, α + β = 8$ and $sec^{2} (tan^{- 1} α) + cosec^{2} (cot^{- 1} β) = 36$ , then $α^{2} + β$ is
Mathematics · Inverse Trigonometric Functions · Numerical
Q50.The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is .
Mathematics · Permutations and Combinations · Numerical