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Mathematics · 2024 · 30 Jan · Shift 2

30 questions from this JEE Main paper

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2024 · 30 Jan · Shift 2
Mathematics

Mathematics · 2024 · 30 Jan · Shift 2

30 questions from this JEE Main paper

Definite Integration4 questions Sequences and Series2 questions Trigonometric Ratio and Identites1 questions Complex Numbers1 questions Differentiation1 questions Matrices and Determinants2 questions Straight Lines and Pair of Straight Lines1 questions 3D Geometry2 questions Vector Algebra2 questions Hyperbola1 questions Application of Derivatives1 questions Binomial Theorem2 questions Functions1 questions Probability1 questions Ellipse1 questions Permutations and Combinations1 questions Differential Equations1 questions Quadratic Equation and Inequalities1 questions Circle1 questions Statistics1 questions Area Under the Curves1 questions Sets and Relations1 questions

Q31.Let $f : R \to R$ be a function defined by $f (x) = \frac{x}{( 1 + x ^{4} ) ^{1/4}}$ , and $g (x) = f (f (f (f (x))))$ . Then, $18 \int_{0}^{25} x^{2} g (x) d x$ is equal to
Mathematics · Definite Integration · MCQ
Q32.Let $a$ and $b$ be be two distinct positive real numbers. Let $1 1^{th}$ term of a GP, whose first term is $a$ and third term is $b$ , is equal to $p^{th}$ term of another GP, whose first term is $a$ and fifth term is $b$ .…
Mathematics · Sequences and Series · MCQ
Q33.Let $y = f (x)$ be a thrice differentiable function in $(- 5, 5)$ . Let the tangents to the curve $y = f (x)$ at $(1, f (1))$ and $(3, f (3))$ make angles $π /6$ and $π /4$ , respectively with positive $x$ -axis. If $27 1 \int 3 ((f^{'} (t))^{2} + 1) f^{''} (t) d t = α + β 3$ …
Mathematics · Definite Integration · MCQ
Q34.For $α, β \in (0, π /2)$ , let $3 sin (α + β) = 2 sin (α - β)$ and a real number $k$ be such that $tan α = k tan β$ . Then, the value of $k$ is equal to
Mathematics · Trigonometric Ratio and Identites · MCQ
Q35.If $z$ is a complex number, then the number of common roots of the equations $z^{1985} + z^{100} + 1 = 0$ and $z^{3} + 2 z^{2} + 2 z + 1 = 0$ , is equal to
Mathematics · Complex Numbers · MCQ
Q36.Let $f : R - {0} \to R$ be a function satisfying $f (\frac{x}{y}) = \frac{f ( x )}{f ( y )}$ for all $x, y, f (y) e q 0$ . If $f^{'} (1) = 2024$ , then
Mathematics · Differentiation · MCQ
Q37.Let $R = x 00 0 y 0 00 z$ be a non-zero $3 \times 3$ matrix, where $x sin θ = y sin (θ + \frac{2 π}{3}) = z sin (θ + \frac{4 π}{3}) e q 0, θ \in (0, 2 π)$ …
Mathematics · Matrices and Determinants · MCQ
Q38.If $x^{2} - y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ is the locus of a point, which moves such that it is always equidistant from the lines $x + 2 y + 7 = 0$ and $2 x - y + 8 = 0$ , then the value of $g + c + h - f$ equals
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Let $a$ and $b$ be real constants such that the function $f$ defined by $f (x) = {x^{2} + 3 x + a b x + 2, x \leq 1, x > 1$ be differentiable on $R$ . Then, the value of $\int_{- 2}^{2} f (x) d x$ …
Mathematics · Definite Integration · MCQ
Q40.Let $f : R \to R$ be defined as $f (x) = a e^{2 x} + b e^{x} + c x$ . If $f (0) = - 1, f^{'} (lo g_{e} 2) = 21$ and $\int_{0}^{l o g_{e} 4} (f (x) - c x) d x = \frac{39}{2}$ , then the value of $∣ a + b + c ∣$ equals
Mathematics · Definite Integration · MCQ
Q41.Let $L_{1} : r = (\hat{i} - \hat{j} + 2 \hat{k}) + λ (\hat{i} - \hat{j} + 2 \hat{k}), λ \in R$ , $L_{2} : r = (\hat{j} - \hat{k}) + μ (3 \hat{i} + \hat{j} + p \hat{k}), μ \in R, and L_{3} : r = δ (ℓ \hat{i} + m \hat{j} + n \hat{k}), δ \in R$ …
Mathematics · 3D Geometry · MCQ
Q42.Let $a = \hat{i} + α \hat{j} + β \hat{k}, α, β \in R$ . Let a vector $b$ be such that the angle between $a$ and $b$ is $\frac{π}{4}$ and $∣ b ∣^{2} = 6$ . If $\vec{a} \cdot \vec{b}=3…
