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Mathematics · 2025 · 28 Jan · Shift 1

25 questions from this JEE Main paper

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2025 · 28 Jan · Shift 1
Mathematics

Mathematics · 2025 · 28 Jan · Shift 1

25 questions from this JEE Main paper

3D Geometry2 questions Functions2 questions Quadratic Equation and Inequalities1 questions Sets and Relations1 questions Sequences and Series2 questions Inverse Trigonometric Functions1 questions Definite Integration1 questions Permutations and Combinations2 questions Probability2 questions Parabola1 questions Differential Equations1 questions Application of Derivatives1 questions Circle1 questions Complex Numbers1 questions Area Under the Curves1 questions Matrices and Determinants1 questions Limits Continuity and Differentiability1 questions Binomial Theorem1 questions Ellipse1 questions Vector Algebra1 questions

Q26.Let $A (x, y, z)$ be a point in $x y$ -plane, which is equidistant from three points $(0, 3, 2), (2, 0, 3)$ and $(0, 0, 1)$ . Let $B = (1, 4, - 1)$ and $C = (2, 0, - 2)$ . Then among the statements (S1) : $△ ABC$ is…
Mathematics · 3D Geometry · MCQ
Q27.If $f (x) = \frac{2 ^{x}}{2 ^{x} + 2}, x \in R$ , then $\sum_{k = 1}^{81} f (\frac{k}{82})$ is equal to
Mathematics · Functions · MCQ
Q28.The sum, of the squares of all the roots of the equation $x^{2} + ∣2 x - 3∣ - 4 = 0$ , is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q29.The relation $R = {(x, y) : x, y \in Z$ and $x + y$ is even $}$ is:
Mathematics · Sets and Relations · MCQ
Q30.Let $⟨ a_{n} ⟩$ be a sequence such that $a_{0} = 0, a_{1} = \frac{1}{2}$ and $2 a_{n + 2} = 5 a_{n + 1} - 3 a_{n}, n = 0, 1, 2, 3, \dots$ . Then $k = 1 \sum 100 a_{k}$ is equal to
Mathematics · Sequences and Series · MCQ
Q31. $cos (sin^{- 1} \frac{3}{5} + sin^{- 1} \frac{5}{13} + sin^{- 1} \frac{33}{65})$ is equal to:
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.If $\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{96 x ^{2} c o s ^{2} x}{( 1 + e ^{x} )} d x = π (α π^{2} + β), α, β \in Z$ , then $(α + β)^{2}$ equals
Mathematics · Definite Integration · MCQ
Q33.Let $T_{r}$ be the $r^{th}$ term of an A.P. If for some $m, T_{m} = \frac{1}{25}, T_{25} = \frac{1}{20}$ , and $20 r = 1 \sum 25 T_{r} = 13$ …
Mathematics · Sequences and Series · MCQ
Q34.Let $^{n} C_{r - 1} = 28,^{n} C_{r} = 56$ and $^{n} C_{r + 1} = 70$ . Let $A (4 cost, 4 sin t), B (2 sin t, - 2 cos t)$ and $C (3 r - n, r^{2} - n - 1)$ be the vertices of a triangle $A B C$ , where $t$ is a parameter. If $(3 x - 1)^{2} + (3 y)^{2} = α$ …
Mathematics · Permutations and Combinations · MCQ
Q35.Two number $k_{1}$ and $k_{2}$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_{1}} + i^{k_{2}}, (i = - 1)$ is non-zero, equals
Mathematics · Probability · MCQ
Q36.Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denote the number of defective oranges, then…
Mathematics · Probability · MCQ
Q37.Let ABCD be a trapezium whose vertices lie on the parabola $y^{2} = 4 x$ . Let the sides AD and BC of the trapezium be parallel to $y$ -axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point…
Mathematics · Parabola · MCQ
Q38.If the image of the point $(4, 4, 3)$ in the line $\frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 1}{3}$ is $(α, β, γ)$ , then $α + β + γ$ is equal to
Mathematics · 3D Geometry · MCQ
Q39.Let for some function $y = f (x), \int_{0}^{x} t f (t) d t = x^{2} f (x), x > 0$ and $f (2) = 3$ . Then $f (6)$ is equal to
Mathematics · Differential Equations · MCQ
Q40.The sum of all local minimum values of the function $f (x) = {1 - 2 x, x 2$ is
Mathematics · Application of Derivatives · MCQ
Q41.The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0 , $1, 2, 3, 4, 5, 6, 7$ , such that the sum of their first and last digits should not be more than 8 , is
Mathematics · Permutations and Combinations · MCQ
Q42.Let the equation of the circle, which touches $x$ -axis at the point $(a, 0), a > 0$ and cuts off an intercept of length $b$ on $y - a x i s$ be $x^{2} + y^{2} - α x + β y + γ = 0$ . If the circle lies below $x - a x i s$ , then the ordered pair…
Mathematics · Circle · MCQ
Q43.Let $f : R \to R$ be a function defined by $f (x) = (2 + 3 a) x^{2} + (\frac{a + 2}{a - 1}) x + b, a e q 1$ . If $f (x + y) = f (x) + f (y) + 1 - \frac{2}{7} x y$ , then the value of $28 i = 1 \sum 5 ∣ f (i) ∣$ is
Mathematics · Functions · MCQ
Q44.Let $O$ be the origin, the point $A$ be $z_{1} = 3 + 22 i$ , the point $B (z_{2})$ be such that $3 ∣ z_{2} ∣ = ∣ z_{1} ∣$ and $ar g (z_{2}) = ar g (z_{1}) + \frac{π}{6}$ . Then
Mathematics · Complex Numbers · MCQ
Q45.The area (in sq. units) of the region ${(x, y) : 0 \leq y \leq 2∣ x ∣ + 1, 0 \leq y \leq x^{2} + 1, ∣ x ∣ \leq 3}$ is
Mathematics · Area Under the Curves · MCQ
Q46.Let M denote the set of all real matrices of order $3 \times 3$ and let $S = {- 3, - 2, - 1, 1, 2}$ . Let $S_{1} = {A = [a_{ij}] \in M : A = A^{T} and a_{ij} \in S, \forall i, j}, S_{2} = {A = [a_{ij}] \in M : A = - A^{T} and a_{ij} \in S, \forall i, j}, S_{3} = {A = [a_{ij}] \in M : a_{11} + a_{22} + a_{33} = 0 and a_{ij} \in S, \forall i, j} .$ …
Mathematics · Matrices and Determinants · Numerical
Q47.Let $f (x) = {3 x, x 2$ where [.] denotes greatest integer function. If $α$ and $β$ are the number of points, where $f$ is not continuous and is not differentiable, respectively,…
Mathematics · Limits Continuity and Differentiability · Numerical
Q48.If $α = 1 + r = 1 \sum 6 (- 3)^{r - 1}^{12} C_{2 r - 1}$ , then the distance of the point $(12, 3)$ from the line $α x - 3 y + 1 = 0$ is .
Mathematics · Binomial Theorem · Numerical
Q49.Let $E_{1} : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ be an ellipse. Ellipses $E_{i}$ 's are constructed such that their centres and eccentricities are same as that of $E_{1}$ , and the length of minor axis of $E_{i}$ …
Mathematics · Ellipse · Numerical
Q50.Let $a = \hat{i} + \hat{j} + \hat{k}, b = 2 \hat{i} + 2 \hat{j} + \hat{k}$ and $d = a \times b$ . If $c$ …
Mathematics · Vector Algebra · Numerical