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Mathematics · 2024 · 4 Apr · Shift 2

30 questions from this JEE Main paper

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2024 · 4 Apr · Shift 2
Mathematics

Mathematics · 2024 · 4 Apr · Shift 2

30 questions from this JEE Main paper

Hyperbola1 questions Binomial Theorem1 questions Sequences and Series2 questions Limits Continuity and Differentiability1 questions 3D Geometry2 questions Application of Derivatives1 questions Definite Integration2 questions Area Under the Curves1 questions Inverse Trigonometric Functions1 questions Vector Algebra2 questions Differential Equations2 questions Probability2 questions Parabola1 questions Circle1 questions Complex Numbers1 questions Sets and Relations1 questions Matrices and Determinants2 questions Trigonometric Functions and Equations1 questions Indefinite Integrals1 questions Properties of Triangle1 questions Functions1 questions Differentiation1 questions Permutations and Combinations1 questions

Q31.Consider a hyperbola $H$ having centre at the origin and foci on the $x$ -axis. Let $C_{1}$ be the circle touching the hyperbola $H$ and having the centre at the origin. Let $C_{2}$ be the circle…
Mathematics · Hyperbola · MCQ
Q32.If the coefficients of $x^{4}, x^{5}$ and $x^{6}$ in the expansion of $(1 + x)^{n}$ are in the arithmetic progression, then the maximum value of $n$ is:
Mathematics · Binomial Theorem · MCQ
Q33.The value of $\frac{1 \times 2 ^{2} + 2 \times 3 ^{2} + \dots + 100 \times ( 101 ) ^{2}}{1 ^{2} \times 2 + 2 ^{2} \times 3 + \dots . + 10 0 ^{2} \times 101}$ is
Mathematics · Sequences and Series · MCQ
Q34.If the function $f (x) = {\frac{7 2 ^{x} - 9 ^{x} - 8 ^{x} + 1}{2 - 1 + c o s x}, a lo g_{e} 2 lo g_{e} 3 x e q 0, x = 0$ is continuous at $x = 0$ , then the value of $a^{2}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Let $P$ be the point of intersection of the lines $\frac{x - 2}{1} = \frac{y - 4}{5} = \frac{z - 2}{1}$ and $\frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 3}{2}$ . Then, the shortest distance of $P$ from the line $4 x = 2 y = z$ is
Mathematics · 3D Geometry · MCQ
Q36.Let $f (x) = 3 x - 2 + 4 - x$ be a real valued function. If $α$ and $β$ are respectively the minimum and the maximum values of $f$ , then $α^{2} + 2 β^{2}$ is equal to
Mathematics · Application of Derivatives · MCQ
Q37.Let $f (x) = \int_{0}^{x} (t + sin (1 - e^{t})) d t, x \in R$ . Then, $lim_{x \to 0} \frac{f ( x )}{x ^{3}}$ is equal to
Mathematics · Definite Integration · MCQ
Q38.The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x, and y \geq 4 x - 1}$ is
Mathematics · Area Under the Curves · MCQ
Q39.Given that the inverse trigonometric function assumes principal values only. Let $[- 1, 1]$ be any two real numbers in $[- 1, 1]$ such that $cos^{- 1} x - sin^{- 1} y = α, \frac{- π}{2} \leq α \leq π$ . Then, the minimum value of $x^{2} + y^{2} + 2 x y sin α$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q40.For $λ > 0$ , let $θ$ be the angle between the vectors $a = \hat{i} + λ \hat{j} - 3 \hat{k}$ and $b = 3 \hat{i} - \hat{j} + 2 \hat{k}$ . If the vectors $a + b$ and $a - b$ are mutually perpendicular,…
Mathematics · Vector Algebra · MCQ
Q41.Let $y = y (x)$ be the solution of the differential equation $(x^{2} + 4)^{2} d y + (2 x^{3} y + 8 x y - 2) d x = 0$ . If $y (0) = 0$ , then $y (2)$ is equal to
Mathematics · Differential Equations · MCQ
Q42.If the mean of the following probability distribution of a radam variable $X$ : is $\frac{46}{9}$ , then the variance of the distribution is Includes table
Mathematics · Probability · MCQ
Q43.Let $P Q$ be a chord of the parabola $y^{2} = 12 x$ and the midpoint of $P Q$ be at $(4, 1)$ . Then, which of the following point lies on the line passing through the points $P$ and $Q$ ?
