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Mathematics · 2024 · 9 Apr · Shift 2

30 questions from this JEE Main paper

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2024 · 9 Apr · Shift 2
Mathematics

Mathematics · 2024 · 9 Apr · Shift 2

30 questions from this JEE Main paper

Hyperbola1 questions Complex Numbers1 questions Functions2 questions Differential Equations2 questions Properties of Triangle1 questions Definite Integration3 questions Quadratic Equation and Inequalities1 questions Differentiation1 questions Probability1 questions Vector Algebra2 questions Statistics1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability1 questions 3D Geometry2 questions Area Under the Curves1 questions Sequences and Series2 questions Binomial Theorem1 questions Parabola2 questions Application of Derivatives1 questions Permutations and Combinations1 questions Inverse Trigonometric Functions1 questions

Q31.Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E : \frac{( x - 1 ) ^{2}}{100} + \frac{( y - 1 ) ^{2}}{75} = 1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$ . If the length of the…
Mathematics · Hyperbola · MCQ
Q32.Let $z$ be a complex number such that the real part of $\frac{z - 2 i}{z + 2 i}$ is zero. Then, the maximum value of $∣ z - (6 + 8 i) ∣$ is equal to
Mathematics · Complex Numbers · MCQ
Q33.Let the range of the function $f (x) = \frac{1}{2 + s i n 3 x + c o s 3 x}, x \in R$ be $[a, b]$ . If $α$ and $β$ ar respectively the A.M. and the G.M. of $a$ and $b$ , then $\frac{α}{β}$ is equal to
Mathematics · Functions · MCQ
Q34.Let $0 \int x 1 - (y^{'} (t))^{2} d t = \int_{0}^{x} y (t) d t, 0 \leq x \leq 3, y \geq 0, y (0) = 0$ . Then at $x = 2, y^{''} + y + 1$ is equal to
Mathematics · Differential Equations · MCQ
Q35.Two vertices of a triangle $ABC$ are $A (3, - 1)$ and $B (- 2, 3)$ , and its orthocentre is $P (1, 1)$ . If the coordinates of the point $C$ are $(α, β)$ and the centre of the of the circle…
Mathematics · Properties of Triangle · MCQ
Q36.The integral $\int_{1/4}^{3/4} cos (2 cot^{- 1} \frac{1 - x}{1 + x}) d x$ is equal to
Mathematics · Definite Integration · MCQ
Q37.Let $α, β; α > β$ , be the roots of the equation $x^{2} - 2 x - 3 = 0$ . Let $P_{n} = α^{n} - β^{n}, n \in N$ . Then $(113 - 102) P_{10} + (112 + 10) P_{11} - 11 P_{12}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.If $lo g_{e} y = 3 sin^{- 1} x$ , then $(1 - x^{2}) y^{''} - x y^{'}$ at $x = \frac{1}{2}$ is equal to
Mathematics · Differentiation · MCQ
Q39.If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{th}$ roll than the number obtained in the $(i - 1)^{th}$ roll, $i = 2, 3$ , is equal to
Mathematics · Probability · MCQ
Q40. $lim_{x \to \frac{π}{2}} (\frac{\int _{x^{3}}^{(π /2)^{3}} ( s i n ( 2 t ^{1/3} ) + c o s ( t ^{1/3} ) ) d t}{( x - \frac{π}{2} ) ^{2}})$ is equal to
Mathematics · Definite Integration · MCQ
Q41.The value of the integral $\int_{- 1}^{2} lo g_{e} (x + x^{2} + 1) d x$ is
Mathematics · Definite Integration · MCQ
Q42.Between the following two statements: Statement I : Let $a = \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $b = 2 \hat{i} + \hat{j} - \hat{k}$ . Then the vector $r$ satisfying $a \times r = a \times b$ and $a \cdot r = 0$ …
Mathematics · Vector Algebra · MCQ
Q43.If the variance of the frequency distribution is 160, then the value of $c \in N$ is Includes table
Mathematics · Statistics · MCQ
