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Mathematics · 2024 · 1 Feb · Shift 2

30 questions from this JEE Main paper

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2024 · 1 Feb · Shift 2
Mathematics

Mathematics · 2024 · 1 Feb · Shift 2

30 questions from this JEE Main paper

Functions1 questions Complex Numbers1 questions 3D Geometry3 questions Sets and Relations1 questions Matrices and Determinants2 questions Definite Integration3 questions Quadratic Equation and Inequalities1 questions Probability1 questions Ellipse1 questions Statistics1 questions Limits Continuity and Differentiability2 questions Trigonometric Functions and Equations1 questions Circle1 questions Differential Equations2 questions Sequences and Series2 questions Binomial Theorem1 questions Area Under the Curves2 questions Differentiation1 questions Straight Lines and Pair of Straight Lines2 questions Vector Algebra1 questions

Q31.If the domain of the function $f (x) = \frac{x ^{2} - 25}{( 4 - x ^{2} )} + lo g_{10} (x^{2} + 2 x - 15)$ is $(- \infty, α) \cup [β, \infty)$ , then $α^{2} + β^{3}$ is equal to :
Mathematics · Functions · MCQ
Q32.If $z$ is a complex number such that $∣ z ∣ ⩽ 1$ , then the minimum value of $z + \frac{1}{2} (3 + 4 i)$ is :
Mathematics · Complex Numbers · MCQ
Q33.Consider a $△ A B C$ where $A (1, 3, 2), B (- 2, 8, 0)$ and $C (3, 6, 7)$ . If the angle bisector of $∠ B A C$ meets the line $B C$ at $D$ , then the length of the projection of the vector $A D$ on the vector $A C$ …
Mathematics · 3D Geometry · MCQ
Q34.Consider the relations $R_{1}$ and $R_{2}$ defined as $a R_{1} b \Leftrightarrow a^{2} + b^{2} = 1$ for all $a, b \in R$ and $(a, b) R_{2} (c, d) \Leftrightarrow a + d = b + c$ for all $(a, b), (c, d) \in N \times N$ . Then :
Mathematics · Sets and Relations · MCQ
Q35.Let the system of equations $x + 2 y + 3 z = 5, 2 x + 3 y + z = 9, 4 x + 3 y + λ z = μ$ have infinite number of solutions. Then $λ + 2 μ$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q36.If $0 \int \frac{π}{3} cos^{4} x d x = a π + b 3$ , where $a$ and $b$ are rational numbers, then $9 a + 8 b$ is equal to :
Mathematics · Definite Integration · MCQ
Q37.Let $α$ and $β$ be the roots of the equation $p x^{2} + q x - r = 0$ , where $p e q 0$ . If $r$ and $r$ be the consecutive terms of a non constant G.P. and $\frac{1}{α} + \frac{1}{β} = \frac{3}{4}$ , then the value of $(α - β)^{2}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.Let Ajay will not appear in JEE exam with probability $p = \frac{2}{7}$ , while both Ajay and Vijay will appear in the exam with probability $q = \frac{1}{5}$ . Then the probability, that Ajay will appear in the exam and Vijay…
Mathematics · Probability · MCQ
Q39.Let $P$ be a point on the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ . Let the line passing through $P$ and parallel to $y$ -axis meet the circle $x^{2} + y^{2} = 9$ at point $Q$ such that $P$ and $Q$ are on…
Mathematics · Ellipse · MCQ
Q40.Consider 10 observations $x_{1}, x_{2}, \dots, x_{10}$ such that $i = 1 \sum 10 (x_{i} - α) = 2$ and $i = 1 \sum 10 (x_{i} - β)^{2} = 40$ , where $α, β$ are positive integers. Let the mean and the…
Mathematics · Statistics · MCQ
Q41.Let $f (x) = 2 x^{2} + 5 x ∣ - 3∣, x \in R$ . If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m + n$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q42.The number of solutions of the equation $4 sin^{2} x - 4 cos^{3} x + 9 - 4 cos x = 0; x \in [- 2 π, 2 π]$ is :
Mathematics · Trigonometric Functions and Equations · MCQ
Q43.Let the locus of the midpoints of the chords of the circle $x^{2} + (y - 1)^{2} = 1$ drawn from the origin intersect the line $x + y = 1$ at $P$ and $Q$ . Then, the length of $PQ$ is :
Mathematics · Circle · MCQ
Q44.Let $α$ be a non-zero real number. Suppose $f : R \to R$ is a differentiable function such that $f (0) = 2$ and $x \to - \infty lim f (x) = 1$ . If $f^{'} (x) = α f (x) + 3$ , for all $x \in R$ …
Mathematics · Differential Equations · MCQ
Q45.Let $P$ and $Q$ be the points on the line $\frac{x + 3}{8} = \frac{y - 4}{2} = \frac{z + 1}{2}$ which are at a distance of 6 units from the point $R (1, 2, 3)$ . If the centroid of the triangle PQR is $(\alpha, \beta,…
Mathematics · 3D Geometry · MCQ
Q46.The value of $0 \int 1 (2 x^{3} - 3 x^{2} - x + 1)^{\frac{1}{3}} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q47.If the mirror image of the point $P (3, 4, 9)$ in the line $\frac{x - 1}{3} = \frac{y + 1}{2} = \frac{z - 2}{1}$ is $(α, β, γ)$ , then 14 $(α + β + γ)$ is :
Mathematics · 3D Geometry · MCQ
Q48.Let $S_{n}$ denote the sum of the first $n$ terms of an arithmetic progression. If $S_{10} = 390$ and the ratio of the tenth and the fifth terms is $15 : 7$ , then $S_{15} - S_{5}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q49.Let $m$ and $n$ be the coefficients of seventh and thirteenth terms respectively in the expansion of $(\frac{1}{3} x^{\frac{1}{3}} + \frac{1}{2 x ^{\frac{2}{3}}})^{18}$ . Then $(\frac{n}{m})^{\frac{1}{3}}$ …
Mathematics · Binomial Theorem · MCQ
Q50.Let $f (x) = {x - 1, x is even, 2 x, x is odd, x \in N$ . If for some $a \in N, f (f (f (a))) = 21$ , then $x \to a^{-} lim {\frac{∣ x ∣ ^{3}}{a} - [\frac{x}{a}]}$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q51.Three points $O (0, 0), P (a, a^{2}), Q (- b, b^{2}), a > 0, b > 0$ , are on the parabola $y = x^{2}$ . Let $S_{1}$ be the area of the region…
Mathematics · Area Under the Curves · Numerical
Q52.The sum of squares of all possible values of $k$ , for which area of the region bounded by the parabolas $2 y^{2} = k x$ and $ky^{2} = 2 (y - x)$ is maximum, is equal to :
Mathematics · Area Under the Curves · Numerical
Q53.If $y = \frac{( x + 1 ) ( x ^{2} - x )}{x x + x + x} + \frac{1}{15} (3 cos^{2} x - 5) cos^{3} x$ , then $96 y^{'} (\frac{π}{6})$ is equal to :
Mathematics · Differentiation · Numerical
Q54.If $\frac{d x}{d y} = \frac{1 + x - y ^{2}}{y}, x (1) = 1$ , then $5 x (2)$ is equal to .
Mathematics · Differential Equations · Numerical
Q55.Let $f : (0, \infty) \to R$ and $F (x) = 0 \int x t f (t) dt$ . If $F (x^{2}) = x^{4} + x^{5}$ , then $r = 1 \sum 12 f (r^{2})$ is equal to …
Mathematics · Definite Integration · Numerical
Q56.Let $A B C$ be an isosceles triangle in which $A$ is at $(- 1, 0), ∠ A = \frac{2 π}{3}, A B = A C$ and $B$ is on the positve $x$ -axis. If $BC = 43$ and the line $BC$ intersects the line $y = x + 3$ at $(\alpha,…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q57.Let $A = I_{2} - 2 M M^{T}$ , where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^{T} M = I_{1}$ holds. If $λ$ is a real number such that the relation $A X = λ X$ holds for some non-zero real matrix $X$ of order $2 \times 1$ …
Mathematics · Matrices and Determinants · Numerical
Q58.Let $a = \hat{i} + \hat{j} + \hat{k}, b = - \hat{i} - 8 \hat{j} + 2 \hat{k}$ and $c = 4 \hat{i} + c_{2} \hat{j} + c_{3} \hat{k}$ be three vectors such that $b \times a = c \times a$ …
Mathematics · Vector Algebra · Numerical
Q59.If three successive terms of a G.P. with common ratio $r (r > 1)$ are the lengths of the sides of a triangle and $[r]$ denotes the greatest integer less than or equal to $r$ , then $3 [r] + [- r]$ is equal to …
Mathematics · Sequences and Series · Numerical
Q60.The lines $L_{1}, L_{2}, \dots, L_{20}$ are distinct. For $n = 1, 2, 3, \dots, 10$ all the lines $L_{2 n - 1}$ are parallel to each other and all the lines $L_{2 n}$ pass through a given point…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical