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Mathematics · 2024 · 4 Apr · Shift 1

30 questions from this JEE Main paper

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2024 · 4 Apr · Shift 1
Mathematics

Mathematics · 2024 · 4 Apr · Shift 1

30 questions from this JEE Main paper

Definite Integration3 questions Area Under the Curves1 questions Matrices and Determinants4 questions Permutations and Combinations1 questions Circle1 questions Statistics1 questions Differentiation1 questions Vector Algebra2 questions Inverse Trigonometric Functions1 questions 3D Geometry1 questions Straight Lines and Pair of Straight Lines1 questions Probability1 questions Differential Equations2 questions Sequences and Series1 questions Binomial Theorem2 questions Quadratic Equation and Inequalities1 questions Application of Derivatives1 questions Complex Numbers1 questions Limits Continuity and Differentiability2 questions Sets and Relations1 questions Parabola1 questions

Q31. $Let f (x) = {- 2, x - 2, - 2 \leq x \leq 0 0 < x \leq 2 and h (x) = f (∣ x ∣) + ∣ f (x) ∣ . Then \int_{- 2}^{2} h (x) d x is equal to:$ …
Mathematics · Definite Integration · MCQ
Q32.One of the points of intersection of the curves $y = 1 + 3 x - 2 x^{2}$ and $y = \frac{1}{x}$ is $(\frac{1}{2}, 2)$ . Let the area of the region enclosed by these curves be $\frac{1}{24} (l 5 + m) - n lo g_{e} (1 + 5)$ …
Mathematics · Area Under the Curves · MCQ
Q33.Let $α \in (0, \infty)$ and $A = 110201 α 12$ . If $det (adj (2 A - A^{T}) \cdot adj (A - 2 A^{T})) = 2^{8}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.There are 5 points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}$ on the side $A B$ , excluding $A$ and $B$ , of a triangle $A B C$ . Similarly there are 6 points $P_{6}, P_{7}, \dots, P_{11}$ on the side $BC$ and 7 points $P_{12}, P_{13}, \dots, P_{18}$ …
Mathematics · Permutations and Combinations · MCQ
Q35.A square is inscribed in the circle $x^{2} + y^{2} - 10 x - 6 y + 30 = 0$ . One side of this square is parallel to $y = x + 3$ . If $(x_{i}, y_{i})$ are the vertices of the square, then $Σ (x_{i}^{2} + y_{i}^{2})$ is equal to:
Mathematics · Circle · MCQ
Q36.Let $α, β \in R$ . Let the mean and the variance of 6 observations $- 3, 4, 7, - 6, α, β$ be 2 and 23, respectively. The mean deviation about the mean of these 6 observations is :
Mathematics · Statistics · MCQ
Q37.Let $f (x) = x^{5} + 2 e^{x /4}$ for all $x \in R$ . Consider a function $g (x)$ such that $(g \circ f) (x) = x$ for all $x \in R$ . Then the value of $8 g^{'} (2)$ is :
Mathematics · Differentiation · MCQ
Q38.Let a unit vector which makes an angle of $6 0^{\circ}$ with $2 \hat{i} + 2 \hat{j} - \hat{k}$ and an angle of $4 5^{\circ}$ with $\hat{i} - \hat{k}$ be $C$ . Then $C + (- \frac{1}{2} \hat{i} + \frac{1}{3 2} \hat{j} - \frac{2}{3} \hat{k})$ …
Mathematics · Vector Algebra · MCQ
Q39.If the domain of the function $sin^{- 1} (\frac{3 x - 22}{2 x - 19}) + lo g_{e} (\frac{3 x ^{2} - 8 x + 5}{x ^{2} - 3 x - 10})$ is $(α, β]$ , then $3 α + 10 β$ is equal to:
Mathematics · Inverse Trigonometric Functions · MCQ
Q40.Let the point, on the line passing through the points $P (1, - 2, 3)$ and $Q (5, - 4, 7)$ , farther from the origin and at a distance of 9 units from the point $P$ , be $(α, β, γ)$ . Then $α^{2} + β^{2} + γ^{2}$ is equal to :
Mathematics · 3D Geometry · MCQ
Q41.The vertices of a triangle are $A (- 1, 3), B (- 2, 2)$ and $C (3, - 1)$ . A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q42.Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from…
Mathematics · Probability · MCQ
Q43.If the solution $y = y (x)$ of the differential equation $(x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 2) d y - (2 x^{2} + 2 x + 3) d x = 0$ satisfies $y (- 1) = - \frac{π}{4}$ , then $y (0)$ is equal to :
