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Mathematics · 2023 · 6 Apr · Shift 1

20 questions from this JEE Main paper

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2023 · 6 Apr · Shift 1
Mathematics

Mathematics · 2023 · 6 Apr · Shift 1

20 questions from this JEE Main paper

Quadratic Equation and Inequalities2 questions Matrices and Determinants2 questions Straight Lines and Pair of Straight Lines1 questions 3D Geometry1 questions Statistics1 questions Definite Integration1 questions Indefinite Integrals1 questions Vector Algebra1 questions Limits Continuity and Differentiability2 questions Binomial Theorem1 questions Differentiation1 questions Differential Equations1 questions Area Under the Curves1 questions Circle2 questions Sets and Relations1 questions Permutations and Combinations1 questions

Q23.Let $A = {x \in R : [x + 3] + [x + 4] \leq 3},$ $B = {x \in R : 3^{x} (r = 1 \sum \infty \frac{3}{10 ^{r}})^{x - 3} < 3^{- 3 x}},$ where [t] denotes greatest integer function. Then,
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.If the system of equations $x + y + a z = b 2 x + 5 y + 2 z = 6 x + 2 y + 3 z = 3$ has infinitely many solutions, then $2 a + 3 b$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q25.The straight lines $l_{1}$ and $l_{2}$ pass through the origin and trisect the line segment of the line L : $9 x + 5 y = 45$ between the axes. If $m_{1}$ and $m_{2}$ are the slopes of the lines $l_{1}$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q26.One vertex of a rectangular parallelopiped is at the origin $O$ and the lengths of its edges along $z$ and $z$ axes are $5$ and $5$ units respectively. Let $P$ be the vertex $(3, 4, 5)$ . Then the shortest distance…
Mathematics · 3D Geometry · MCQ
Q27.The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and $σ^{2}$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then $σ^{2}$ …
Mathematics · Statistics · MCQ
Q28.Let $A = [a_{ij}]_{2 \times 2}$ , where $a_{ij} e q 0$ for all $A^{2} = I$ and $A^{2} = I$ . Let a be the sum of all diagonal elements of $A$ and $b = ∣ A ∣$ …
Mathematics · Matrices and Determinants · MCQ
Q29.Let $5 f (x) + 4 f (\frac{1}{x}) = \frac{1}{x} + 3, x > 0$ . Then $18 \int_{1}^{2} f (x) d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q30.Let $I (x) = \int \frac{x ^{2} ( x s e c ^{2} x + t a n x )}{( x t a n x + 1 ) ^{2}} d x$ . If $I (0) = 0$ , then $I (\frac{π}{4})$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q31.Let $a = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}, b = \hat{i} - 2 \hat{j} - 2 \hat{k}$ and $c = - \hat{i} + 4 \hat{j} + 3 \hat{k}$ . If $d$ is a vector perpendicular to both $b$ and $c$ , and $a \cdot d = 18$ , then $∣ a \times d ∣^{2}$ …
Mathematics · Vector Algebra · MCQ
Q32.Let $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ be $n$ positive consecutive terms of an arithmetic progression. If $d > 0$ is its common difference, then $lim_{n \to \infty} \frac{d}{n} (\frac{1}{a _{1} + a _{2}} + \frac{1}{a _{2} + a _{3}} + \dots\dots\dots + \frac{1}{a _{n - 1} + a _{n}})$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.The sum of all the roots of the equation $x^{2} - 8 x + 15 - 2 x + 7 = 0$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $(42 + \frac{1}{4 3})^{n}$ is $6 : 1$ , then the third term from the beginning is :
Mathematics · Binomial Theorem · MCQ
Q35.If $2 x^{y} + 3 y^{x} = 20$ , then $\frac{d y}{d x}$ at $(2, 2)$ is equal to :
Mathematics · Differentiation · MCQ
Q36.Let $y = y (x)$ be a solution of the differential equation $(x cos x) d y + (x y sin x + y cos x - 1) d x = 0, 0 < x < \frac{π}{2}$ . If $\frac{π}{3} y (\frac{π}{3}) = 3$ , then $\frac{π}{6} y^{''} (\frac{π}{6}) + 2 y^{'} (\frac{π}{6})$ …
Mathematics · Differential Equations · Numerical
Q37.If the area of the region $S = {(x, y) : 2 y - y^{2} \leq x^{2} \leq 2 y, x \geq y}$ is equal to $\frac{n + 2}{n + 1} - \frac{π}{n - 1}$ , then the natural number $n$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q38.Let the point $(p, p + 1)$ lie inside the region $E = {(x, y) : 3 - x \leq y \leq 9 - x^{2}, 0 \leq x \leq 3}$ . If the set of all values of $p$ is the interval $(a, b)$ , then $b^{2} + b - a^{2}$ is equal to …
Mathematics · Circle · Numerical
Q39.Let $a \in Z$ and $[t]$ be the greatest integer $f (x) = [a + 13 sin x], x \in (0, π)$ . Then the number of points, where the function $f (x) = [a + 13 sin x], x \in (0, π)$ is not differentiable, is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.Let $A = {1, 2, 3, 4, \dots ., 10}$ and $B = {0, 1, 2, 3, 4}$ . The number of elements in the relation $R = {(a, b) \in A \times A : 2 (a - b)^{2} + 3 (a - b) \in B}$ is .
Mathematics · Sets and Relations · Numerical
Q41.A circle passing through the point $P (α, β)$ in the first quadrant touches the two coordinate axes at the points $A$ and $B$ . The point $P$ is above the line $A B$ . The point $Q$ on the line segment $A B$ is the foot of…
Mathematics · Circle · Numerical
Q42.The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is .
Mathematics · Permutations and Combinations · Numerical