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Mathematics · 2022 · 28 Jul · Shift 2

19 questions from this JEE Main paper

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2022 · 28 Jul · Shift 2
Mathematics

Mathematics · 2022 · 28 Jul · Shift 2

19 questions from this JEE Main paper

Quadratic Equation and Inequalities2 questions Matrices and Determinants1 questions Functions1 questions Limits Continuity and Differentiability1 questions Application of Derivatives1 questions Inverse Trigonometric Functions1 questions Differentiation1 questions Definite Integration2 questions Area Under the Curves1 questions Differential Equations1 questions Hyperbola1 questions Vector Algebra1 questions Probability2 questions Binomial Theorem1 questions Permutations and Combinations1 questions Complex Numbers1 questions

Q21. $Let S = {x \in [- 6, 3] - {- 2, 2} : \frac{∣ x + 3∣ - 1}{∣ x ∣ - 2} \geq 0} and T = {x \in Z : x^{2} - 7∣ x ∣ + 9 \leq 0} .$ Then the number of elements in $S \cap T$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q22.Let $α$ , $β$ be the roots of the equation $x^{2} - 2 x + 6 = 0$ and $\frac{1}{α ^{2}} + 1, \frac{1}{β ^{2}} + 1$ be the roots of the equation $x^{2} + a x + b = 0$ . Then the roots of the equation $x^{2} - (a + b - 2) x + (a + b + 2) = 0$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q23.Let $A$ and $B$ be any two $3 \times 3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?
Mathematics · Matrices and Determinants · MCQ
Q24. $Let f (x) = a x^{2} + b x + c be such that f (1) = 3, f (- 2) = λ and$ $f (3) = 4$ . If $f (0) + f (1) + f (- 2) + f (3) = 14$ , then $λ$ is equal to :
Mathematics · Functions · MCQ
Q25.The function $f : R \to R$ defined by $f (x) = n \to \infty lim \frac{c o s ( 2 π x ) - x ^{2 n} s i n ( x - 1 )}{1 + x ^{2 n + 1} - x ^{2 n}}$ is continuous for all x in :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.The function $f (x) = x e^{x (1 - x)}, x \in R$ , is :
Mathematics · Application of Derivatives · MCQ
Q27.The sum of the absolute maximum and absolute minimum values of the function $f (x) = tan^{- 1} (sin x - cos x)$ in the interval $[0, π]$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q28.Let $x (t) = 22 cos t sin 2 t$ and $y (t) = 22 sin t sin 2 t, t \in (0, \frac{π}{2})$ . Then $\frac{1 + ( \frac{d y}{d x} ) ^{2}}{\frac{d ^{2} y}{d x ^{2}}}$ at $t = \frac{π}{4}$ is equal to :
Mathematics · Differentiation · MCQ
Q29.Let $I_{n} (x) = \int_{0}^{x} \frac{1}{( t ^{2} + 5 ) ^{n}} d t, n = 1, 2, 3, \dots .$ Then :
Mathematics · Definite Integration · MCQ
Q30.The area enclosed by the curves $y = lo g_{e} (x + e^{2}), x = lo g_{e} (\frac{2}{y})$ and $x = lo g_{e} 2$ , above the line $y = 1$ is:
Mathematics · Area Under the Curves · MCQ
Q31.Let $y = y (x)$ be the solution curve of the differential equation $\frac{d y}{d x} + \frac{1}{x ^{2} - 1} y = (\frac{x - 1}{x + 1})^{1/2}$ , $x > 1$ passing through the point $(2, \frac{1}{3})$ . Then $\sqrt{7}\,…
Mathematics · Differential Equations · MCQ
Q32.Let the hyperbola $H : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ pass through the point $(22, - 22)$ . A parabola is drawn whose focus is same as the focus of $H$ with positive abscissa and the directrix of the…
Mathematics · Hyperbola · MCQ
Q33.Let S be the set of all a $u = a (lo g_{e} b) \hat{i} - 6 \hat{j} + 3 \hat{k}$ for which the angle between the vectors $u = a (lo g_{e} b) \hat{i} - 6 \hat{j} + 3 \hat{k}$ and $v = (lo g_{e} b) \hat{i} + 2 \hat{j} + 2 a (lo g_{e} b) \hat{k}$ , $(b > 1)$ …
Mathematics · Vector Algebra · MCQ
Q34.Let $A$ and $B$ be two events such that $P (B ∣ A) = \frac{2}{5}, P (A ∣ B) = \frac{1}{7}$ and $P (A \cap B) = \frac{1}{9} \cdot$ Consider (S1) $P (A^{'} \cup B) = \frac{5}{6}$ , (S2) $P (A^{'} \cap B^{'}) = \frac{1}{18}$ …
Mathematics · Probability · MCQ
Q35.Let the coefficients of the middle terms in the expansion of $(\frac{1}{6} + β x)^{4}, (1 - 3 β x)^{2}$ and $(1 - \frac{β}{2} x)^{6}, β > 0$ , respectively form the first three terms of an A.P. If…
Mathematics · Binomial Theorem · Numerical
Q36.A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then $b + 3 g$ is equal to .
Mathematics · Permutations and Combinations · Numerical
Q37.Let $z = a + ib, b e q 0$ be complex numbers satisfying $z^{2} = \overset{z}{ˉ} \cdot 2^{1 - z}$ . Then the least value of $n \in N$ , such that $z^{n} = (z + 1)^{n}$ , is equal to .
Mathematics · Complex Numbers · Numerical
Q38.A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $X$ be the number of white balls, among the drawn balls. If $σ^{2}$ is the variance of $X$ , then $100 σ^{2}$ is equal…
Mathematics · Probability · Numerical
Q39.The value of the integral $0 \int \frac{π}{2} 60 \frac{s i n ( 6 x )}{s i n x} d x$ is equal to .
Mathematics · Definite Integration · Numerical