Mathematics · Differential Equations · MCQ
Q44.Let the first three terms 2, p and q, with $q e q 2$ , of a G.P. be respectively the $7^{th}, 8^{th}$ and $1 3^{th}$ terms of an A.P. If the $5^{th}$ term of the G.P. is the $n^{th}$ term of the…
Mathematics · Sequences and Series · MCQ
Q45.The sum of all rational terms in the expansion of $(2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q46.If 2 and 6 are the roots of the equation $a x^{2} + b x + 1 = 0$ , then the quadratic equation, whose roots are $\frac{1}{2 a + b}$ and $\frac{1}{6 a + b}$ , is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q47.Let the sum of the maximum and the minimum values of the function $f (x) = \frac{2 x ^{2} - 3 x + 8}{2 x ^{2} + 3 x + 8}$ be $\frac{m}{n}$ , where $gcd (m, n) = 1$ . Then $m + n$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q48.If the system of equations $x + (2 sin α) y + (2 cos α) z = 0 x + (cos α) y + (sin α) z = 0 x + (sin α) y - (cos α) z = 0$ has a non-trivial solution,…
Mathematics · Matrices and Determinants · MCQ
Q49.Let $α$ and $β$ be the sum and the product of all the non-zero solutions of the equation $(\overset{z}{ˉ})^{2} + ∣ z ∣ = 0, z \in C$ . Then $4 (α^{2} + β^{2})$ is equal to :
Mathematics · Complex Numbers · MCQ
Q50.Let $f : R \to R$ be a function given by $f (x) = {\frac{1 - c o s 2 x}{x ^{2}}, x 0$ where $α, β \in R$ . If $f$ is continuous at $x = 0$ , then $α^{2} + β^{2}$ is equal…
Mathematics · Limits Continuity and Differentiability · MCQ
Q51.Let the solution $y = y (x)$ of the differential equation $\frac{d y}{d x} - y = 1 + 4 sin x$ satisfy $y (π) = 1$ . Then $y (\frac{π}{2}) + 10$ is equal to .
Mathematics · Differential Equations · Numerical
Q52.If the shortest distance between the lines $\frac{x + 2}{2} = \frac{y + 3}{3} = \frac{z - 5}{4}$ and $\frac{x - 3}{1} = \frac{y - 2}{- 3} = \frac{z + 4}{2}$ is $\frac{38}{3 5} k$ , and $0 \int k [x^{2}] d x = α - α$ …
Mathematics · Definite Integration · Numerical
Q53.Let $A$ be a square matrix of order 2 such that $∣ A ∣ = 2$ and the sum of its diagonal elements is $-$ 3 . If the points $(x, y)$ satisfying $A^{2} + x A + y I = O$ lie on a hyperbola, whose transverse axis is…
Mathematics · Matrices and Determinants · Numerical
Q54.If $lim_{x \to 1} \frac{( 5 x + 1 ) ^{1/3} - ( x + 5 ) ^{1/3}}{( 2 x + 3 ) ^{1/2} - ( x + 4 ) ^{1/2}} = \frac{m 5}{n ( 2 n ) ^{2/3}}$ , where $gcd (m, n) = 1$ , then $8 m + 12 n$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q55.Let $A$ be a $3 \times 3$ matrix of non-negative real elements such that $A 111 = 3111$ . Then the maximum value of $det (A)$ …
Mathematics · Matrices and Determinants · Numerical
Q56.If $\int_{0}^{\frac{π}{4}} \frac{s i n ^{2} x}{1 + s i n x c o s x} d x = \frac{1}{a} lo g_{e} (\frac{a}{3}) + \frac{π}{b 3}$ , where $a, b \in N$ , then $a + b$ …
Mathematics · Definite Integration · Numerical
Q57.In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied…
Mathematics · Sets and Relations · Numerical
Q58.Let the length of the focal chord PQ of the parabola $y^{2} = 12 x$ be 15 units. If the distance of $PQ$ from the origin is $p$ , then $10 p^{2}$ is equal to .
Mathematics · Parabola · Numerical
Q59.Let $ABC$ be a triangle of area $152$ and the vectors $AB = \hat{i} + 2 \hat{j} - 7 \hat{k}, BC = a \hat{i} + b \hat{j} + c \hat{k}$ and $AC = 6 \hat{i} + d \hat{j} - 2 \hat{k}, d > 0$ …
Mathematics · Vector Algebra · Numerical
Q60.Let $a = 1 + \frac{^{2} C _{2}}{3 !} + \frac{^{3} C _{2}}{4 !} + \frac{^{4} C _{2}}{5 !} + ...., b = 1 + \frac{^{1} C _{0} + ^{1} C _{1}}{1 !} + \frac{^{2} C _{0} + ^{2} C _{1} + ^{2} C _{2}}{2 !} + \frac{^{3} C _{0} + ^{3} C _{1} + ^{3} C _{2} + ^{3} C _{3}}{3 !} + ....$ …
Mathematics · Binomial Theorem · Numerical