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Mathematics · 2024 · 30 Jan · Shift 1

30 questions from this JEE Main paper

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2024 · 30 Jan · Shift 1
Mathematics

Mathematics · 2024 · 30 Jan · Shift 1

30 questions from this JEE Main paper

Differentiation2 questions Definite Integration3 questions Circle1 questions Vector Algebra1 questions Application of Derivatives1 questions 3D Geometry3 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants1 questions Ellipse1 questions Statistics1 questions Probability2 questions Differential Equations2 questions Complex Numbers1 questions Trigonometric Functions and Equations1 questions Functions2 questions Sequences and Series2 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions Binomial Theorem1 questions Hyperbola1 questions Limits Continuity and Differentiability1 questions

Q31.Let $g : R \to R$ be a non constant twice differentiable function such that $g^{'} (\frac{1}{2}) = g^{'} (\frac{3}{2})$ . If a real valued function $f$ is defined as…
Mathematics · Differentiation · MCQ
Q32.The value of $lim_{n \to \infty} \sum_{k = 1}^{n} \frac{n ^{3}}{( n ^{2} + k ^{2} ) ( n ^{2} + 3 k ^{2} )}$ is :
Mathematics · Definite Integration · MCQ
Q33.If the circles $(x + 1)^{2} + (y + 2)^{2} = r^{2}$ and $x^{2} + y^{2} - 4 x - 4 y + 4 = 0$ intersect at exactly two distinct points, then
Mathematics · Circle · MCQ
Q34.Let $a = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}$ and $b = b_{1} \hat{i} + b_{2} \hat{j} + b_{3} \hat{k}$ be two vectors such that $∣ a ∣ = 1, a \cdot b = 2$ …
Mathematics · Vector Algebra · MCQ
Q35.The maximum area of a triangle whose one vertex is at $(0, 0)$ and the other two vertices lie on the curve $y = - 2 x^{2} + 54$ at points $(x, y)$ and $(- x, y)$ , where $y > 0$ , is :
Mathematics · Application of Derivatives · MCQ
Q36.If $f (x) = 2 cos^{4} x 3 + 2 cos^{4} x 2 cos^{4} x 2 sin^{4} x 2 sin^{4} x 3 + 2 sin^{4} x 3 + sin^{2} 2 x sin^{2} 2 x sin^{2} 2 x,$ then $\frac{1}{5} f^{'} (0) =$ …
Mathematics · Differentiation · MCQ
Q37.Let $(α, β, γ)$ be the foot of perpendicular from the point $(1, 2, 3)$ on the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ . Then $19 (α + β + γ)$ is equal to :
Mathematics · 3D Geometry · MCQ
Q38.A line passing through the point $A (9, 0)$ makes an angle of $3 0^{\circ}$ with the positive direction of $x$ -axis. If this line is rotated about A through an angle of $1 5^{\circ}$ in the clockwise direction, then its equation in…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q39.Consider the system of linear equations $x + y + z = 4 μ, x + 2 y + 2 λ z = 10 μ, x + 3 y + 4 λ^{2} z = μ^{2} + 15$ where $λ, μ \in R$ . Which one of the following statements is NOT correct ?
Mathematics · Matrices and Determinants · MCQ
Q40.Let $f : [- \frac{π}{2}, \frac{π}{2}] \to R$ be a differentiable function such that $f (0) = \frac{1}{2}$ . If the $$\lim_{x \rightarrow 0} \frac{x \int_0^x f(\mathrm{t})…
Mathematics · Definite Integration · MCQ
Q41.If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :
Mathematics · Ellipse · MCQ
Q42.Let M denote the median of the following frequency distribution Then 20M is equal to : Includes table
Mathematics · Statistics · MCQ
Q43.Two integers $x$ and $y$ are chosen with replacement from the set ${0, 1, 2, 3, \dots, 10}$ . Then the probability that $∣ x - y ∣ > 5$ , is :
Mathematics · Probability · MCQ
