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Mathematics · 2024 · 5 Apr · Shift 2

30 questions from this JEE Main paper

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2024 · 5 Apr · Shift 2
Mathematics

Mathematics · 2024 · 5 Apr · Shift 2

30 questions from this JEE Main paper

Circle2 questions Functions1 questions 3D Geometry2 questions Complex Numbers1 questions Binomial Theorem1 questions Vector Algebra2 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants2 questions Differentiation1 questions Definite Integration2 questions Limits Continuity and Differentiability2 questions Permutations and Combinations2 questions Probability1 questions Sequences and Series2 questions Area Under the Curves1 questions Differential Equations2 questions Statistics1 questions Application of Derivatives1 questions Quadratic Equation and Inequalities1 questions Trigonometric Functions and Equations1 questions Parabola1 questions

Q31.Let the circle $C_{1} : x^{2} + y^{2} - 2 (x + y) + 1 = 0$ and $C_{2}$ be a circle having centre at $(- 1, 0)$ and radius 2 . If the line of the common chord of $C_{1}$ and $C_{2}$ intersects the $y$ -axis at the point…
Mathematics · Circle · MCQ
Q32.Let $f, g : R \to R$ be defined as : $f (x) = ∣ x - 1∣ and g (x) = {e^{x}, x + 1, x \geq 0 x \leq 0.$ Then the function $f (g (x))$ is
Mathematics · Functions · MCQ
Q33.Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC…
Mathematics · Circle · MCQ
Q34.Let $(α, β, γ)$ be the image of the point $(8, 5, 7)$ in the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 2}{5}$ . Then $α + β + γ$ is equal to :
Mathematics · 3D Geometry · MCQ
Q35.Let $S_{1} = {z \in C : ∣ z ∣ \leq 5}, S_{2} = {z \in C : Im (\frac{z + 1 - 3 i}{1 - 3 i}) \geq 0}$ and $S_{3} = {z \in C : Re (z) \geq 0}$ . Then the area of the…
Mathematics · Complex Numbers · MCQ
Q36.If the constant term in the expansion of $(\frac{5 3}{x} + \frac{2 x}{3 5})^{12}, x e q 0$ , is $α \times 2^{8} \times 53$ , then $25 α$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q37.Let $a = 2 \hat{i} + 5 \hat{j} - \hat{k}, b = 2 \hat{i} - 2 \hat{j} + 2 \hat{k}$ and $c$ be three vectors such that $(c + \hat{i}) \times (a + b + \hat{i}) = a \times (c + \hat{i})$ . If $a \cdot c = - 29$ …
Mathematics · Vector Algebra · MCQ
Q38.Let $A (- 1, 1)$ and $B (2, 3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $△ PAB$ is 10. If the locus of $P$ is $\mathrm{a}…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.The values of $x + y + z = 4, 2 x + 5 y + 5 z = 17, x + 2 y + m z = n$ , for which the system of equations $x + y + z = 4, 2 x + 5 y + 5 z = 17, x + 2 y + m z = n$ has infinitely many solutions, satisfy the equation :
Mathematics · Matrices and Determinants · MCQ
Q40.If $y (θ) = \frac{2 c o s θ + c o s 2 θ}{c o s 3 θ + 4 c o s 2 θ + 5 c o s θ + 2}$ , then at $θ = \frac{π}{2}, y^{''} + y^{'} + y$ is equal to :
Mathematics · Differentiation · MCQ
Q41.Let $β (m, n) = 0 \int 1 x^{m - 1} (1 - x)^{n - 1} d x, m, n > 0$ . If $0 \int 1 (1 - x^{10})^{20} d x = a \times β (b, c)$ …
Mathematics · Definite Integration · MCQ
Q42.Let , $f : [- 1, 2] \to R$ be given by $f (x) = 2 x^{2} + x + [x^{2}] - [x]$ , where $[t]$ denotes the greatest integer less than or equal to $t$ . The number of points, where $f$ is not continuous, is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q43.Let the set $S = {2, 4, 8, 16, \dots, 512}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = ϕ$ …
Mathematics · Permutations and Combinations · MCQ
