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Mathematics · 2025 · 22 Jan · Shift 1

25 questions from this JEE Main paper

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2025 · 22 Jan · Shift 1
Mathematics

Mathematics · 2025 · 22 Jan · Shift 1

25 questions from this JEE Main paper

Area Under the Curves1 questions Hyperbola1 questions Complex Numbers1 questions 3D Geometry2 questions Sets and Relations2 questions Straight Lines and Pair of Straight Lines1 questions Logarithm1 questions Permutations and Combinations1 questions Circle1 questions Differential Equations3 questions Probability2 questions Sequences and Series1 questions Definite Integration1 questions Parabola1 questions Inverse Trigonometric Functions1 questions Limits Continuity and Differentiability2 questions Vector Algebra1 questions Binomial Theorem1 questions Matrices and Determinants1 questions

Q25.The area of the region, inside the circle $(x - 23)^{2} + y^{2} = 12$ and outside the parabola $y^{2} = 23 x$ is :
Mathematics · Area Under the Curves · MCQ
Q26.Let the foci of a hyperbola be $(1, 14)$ and $(1, - 12)$ . If it passes through the point $(1, 6)$ , then the length of its latus-rectum is :
Mathematics · Hyperbola · MCQ
Q27.Let $z_{1}, z_{2}$ and $z_{3}$ be three complex numbers on the circle $∣ z ∣ = 1$ with $ar g (z_{1}) = \frac{- π}{4}, ar g (z_{2}) = 0$ and $ar g (z_{3}) = \frac{π}{4}$ . If $∣ z_{1} \overset{z}{ˉ}_{2} + z_{2} \overset{z}{ˉ}_{3} + z_{3} \overset{z}{ˉ}_{1} ∣^{2} = α + β 2, α, β \in Z$ …
Mathematics · Complex Numbers · MCQ
Q28.Let $L_{1} : \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $L_{2} : \frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_{1}$ …
Mathematics · 3D Geometry · MCQ
Q29.Let $A = {1, 2, 3, \dots, 10}$ and $B = {\frac{m}{n} : m, n \in A, m < n$ and $gcd (m, n) = 1}$ . Then $n (B)$ is equal to :
Mathematics · Sets and Relations · MCQ
Q30.Let the triangle PQR be the image of the triangle with vertices $(1, 3), (3, 1)$ and $(2, 4)$ in the line $x + 2 y = 2$ . If the centroid of $△ PQR$ is the point $(α, β)$ , then $15 (α - β)$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.The product of all solutions of the equation $e^{5 (l o g_{e} x)^{2} + 3} = x^{8}, x > 0$ , is :
Mathematics · Logarithm · MCQ
Q32.From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :
Mathematics · Permutations and Combinations · MCQ
Q33.A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point $(2, 5)$ and intersects the circle $C$ at exactly two points. If the set of all possible…
Mathematics · Circle · MCQ
Q34.Let $x = x (y)$ be the solution of the differential equation $y^{2} d x + (x - \frac{1}{y}) d y = 0$ . If $x (1) = 1$ , then $x (\frac{1}{2})$ is :
Mathematics · Differential Equations · MCQ
Q35.A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $μ$ and $σ^{2}$ denote the mean and variance of $X$ , then the value of $64 (μ + σ^{2})$ is:
Mathematics · Probability · MCQ
Q36.Let $f (x)$ be a real differentiable function such that $f (0) = 1$ and $f (x + y) = f (x) f^{'} (y) + f^{'} (x) f (y)$ for all $x, y \in R$ . Then $\sum_{n = 1}^{100} lo g_{e} f (n)$ is equal to :
Mathematics · Differential Equations · MCQ
Q37.Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{m}{n}$ ,…
Mathematics · Probability · MCQ
Q38.Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive terms. If $a_{1} a_{5} = 28$ and $a_{2} + a_{4} = 29$ , then $a_{6}$ is equal to:
Mathematics · Sequences and Series · MCQ
Q39.Let for $f (x) = 7 tan^{8} x + 7 tan^{6} x - 3 tan^{4} x - 3 tan^{2} x, I_{1} = \int_{0}^{π /4} f (x) d x$ and $I_{2} = \int_{0}^{π /4} x f (x) d x$ . Then $7 I_{1} + 12 I_{2}$ is equal to :
Mathematics · Definite Integration · MCQ
Q40.The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :
Mathematics · Sets and Relations · MCQ
Q41.Let the parabola $y = x^{2} + p x - 3$ , meet the coordinate axes at the points $(- 1, - 1)$ and R . If the circle C with centre at $(- 1, - 1)$ passes through the points $R$ and $R$ , then the area of $△ P QR$ is :
Mathematics · Parabola · MCQ
Q42.Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of $16 ((sec^{- 1} x)^{2} + (cosec^{- 1} x)^{2})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q43.Let $f : R \to R$ be a twice differentiable function such that $f (x + y) = f (x) f (y)$ for all $x, y \in R$ . If $f^{'} (0) = 4 a$ and $f$ satisfies $f^{''} (x) - 3 a f^{'} (x) - f (x) = 0, a > 0$ …
Mathematics · Differential Equations · MCQ
Q44.If $\sum_{r = 1}^{n} T_{r} = \frac{( 2 n - 1 ) ( 2 n + 1 ) ( 2 n + 3 ) ( 2 n + 5 )}{64}$ , then $lim_{n \to \infty} \sum_{r = 1}^{n} (\frac{1}{T _{r}})$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q45.Let the function, $f (x) = {- 3 ax^{2} - 2, a^{2} + b x, x < 1 x ⩾ 1$ be differentiable for all $x \in R$ , where $a > 1, b \in R$ . If…
Mathematics · Limits Continuity and Differentiability · Numerical
Q46.Let $c$ be the projection vector of $b = λ \hat{i} + 4 \hat{k}, λ > 0$ , on the vector $a = \hat{i} + 2 \hat{j} + 2 \hat{k}$ . If $∣ a + c ∣ = 7$ , then the area of the parallelogram formed by the vectors $b$ …
Mathematics · Vector Algebra · Numerical
Q47.If $\sum_{r = 0}^{5} \frac{^{11} C _{2 r + 1}}{2 r + 2} = \frac{m}{n}, gcd (m, n) = 1$ , then $m - n$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q48.Let $L_{1} : \frac{x - 1}{3} = \frac{y - 1}{- 1} = \frac{z + 1}{0}$ and $L_{2} : \frac{x - 2}{2} = \frac{y}{0} = \frac{z + 4}{α}, α \in R$ , be two lines, which intersect at the point $B$ . If $P$ is the foot of perpendicular…
Mathematics · 3D Geometry · Numerical
Q49.Let $A$ be a square matrix of order 3 such that $det (A) = - 2$ and $det (3 adj (- 6 adj (3 A))) = 2^{m + n} \cdot 3^{mn}, m > n$ . Then $4 m + 2 n$ is equal to .
Mathematics · Matrices and Determinants · Numerical