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Mathematics · 2024 · 9 Apr · Shift 1

30 questions from this JEE Main paper

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2024 · 9 Apr · Shift 1
Mathematics

Mathematics · 2024 · 9 Apr · Shift 1

30 questions from this JEE Main paper

Functions2 questions Vector Algebra2 questions Differentiation1 questions Area Under the Curves1 questions Differential Equations2 questions Trigonometric Functions and Equations1 questions Sequences and Series1 questions Binomial Theorem2 questions Statistics1 questions Circle2 questions Indefinite Integrals1 questions Quadratic Equation and Inequalities1 questions Ellipse1 questions 3D Geometry2 questions Straight Lines and Pair of Straight Lines2 questions Matrices and Determinants2 questions Sets and Relations1 questions Definite Integration1 questions Limits Continuity and Differentiability1 questions Complex Numbers1 questions Application of Derivatives1 questions Probability1 questions

Q31.If the domain of the function $f (x) = sin^{- 1} (\frac{x - 1}{2 x + 3})$ is $R - (α, β)$ , then $12 α β$ is equal to :
Mathematics · Functions · MCQ
Q32.Let three vectors , $a = α \hat{i} + 4 \hat{j} + 2 \hat{k}, b = 5 \hat{i} + 3 \hat{j} + 4 \hat{k}, c = x \hat{i} + y \hat{j} + z \hat{k}$ form a triangle such that $c = a - b$ …
Mathematics · Vector Algebra · MCQ
Q33.Let $f (x) = a x^{3} + b x^{2} + c x + 41$ be such that $f (1) = 40, f^{'} (1) = 2$ and $f^{''} (1) = 4$ . Then $a^{2} + b^{2} + c^{2}$ is equal to:
Mathematics · Differentiation · MCQ
Q34.The parabola $y^{2} = 4 x$ divides the area of the circle $x^{2} + y^{2} = 5$ in two parts. The area of the smaller part is equal to :
Mathematics · Area Under the Curves · MCQ
Q35.The solution of the differential equation $(x^{2} + y^{2}) d x - 5 x y d y = 0, y (1) = 0$ , is :
Mathematics · Differential Equations · MCQ
Q36.Let $∣ cos θ cos (60 - θ) cos (60 + θ) ∣ \leq \frac{1}{8}, θ ϵ [0, 2 π]$ . Then, the sum of all $θ \in [0, 2 π]$ , where $cos 3 θ$ attains its maximum value, is :
Mathematics · Trigonometric Functions and Equations · MCQ
Q37.If the sum of the series $\frac{1}{1 \cdot ( 1 + d )} + \frac{1}{( 1 + d ) ( 1 + 2 d )} + \dots + \frac{1}{( 1 + 9 d ) ( 1 + 10 d )}$ is equal to 5, then $50 d$ is equal to :
Mathematics · Sequences and Series · MCQ
Q38.The coefficient of $x^{70}$ in $x^{2} (1 + x)^{98} + x^{3} (1 + x)^{97} + x^{4} (1 + x)^{96} + \dots + x^{54} (1 + x)^{46}$ is $^{99} C_{p} -^{46} C_{q}$ . Then a possible value of $p + q$ is :
Mathematics · Binomial Theorem · MCQ
Q39.The frequency distribution of the age of students in a class of 40 students is given below. If the mean deviation about the median is 1.25, then $4 x + 5 y$ is equal to : Includes table
Mathematics · Statistics · MCQ
Q40.Let a circle passing through $(2, 0)$ have its centre at the point $(h, k)$ . Let $(x_{c}, y_{c})$ be the point of intersection of the lines $3 x + 5 y = 1$ and $(2 + c) x + 5 c^{2} y = 1$ . If $h = lim_{c \to 1} x_{c}$ …
Mathematics · Circle · MCQ
Q41.Let $\int \frac{2 - t a n x}{3 + t a n x} d x = \frac{1}{2} (α x + lo g_{e} ∣ β sin x + γ cos x ∣) + C$ , where $C$ is the constant of integration. Then $α + \frac{γ}{β}$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q42.Let $x^{2} + 22 x - 1 = 0$ be the roots of the equation $x^{2} + 22 x - 1 = 0$ . The quadratic equation, whose roots are $α^{4} + β^{4}$ and $\frac{1}{10} (α^{6} + β^{6})$ , is:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q43.Let $f (x) = x^{2} + 9, g (x) = \frac{x}{x - 9}$ and $a = f \circ g (10), b = g \circ f (3)$ . If $e$ and $l$ denote the eccentricity and the length of the latus rectum of the ellipse $\frac{x ^{2}}{a} + \frac{y ^{2}}{b} = 1$ …
Mathematics · Ellipse · MCQ
Q44.The shortest distance between the lines $\frac{x - 3}{4} = \frac{y + 7}{- 11} = \frac{z - 1}{5}$ and $\frac{x - 5}{3} = \frac{y - 9}{- 6} = \frac{z + 2}{1}$ is:
Mathematics · 3D Geometry · MCQ
Q45.A variable line $L$ passes through the point $(3, 5)$ and intersects the positive coordinate axes at the points $A$ and $B$ . The minimum area of the triangle $OAB$ , where $O$ is the origin, is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q46.The solution curve, of the differential equation $2 y \frac{d y}{d x} + 3 = 5 \frac{d y}{d x}$ , passing through the point $(0, 1)$ is a conic, whose vertex lies on the line :
Mathematics · Differential Equations · MCQ
Q47.Let $λ, μ \in R$ . If the system of equations $3 x + 5 y + λ z = 3 7 x + 11 y - 9 z = 2 97 x + 155 y - 189 z = μ$ has infinitely many solutions, then $μ + 2 λ$ is equal to…
Mathematics · Matrices and Determinants · MCQ
Q48.A ray of light coming from the point $P (1, 2)$ gets reflected from the point $Q$ on the $x$ -axis and then passes through the point $R (4, 3)$ . If the point $S (h, k)$ is such that $P QR S$ is a parallelogram, then $h k^{2}$ is…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q49.Let the line $L$ intersect the lines $x - 2 = - y = z - 1, 2 (x + 1) = 2 (y - 1) = z + 1$ and be parallel to the line $\frac{x - 2}{3} = \frac{y - 1}{1} = \frac{z - 2}{2}$ . Then which of the following points lies on $L$ ?
Mathematics · 3D Geometry · MCQ
Q50.Let $O A = 2 a, O B = 6 a + 5 b$ and $O C = 3 b$ , where $O$ is the origin. If the area of the parallelogram with adjacent sides $O A$ and $O C$ …
Mathematics · Vector Algebra · MCQ
Q51.Let $A = {2, 3, 6, 7}$ and $B = {4, 5, 6, 8}$ . Let $R$ be a relation defined on $A \times B$ by $(a_{1}, b_{1}) R (a_{2}, b_{2})$ if and only if $a_{1} + a_{2} = b_{1} + b_{2}$ . Then the number of elements in $R$ is .
Mathematics · Sets and Relations · Numerical
Q52.Let $lim_{n \to \infty} (\frac{n}{n ^{4} + 1} - \frac{2 n}{( n ^{2} + 1 ) n ^{4} + 1} + \frac{n}{n ^{4} + 16} - \frac{8 n}{( n ^{2} + 4 ) n ^{4} + 16} + \dots + \frac{n}{n ^{4} + n ^{4}} - \frac{2 n \cdot n ^{2}}{( n ^{2} + n ^{2} ) n ^{4} + n ^{4}})$ …
Mathematics · Definite Integration · Numerical
Q53.Let $f : (0, π) \to R$ be a function given by $f (x) = ⎩ ⎨ ⎧ (\frac{8}{7})^{\frac{t a n 8 x}{t a n 7 x}}, a - 8, (1 + ∣ cot x ∣)^{\frac{b}{a} ∣ t a n x ∣}, 0 < x < \frac{π}{2} x = \frac{π}{2} \frac{π}{2} < x < π$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q54.The remainder when $42 8^{2024}$ is divided by 21 is .
Mathematics · Binomial Theorem · Numerical
Q55.If a function $f$ satisfies $f (m + n) = f (m) + f (n)$ for all $m, n \in N$ and $f (1) = 1$ , then the largest natural number $λ$ such that $\sum_{k = 1}^{2022} f (λ + k) \leq (2022)^{2}$ …
Mathematics · Functions · Numerical
Q56.Let the centre of a circle, passing through the points $(0, 0), (1, 0)$ and touching the circle $x^{2} + y^{2} = 9$ , be $(h, k)$ . Then for all possible values of the coordinates of the centre $(h, k), 4 (h^{2} + k^{2})$ is equal to …
Mathematics · Circle · Numerical
Q57.The sum of the square of the modulus of the elements in the set ${z = a + ib : a, b \in Z, z \in C, ∣ z - 1∣ \leq 1, ∣ z - 5∣ \leq ∣ z - 5 i ∣}$ is .
Mathematics · Complex Numbers · Numerical
Q58.Let the set of all positive values of $λ$ , for which the point of local minimum of the function $(1 + x (λ^{2} - x^{2}))$ satisfies $\frac{x ^{2} + x + 2}{x ^{2} + 5 x + 6} < 0$ , be $(α, β)$ . Then $α^{2} + β^{2}$ is equal to …
Mathematics · Application of Derivatives · Numerical
Q59.Let $A$ be a non-singular matrix of order 3. If $det (3 adj (2 adj ((det A) A))) = 3^{- 13} \cdot 2^{- 10}$ and $det (3 adj (2 A)) = 2^{m} \cdot 3^{n}$ …
Mathematics · Matrices and Determinants · Numerical
Q60.Let $c$ and $c$ denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked $1, 2, 3, 4$ . If the probability that $a x^{2} + b x + c = 0$ has all real roots is $\frac{m}{n}, gcd (m, n) = 1$ …
Mathematics · Probability · Numerical