New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2023 · 8 Apr · Shift 2

20 questions from this JEE Main paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2023 · 8 Apr · Shift 2
Mathematics

Mathematics · 2023 · 8 Apr · Shift 2

20 questions from this JEE Main paper

Complex Numbers1 questions Binomial Theorem2 questions Indefinite Integrals1 questions Probability1 questions Sets and Relations1 questions Statistics1 questions Vector Algebra1 questions Permutations and Combinations1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability2 questions Trigonometric Ratio and Identites1 questions Definite Integration1 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions Functions2 questions Differential Equations1 questions

Q22.Let $A = {θ \in (0, 2 π) : \frac{1 + 2 i s i n θ}{1 - i s i n θ}$ is purely imaginary $}$ . Then the sum of the elements in $A$ is :
Mathematics · Complex Numbers · MCQ
Q23. $2 5^{190} - 1 9^{190} - 8^{190} + 2^{190}$ is divisible by :
Mathematics · Binomial Theorem · MCQ
Q24.The integral $\int [(\frac{x}{2})^{x} + (\frac{2}{x})^{x}] ln (\frac{e x}{2}) d x$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q25.If the probability that the random variable $X$ takes values $x$ is given by $P (X = x) = k (x + 1) 3^{- x}, x = 0, 1, 2, 3, \dots$ , where $k$ is a constant, then $P (X \geq 2)$ is equal…
Mathematics · Probability · MCQ
Q26.Let $A = {1, 2, 3, 4, 5, 6, 7}$ . Then the relation $R = {(x, y) \in A \times A : x + y = 7}$ is :
Mathematics · Sets and Relations · MCQ
Q27.Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{m}{n}$ , where…
Mathematics · Statistics · MCQ
Q28.The absolute difference of the coefficients of $x^{10}$ and $x^{7}$ in the expansion of $(2 x^{2} + \frac{1}{2 x})^{11}$ is equal to :
Mathematics · Binomial Theorem · MCQ
Q29.The area of the quadrilateral $ABCD$ with vertices $A (2, 1, 1), B (1, 2, 5), C (- 2, - 3, 5)$ and $D (1, - 6, - 7)$ is equal to :
Mathematics · Vector Algebra · MCQ
Q30.If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which $C$ and $S$ do not come together, is $(6!) k$ , then $k$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q31.If $A = [1 λ 510], A^{- 1} = α A + β I$ and $α + β = - 2$ , then $4 α^{2} + β^{2} + λ^{2}$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q32.If $α > β > 0$ are the roots of the equation $a x^{2} + b x + 1 = 0$ , and $lim_{x \to \frac{1}{α}} (\frac{1 - c o s ( x ^{2} + b x + a )}{2 ( 1 - α x ) ^{2}})^{\frac{1}{2}} = \frac{1}{k} (\frac{1}{β} - \frac{1}{α}), then k is equal to$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q33.The value of $36 (4 cos^{2} 9^{\circ} - 1) (4 cos^{2} 2 7^{\circ} - 1) (4 cos^{2} 8 1^{\circ} - 1) (4 cos^{2} 24 3^{\circ} - 1)$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.Let S be the set of all values of $θ \in [- π, π]$ for which the system of linear equations $x + y + 3 z = 0 - x + (tan θ) y + 7 z = 0 x + y + (tan θ) z = 0$ has non-trivial solution. Then $\frac{120}{π} \sum_{θ \in s} θ$ …
Mathematics · Matrices and Determinants · MCQ
Q35.Let $[t]$ denote the greatest integer function. If $\int_{0}^{2.4} [x^{2}] d x = α + β 2 + γ 3 + δ 5$ , then $α + β + γ + δ$ is equal to .
Mathematics · Definite Integration · Numerical
Q36.Let the area enclosed by the lines $x + y = 2, y = 0, x = 0$ and the curve $f (x) = min {x^{2} + \frac{3}{4}, 1 + [x]}$ where $[x]$ denotes the greatest integer $A$ , be $A$ . Then the value of is …
Mathematics · Area Under the Curves · Numerical
Q37.Let m and $n$ be the numbers of real roots of the quadratic equations $x^{2} - 12 x + [x] + 31 = 0$ and $x^{2} - 5∣ x + 2∣ - 4 = 0$ respectively, where $[x]$ denotes the greatest integer $m^{2} + mn + n^{2}$ . Then $m^{2} + mn + n^{2}$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q38.Let $R = {a, b, c, d, e}$ and $S = {1, 2, 3, 4}$ . Total number of onto functions $f : R \to S$ such that $f (a) e q 1$ , is equal to …
Mathematics · Functions · Numerical
Q39.Let $k$ and $m$ be positive real numbers such that the function $f (x) = {3 x^{2} + k x + 1, m x^{2} + k^{2}, 0 < x < 1 x \geq 1$ is differentiable for all $x > 0$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.Let the solution curve $x = x (y), 0 < y < \frac{π}{2}$ , of the differential equation $(lo g_{e} (cos y))^{2} cos y d x - (1 + 3 x lo g_{e} (cos y)) sin y d y = 0$ satisfy $x (\frac{π}{3}) = \frac{1}{2 l o g _{e} 2}$ …
Mathematics · Differential Equations · Numerical
Q41.If domain of the function $lo g_{e} (\frac{6 x ^{2} + 5 x + 1}{2 x - 1}) + cos^{- 1} (\frac{2 x ^{2} - 3 x + 4}{3 x - 5})$ is $(α, β) \cup (γ, δ]$ , then…
Mathematics · Functions · Numerical