Q44.Let $B = [1135]$ and $A$ be a $2 \times 2$ matrix such that $A B^{- 1} = A^{- 1}$ . If $B C B^{- 1} = A$ and $C^{4} + α C^{2} + β I = O$ , then $2 β - α$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q45. $lim_{x \to 0} \frac{e - ( 1 + 2 x ) ^{\frac{1}{2 x}}}{x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.Consider the line $L$ passing through the points $(1, 2, 3)$ and $(2, 3, 5)$ . The distance of the point $(\frac{11}{3}, \frac{11}{3}, \frac{19}{3})$ from the line $L$ along the line $\frac{3 x - 11}{2} = \frac{3 y - 11}{1} = \frac{3 z - 19}{2}$ …
Mathematics · 3D Geometry · MCQ
Q47.The area (in square units) of the region enclosed by the ellipse $x^{2} + 3 y^{2} = 18$ in the first quadrant below the line $y = x$ is
Mathematics · Area Under the Curves · MCQ
Q48.Let $a, a r, a r^{2}$ , ............ be an infinite G.P. If $\sum_{n = 0}^{\infty} a r^{n} = 57$ and $\sum_{n = 0}^{\infty} a^{3} r^{3 n} = 9747$ , then $a + 18 r$ is equal to
Mathematics · Sequences and Series · MCQ
Q49.The sum of the coefficient of $x^{2/3}$ and $x^{- 2/5}$ in the binomial expansion of $(x^{2/3} + \frac{1}{2} x^{- 2/5})^{9}$ is
Mathematics · Binomial Theorem · MCQ
Q50.Let $a = 2 \hat{i} + α \hat{j} + \hat{k}, b = - \hat{i} + \hat{k}, c = β \hat{j} - \hat{k}$ , where $α$ and $β$ are integers and $α β = - 6$ . Let the values of the ordered pair $(α, β)$ , for which the…
Mathematics · Vector Algebra · MCQ
Q51.Let $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$ and $B = {x : (x, y) \in A}$ . Then the number of one-one functions from $A$ to $B$ is equal to .
Mathematics · Functions · Numerical
Q52.Let $C$ and $C$ be three points on the parabola $y^{2} = 6 x$ and let the line segment $A B$ meet the line $L$ through $C$ parallel to the $x$ -axis at the point $D$ . Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ …
Mathematics · Parabola · Numerical
Q53.Consider the matrices : $A = [23 - 5 m], B = [20 m]$ and $X = [x y]$ . Let the set of all $m$ , for which…
Mathematics · Matrices and Determinants · Numerical
Q54.For a differentiable function $f : R \to R$ , suppose $f^{'} (x) = 3 f (x) + α$ , where $α \in R, f (0) = 1$ and $lim_{x \to - \infty} f (x) = 7$ . Then $9 f (- lo g_{e} 3)$ is equal…
Mathematics · Differential Equations · Numerical
Q55.Consider the circle $C : x^{2} + y^{2} = 4$ and the parabola $P : y^{2} = 8 x$ . If the set of all values of $α$ , for which three chords of the circle $C$ on three distinct lines passing through the point $(α, 0)$ are bisected by the parabola $P$ …
Mathematics · Parabola · Numerical
Q56.The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x - 1}{3} = \frac{y}{2} = \frac{z - 2}{4}$ , from the origin is .
Mathematics · 3D Geometry · Numerical
Q57.Let the set of all values of $p$ , for which $f (x) = (p^{2} - 6 p + 8) (sin^{2} 2 x - cos^{2} 2 x) + 2 (2 - p) x + 7$ does not have any critical point, be the interval $(a, b)$ . Then $16 ab$ is equal to .
Mathematics · Application of Derivatives · Numerical
Q58.The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is .
Mathematics · Permutations and Combinations · Numerical
Q59.Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2 sin^{- 1} x + 3 cos^{- 1} x = \frac{2 π}{5}$ , is .
Mathematics · Inverse Trigonometric Functions · Numerical
Q60.If $(\frac{1}{α + 1} + \frac{1}{α + 2} + \dots .. + \frac{1}{α + 1012}) - (\frac{1}{2 \cdot 1} + \frac{1}{4 \cdot 3} + \frac{1}{6 \cdot 5} + \dots\dots + \frac{1}{2024 \cdot 2023}) = \frac{1}{2024}$ , then $α$ is…
Mathematics · Sequences and Series · Numerical