Mathematics · Vector Algebra · MCQ
Q43.Let $P$ be a point on the hyperbola $H : \frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ , in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $213$ . Then, the square of the distance of $P$ from the origin is
Mathematics · Hyperbola · MCQ
Q44.Let $f (x) = (x + 3)^{2} (x - 2)^{3}, x \in [- 4, 4]$ . If $M$ and $m$ are the maximum and minimum values of $f$ , respectively in $[- 4, 4]$ , then the value of $M - m$ is
Mathematics · Application of Derivatives · MCQ
Q45.Suppose $2 - p, p, 2 - α, α$ are the coefficients of four consecutive terms in the expansion of $(1 + x)^{n}$ . Then the value of $p^{2} - α^{2} + 6 α + 2 p$ equals
Mathematics · Binomial Theorem · MCQ
Q46.Consider the system of linear equations $x + y + z = 5, x + 2 y + λ^{2} z = 9, x + 3 y + λ z = μ$ , where $λ, μ \in R$ . Then, which of the following statement is NOT correct?
Mathematics · Matrices and Determinants · MCQ
Q47.Let $a$ and $b$ be two vectors such that $∣ b ∣ = 1$ and $∣ b \times a ∣ = 2$ . Then $∣ (b \times a) - b ∣^{2}$ is equal to
Mathematics · Vector Algebra · MCQ
Q48.If the domain of the function $f (x) = lo g_{e} (\frac{2 x + 3}{4 x ^{2} + x - 3}) + cos^{- 1} (\frac{2 x - 1}{x + 2})$ is $(α, β]$ , then the value of $5 β - 4 α$ is equal to
Mathematics · Functions · MCQ
Q49.Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is
Mathematics · Probability · MCQ
Q50.Let $A (α, 0)$ and $B (0, β)$ be the points on the line $5 x + 7 y = 50$ . Let the point $P$ divide the line segment $A B$ internally in the ratio $7 : 3$ . Let $3 x - 25 = 0$ be a directrix of the ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ …
Mathematics · Ellipse · MCQ
Q51.In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $C$ and $C$ . A student is required to attempt total 15 questions taking at least 4 questions from each…
Mathematics · Permutations and Combinations · Numerical
Q52.Let $Y = Y (X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y - y = Y^{'} (x) (X - x)$ and the co-ordinate axes, where $(x, y)$ is any point on the curve, is always $\frac{- y ^{2}}{2 Y ^{'} ( x )} + 1, Y^{'} (x) e q 0$ …
Mathematics · Differential Equations · Numerical
Q53.The number of real solutions of the equation $x (x^{2} + 3∣ x ∣ + 5∣ x - 1∣ + 6∣ x - 2∣) = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q54.Consider two circles $C_{1} : x^{2} + y^{2} = 25$ and $C_{2} : (x - α)^{2} + y^{2} = 16$ , where $α \in (5, 9)$ . Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_{1}$ and $C_{2}$ be $sin^{- 1} (\frac{63}{8})$ …
Mathematics · Circle · Numerical
Q55.Let a line passing through the point $(- 1, 2, 3)$ intersect the lines $L_{1} : \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z + 1}{- 2}$ at $M (α, β, γ)$ and $L_{2} : \frac{x + 2}{- 3} = \frac{y - 2}{- 2} = \frac{z - 1}{4}$ at $N (a, b, c)$ . Then, the value of $\frac{( α + β + γ ) ^{2}}{( a + b + c ) ^{2}}$ …
Mathematics · 3D Geometry · Numerical
Q56.The variance $σ^{2}$ of the data is . Includes table
Mathematics · Statistics · Numerical
Q57.The area of the region enclosed by the parabola $(y - 2)^{2} = x - 1$ , the line $x - 2 y + 4 = 0$ and the positive coordinate axes is .
Mathematics · Area Under the Curves · Numerical
Q58.The number of symmetric relations defined on the set ${1, 2, 3, 4}$ which are not reflexive is .
Mathematics · Sets and Relations · Numerical
Q59.Let $α = \sum_{k = 0}^{n} (\frac{( ^{n} C _{k} ) ^{2}}{k + 1})$ and $β = \sum_{k = 0}^{n - 1} (\frac{^{n} C _{k} ^{n} C _{k + 1}}{k + 2})$ If $5 α = 6 β$ , then $n$ equals .
Mathematics · Binomial Theorem · Numerical
Q60.Let $S_{n}$ be the sum to $n$ -terms of an arithmetic progression $3, 7, 11$ , If $40 < (\frac{6}{n ( n + 1 )} \sum_{k = 1}^{n} S_{k}) < 42$ , then $n$ equals .
Mathematics · Sequences and Series · Numerical