Mathematics · Parabola · MCQ
Q44.Let $C$ be a circle with radius $10$ units and centre at the origin. Let the line $x + y = 2$ intersects the circle $C$ at the points $P$ and $Q$ . Let $MN$ be a chord of $C$ of…
Mathematics · Circle · MCQ
Q45.The area (in sq. units) of the region $S = {z \in C : ∣ z - 1∣ \leq 2; (z + \overset{z}{ˉ}) + i (z - \overset{z}{ˉ}) \leq 2, lm (z) \geq 0}$ is
Mathematics · Complex Numbers · MCQ
Q46.If the value of the integral $- 1 \int 1 \frac{c o s α x}{1 + 3 ^{x}} d x$ is $\frac{2}{π}$ .Then, a value of $α$ is
Mathematics · Definite Integration · MCQ
Q47.Let three real numbers $a, b, c$ be in arithmetic progression and $a + 1, b, c + 3$ be in geometric progression. If $a > 10$ and the arithmetic mean of $c$ and $c$ is 8, then the cube of the geometric mean of $c$ and $c$ is
Mathematics · Sequences and Series · MCQ
Q48.Let a relation $R$ on $N \times N$ be defined as: $(x_{1}, y_{1}) R (x_{2}, y_{2})$ if and only if $x_{1} \leq x_{2}$ or $y_{1} \leq y_{2}$ . Consider the two statements: (I) $R$ is…
Mathematics · Sets and Relations · MCQ
Q49.Let $A = [1021]$ and $B = I + adj (A) + (adj A)^{2} + \dots + (adj A)^{10}$ . Then, the sum of all the elements of the matrix $B$ is:
Mathematics · Matrices and Determinants · MCQ
Q50.Let $a = \hat{i} + \hat{j} + \hat{k}, b = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $c = x \hat{i} + 2 \hat{j} + 3 \hat{k}, x \in R$ . If $d$ is the unit vector in the direction of $b + c$ such that $a \cdot d = 1$ …
Mathematics · Vector Algebra · MCQ
Q51.Let $S = {sin^{2} 2 θ : (sin^{4} θ + cos^{4} θ) x^{2} + (sin 2 θ) x + (sin^{6} θ + cos^{6} θ) = 0$ has real roots $}$ . If $α$ and $β$ be the smallest and largest elements of the…
Mathematics · Trigonometric Functions and Equations · Numerical
Q52.If $\int cosec^{5} x d x = α cot x cosec x (cosec^{2} x + \frac{3}{2}) + β lo g_{x} tan \frac{x}{2} + C$ where $α, β \in R$ and $C$ is…
Mathematics · Indefinite Integrals · Numerical
Q53.Let $A$ be a $2 \times 2$ symmetric matrix such that $A [11] = [37]$ and the determinant of $A$ be 1 . If $A^{- 1} = α A + β I$ , where $I$ is an…
Mathematics · Matrices and Determinants · Numerical
Q54.Consider a triangle $ABC$ having the vertices $A (1, 2), B (α, β)$ and $C (γ, δ)$ and angles $∠ A B C = \frac{π}{6}$ and $∠ B A C = \frac{2 π}{3}$ . If the points $B$ and…
Mathematics · Properties of Triangle · Numerical
Q55.In a tournament, a team plays 10 matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$ respectively. Let $x$ be the number of matches that the team wins, and $y$ be the number of matches that team…
Mathematics · Probability · Numerical
Q56.Consider the function $f : R \to R$ defined by $f (x) = \frac{2 x}{1 + 9 x ^{2}}$ . If the composition of $f, 10 times (f \circ f \circ f \circ \dots \circ f) (x) = \frac{2 ^{10} x}{1 + 9 α x ^{2}}$ …
Mathematics · Functions · Numerical
Q57.Let $y = y (x)$ be the solution of the differential equation $(x + y + 2)^{2} d x = d y, y (0) = - 2$ . Let the maximum and minimum values of the function $y = y (x)$ in $[0, \frac{π}{3}]$ be $α$ and $β$ , respectively. If $(3 α + π)^{2} + β^{2} = γ + δ 3, γ, δ \in Z$ …
Mathematics · Differential Equations · Numerical
Q58.Let $f : R \to R$ be a thrice differentiable function such that $f (0) = 0, f (1) = 1, f (2) = - 1, f (3) = 2$ and $f (4) = - 2$ . Then, the minimum number of zeros of $(3 f^{'} f^{''} + f f^{'''}) (x)$ …
Mathematics · Differentiation · Numerical
Q59.Consider a line $L$ passing through the points $P (1, 2, 1)$ and $Q (2, 1, - 1)$ . If the mirror image of the point $A (2, 2, 2)$ in the line $L$ is $(α, β, γ)$ , then $α + β + 6 γ$ …
Mathematics · 3D Geometry · Numerical
Q60.There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .
Mathematics · Permutations and Combinations · Numerical