Q44.The coefficients $a, b, c$ in the quadratic equation $a x^{2} + bx + c = 0$ are from the set ${1, 2, 3, 4, 5, 6}$ . If the probability of this equation having one real root bigger than the other is…
Mathematics · Probability · MCQ
Q45.Let $α β e q 0$ and $A = β α - β α α α 3 β 2 α$ . If $B = 3 α - α - 2 α - 9 75 3 α - 2 α - 2 β$ …
Mathematics · Matrices and Determinants · MCQ
Q46.For $x ⩾ 0$ , the least value of $K$ , for which $4^{1 + x} + 4^{1 - x}, \frac{K}{2}, 1 6^{x} + 1 6^{- x}$ are three consecutive terms of an A.P., is equal to :
Mathematics · Sequences and Series · MCQ
Q47.The area enclosed between the curves $y = x ∣ x ∣$ and $y = x - ∣ x ∣$ is :
Mathematics · Area Under the Curves · MCQ
Q48.60 words can be made using all the letters of the word $BHBJO$ , with or without meaning. If these words are written as in a dictionary, then the $5 0^{th}$ word is:
Mathematics · Permutations and Combinations · MCQ
Q49.Consider three vectors $a, b, c$ . Let $∣ a ∣ = 2, ∣ b ∣ = 3$ and $a = b \times c$ . If $α \in [0, \frac{π}{3}]$ is the angle between the vectors $b$ and $c$ , then the…
Mathematics · Vector Algebra · MCQ
Q50.The differential equation of the family of circles passing through the origin and having centre at the line $y = x$ is :
Mathematics · Differential Equations · MCQ
Q51.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + \frac{2 x}{( 1 + x ^{2} ) ^{2}} y = x e^{\frac{1}{( 1 + x ^{2} )}}; y (0) = 0.$ Then the area enclosed by the curve $f (x) = y (x) e^{- \frac{1}{( 1 + x ^{2} )}}$ …
Mathematics · Differential Equations · Numerical
Q52.Let the mean and the standard deviation of the probability distribution be $μ$ and $σ$ , respectively. If $σ - μ = 2$ , then $σ + μ$ is equal to . Includes table
Mathematics · Statistics · Numerical
Q53.Let the maximum and minimum values of $(8 x - x^{2} - 12 - 4)^{2} + (x - 7)^{2}, x \in R$ be $M$ and $m$ , respectively. Then $M^{2} - m^{2}$ is equal to .
Mathematics · Application of Derivatives · Numerical
Q54.Let the point $(- 1, α, β)$ lie on the line of the shortest distance between the lines $\frac{x + 2}{- 3} = \frac{y - 2}{4} = \frac{z - 5}{2}$ and $\frac{x + 2}{- 1} = \frac{y + 6}{2} = \frac{z - 1}{0}$ . Then $(α - β)^{2}$ is equal to …
Mathematics · 3D Geometry · Numerical
Q55.If $1 + \frac{3 - 2}{2 3} + \frac{5 - 2 6}{18} + \frac{9 3 - 11 2}{36 3} + \frac{49 - 20 6}{180} + \dots$ upto $\infty = 2 + (\frac{b}{a} + 1) lo g_{e} (\frac{a}{b})$ , where a…
Mathematics · Sequences and Series · Numerical
Q56.Let $a > 0$ be a root of the equation $2 x^{2} + x - 2 = 0$ . If $lim_{x \to \frac{1}{a}} \frac{16 ( 1 - c o s ( 2 + x - 2 x ^{2} ) )}{( 1 - a x ) ^{2}} = α + β 17$ , where $α, β \in Z$ , then $α + β$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q57.If $f (t) = 0 \int π \frac{2 x d x}{1 - c o s ^{2} t s i n ^{2} x}, 0 < t < π$ , then the value of $0 \int \frac{π}{2} \frac{π ^{2} dt}{f ( t )}$ equals .
Mathematics · Definite Integration · Numerical
Q58.The number of real solutions of the equation $x ∣ x + 5∣ + 2∣ x + 7∣ - 2 = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q59.The number of solutions of $sin^{2} x + (2 + 2 x - x^{2}) sin x - 3 (x - 1)^{2} = 0$ , where $- π \leq x \leq π$ , is .
Mathematics · Trigonometric Functions and Equations · Numerical
Q60.Let a line perpendicular to the line $2 x - y = 10$ touch the parabola $y^{2} = 4 (x - 9)$ at the point P. The distance of the point P from the centre of the circle $x^{2} + y^{2} - 14 x - 8 y + 56 = 0$ is .
Mathematics · Parabola · Numerical