Q44.Let $A (2, 3, 5)$ and $C (- 3, 4, - 2)$ be opposite vertices of a parallelogram $A B C D$ . If the diagonal $BD = \hat{i} + 2 \hat{j} + 3 \hat{k}$ , then the area of the parallelogram is equal to :
Mathematics · 3D Geometry · MCQ
Q45.Let $y = y (x)$ be the solution of the differential equation $sec x d y + {2 (1 - x) tan x + x (2 - x)} d x = 0$ such that $y (0) = 2$ . Then $y (2)$ is equal to:
Mathematics · Differential Equations · MCQ
Q46.If $z = x + i y, x y e q 0$ , satisfies the equation $z^{2} + i \overset{z}{ˉ} = 0$ , then $z^{2}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q47.If $2 sin^{3} x + sin 2 x cos x + 4 sin x - 4 = 0$ has exactly 3 solutions in the interval $[0, \frac{n π}{2}], n \in N$ , then the roots of the equation $x^{2} + n x + (n - 3) = 0$ belong to :
Mathematics · Trigonometric Functions and Equations · MCQ
Q48.If the domain of the function $f (x) = cos^{- 1} (\frac{2 - ∣ x ∣}{4}) + {lo g_{e} (3 - x)}^{- 1}$ is $[- α, β) - {γ}$ , then $α + β + γ$ is equal to :
Mathematics · Functions · MCQ
Q49.Let $S_{n}$ denote the sum of first $n$ terms of an arithmetic progression. If $S_{20} = 790$ and $S_{10} = 145$ , then $S_{15} - S_{5}$ is :
Mathematics · Sequences and Series · MCQ
Q50.The area (in square units) of the region bounded by the parabola $y^{2} = 4 (x - 2)$ and the line $y = 2 x - 8$ , is :
Mathematics · Area Under the Curves · MCQ
Q51.A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics,…
Mathematics · Probability · Numerical
Q52.Let $y = y (x)$ be the solution of the differential equation $(1 - x^{2}) d y = [x y + (x^{3} + 2) 3 (1 - x^{2})] d x, - 1 < x < 1, y (0) = 0$ . If $y (\frac{1}{2}) = \frac{m}{n}, m$ …
Mathematics · Differential Equations · Numerical
Q53.The value of $9 0 \int 9 [\frac{10 x}{x + 1}] d x$ , where $[t]$ denotes the greatest integer less than or equal to $t$ , is
Mathematics · Definite Integration · Numerical
Q54.Let $α, β \in N$ be roots of the equation $x^{2} - 70 x + λ = 0$ , where $\frac{λ}{2}, \frac{λ}{3} o t in N$ . If $λ$ assumes the minimum possible value, then $\frac{( α - 1 + β - 1 ) ( λ + 35 )}{∣ α - β ∣}$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q55. $Number of integral terms in the expansion of {7^{(\frac{1}{2})} + 1 1^{(\frac{1}{6})}}^{824} is equal to .$
Mathematics · Binomial Theorem · Numerical
Q56.Let the latus rectum of the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{b ^{2}} = 1$ subtend an angle of $\frac{π}{3}$ at the centre of the hyperbola. If $b^{2}$ is equal to $\frac{l}{m} (1 + n)$ , where $l$ and $m$ …
Mathematics · Hyperbola · Numerical
Q57.If $d_{1}$ is the shortest distance between the lines $x + 1 = 2 y = - 12 z, x = y + 2 = 6 z - 6$ and $d_{2}$ is the shortest distance between the lines $\frac{x - 1}{2} = \frac{y + 8}{- 7} = \frac{z - 4}{5}, \frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 6}{- 3}$ …
Mathematics · 3D Geometry · Numerical
Q58.Let $α = 1^{2} + 4^{2} + 8^{2} + 1 3^{2} + 1 9^{2} + 2 6^{2} + \dots$ upto 10 terms and $β = \sum_{n = 1}^{10} n^{4}$ . If $4 α - β = 55 k + 40$ , then $k$ is equal to .
Mathematics · Sequences and Series · Numerical
Q59.Let $A = {1, 2, 3, \dots, 7}$ and let $P (A)$ denote the power set of $A$ . If the number of functions $f : A \to P (A)$ such that $a \in f (a), \forall a \in A$ …
Mathematics · Functions · Numerical
Q60.If the function $f (x) = {\frac{1}{∣ x ∣}, a x^{2} + 2 b, ∣ x ∣ ⩾ 2 ∣ x ∣ < 2$ is differentiable on $R$ , then $48 (a + b)$ is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical