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Mathematics · 2025 · 3 Apr · Shift 2

25 questions from this JEE Main paper

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2025 · 3 Apr · Shift 2
Mathematics

Mathematics · 2025 · 3 Apr · Shift 2

25 questions from this JEE Main paper

Area Under the Curves1 questions Permutations and Combinations1 questions 3D Geometry2 questions Complex Numbers1 questions Ellipse1 questions Application of Derivatives2 questions Straight Lines and Pair of Straight Lines1 questions Differential Equations1 questions Functions2 questions Quadratic Equation and Inequalities1 questions Sets and Relations1 questions Statistics1 questions Definite Integration1 questions Probability1 questions Trigonometric Functions and Equations1 questions Sequences and Series1 questions Circle1 questions Limits Continuity and Differentiability1 questions Hyperbola1 questions Binomial Theorem1 questions Vector Algebra1 questions Matrices and Determinants1 questions

Q26.The area of the region ${(x, y) : ∣ x - y ∣ \leq y \leq 4 x}$ is
Mathematics · Area Under the Curves · MCQ
Q27.Line $L_{1}$ of slope 2 and line $L_{2}$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, $P_{1}$ , $P_{2}, \dots, P_{12}$ are 12 points on line $L_{1}$ and $Q_{1}, Q_{2}, \dots, Q_{9}$ are 9 points on line $L_{2}$ . Then…
Mathematics · Permutations and Combinations · MCQ
Q28.Each of the angles $β$ and $γ$ that a given line makes with the positive $y$ - and $z$ -axes, respectively, is half of the angle that this line makes with the positive $x$ -axes. Then the sum of all possible values of the angle $β$ …
Mathematics · 3D Geometry · MCQ
Q29.If $z_{1}, z_{2}, z_{3} \in C$ are the vertices of an equilateral triangle, whose centroid is $z_{0}$ , then $k = 1 \sum 3 (z_{k} - z_{0})^{2}$ is equal to
Mathematics · Complex Numbers · MCQ
Q30.Let $C$ be the circle of minimum area enclosing the ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ with eccentricity $\frac{1}{2}$ and foci $(\pm 2, 0)$ . Let $P QR$ be a variable triangle, whose vertex $P$ is on the circle $C$ and the…
Mathematics · Ellipse · MCQ
Q31.The shortest distance between the curves $y^{2} = 8 x$ and $x^{2} + y^{2} + 12 y + 35 = 0$ is:
Mathematics · Application of Derivatives · MCQ
Q32.Consider the lines $x (3 λ + 1) + y (7 λ + 2) = 17 λ + 5, λ$ being a parameter, all passing through a point P. One of these lines (say $L$ ) is farthest from the origin. If the distance of $L$ from the point $(3, 6)$ is $d$ , then…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + 3 (tan^{2} x) y + 3 y = sec^{2} x, y (0) = \frac{1}{3} + e^{3}$ . Then $y (\frac{π}{4})$ is equal to :
Mathematics · Differential Equations · MCQ
Q34.Let $f$ be a function such that $f (x) + 3 f (\frac{24}{x}) = 4 x, x e q 0$ . Then $f (3) + f (8)$ is equal to
Mathematics · Functions · MCQ
Q35.Let the equation $x (x + 2) (12 - k) = 2$ have equal roots. Then the distance of the point $(k, \frac{k}{2})$ from the line $3 x + 4 y + 5 = 0$ is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q36.Let $A = {- 2, - 1, 0, 1, 2, 3}$ . Let R be a relation on $A$ defined by $x R y$ if and only if $y = max {x, 1}$ . Let $l$ be the number of elements in R . Let $m$ and $n$ be the minimum number of elements required to be added in R to…
Mathematics · Sets and Relations · MCQ
Q37.Let the Mean and Variance of five observations $x_{1} = 1, x_{2} = 3, x_{3} = a, x_{4} = 7$ and $x_{5} = b, a > b$ , be 5 and 10 respectively. Then the Variance of the observations $n + x_{n}, n = 1, 2, \dots, 5$ is
Mathematics · Statistics · MCQ
Q38.The integral $\int_{0}^{π} \frac{8 x d x}{4 c o s ^{2} x + s i n ^{2} x}$ is equal to
Mathematics · Definite Integration · MCQ
Q39.The distance of the point $(7, 10, 11)$ from the line $\frac{x - 4}{1} = \frac{y - 4}{0} = \frac{z - 2}{3}$ along the line $\frac{x - 9}{2} = \frac{y - 13}{3} = \frac{z - 17}{6}$ is
Mathematics · 3D Geometry · MCQ
Q40.If the probability that the random variable $X$ takes the value $x$ is given by $P (X = x) = k (x + 1) 3^{- x}, x = 0, 1, 2, 3 \dots$ , where $k$ is a constant, then $P (X \geq 3)$ is equal to
Mathematics · Probability · MCQ
Q41.The number of solutions of the equation $(4 - 3) sin x - 23 cos^{2} x = - \frac{4}{1 + 3}, x \in [- 2 π, \frac{5 π}{2}]$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q42.If the domain of the function $f (x) = lo g_{7} (1 - lo g_{4} (x^{2} - 9 x + 18))$ is $(α, β) \cup (γ, o)$ , then $α + β + γ + \overset{o}{^}$ is equal to
Mathematics · Functions · MCQ
Q43.Let $f : R \to R$ be a function defined by $f (x) = ∣∣ x + 2∣ - 2∣ x ∥$ . If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$ , then $m + n$ is
Mathematics · Application of Derivatives · MCQ
Q44.The sum $1 + \frac{1 + 3}{2 !} + \frac{1 + 3 + 5}{3 !} + \frac{1 + 3 + 5 + 7}{4 !} + \dots$ upto $\infty$ terms, is equal to
Mathematics · Sequences and Series · MCQ
Q45.If the four distinct points $(4, 6), (- 1, 5), (0, 0)$ and $(k, 3 k)$ lie on a circle of radius $r$ , then $10 k + r^{2}$ is equal to
Mathematics · Circle · MCQ
Q46.If $x \to 0 lim (\frac{t a n x}{x})^{\frac{1}{x ^{2}}} = p$ , then $96 lo g_{e} p$ is equal to
Mathematics · Limits Continuity and Differentiability · Numerical
Q47.If the equation of the hyperbola with foci $(4, 2)$ and $(8, 2)$ is $3 x^{2} - y^{2} - α x + β y + γ = 0$ , then $α + β + γ$ is equal to .
Mathematics · Hyperbola · Numerical
Q48.Let $(1 + x + x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{20} x^{20}$ . If $(a_{1} + a_{3} + a_{5} + \dots + a_{19}) - 11 a_{2} = 121 k$ , then $k$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q49.Let $a = \hat{i} + 2 \hat{j} + \hat{k}, b = 3 \hat{i} - 3 \hat{j} + 3 \hat{k}, c = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $d$ be a vector such that $b \times d = c \times d$ and $a \cdot d = 4$ . Then $∣ (a \times d) ∣^{2}$ …
Mathematics · Vector Algebra · Numerical
Q50.Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A = λ 47 25 - 1 362, ∣ A ∣ = - 1$ . Let $B$ be the inverse of the matrix $adj (Aadj (A^{2}))$ …
Mathematics · Matrices and Determinants · Numerical