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Mathematics · 2023 · 30 Jan · Shift 2

22 questions from this JEE Main paper

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2023 · 30 Jan · Shift 2
Mathematics

Mathematics · 2023 · 30 Jan · Shift 2

22 questions from this JEE Main paper

Inverse Trigonometric Functions1 questions Matrices and Determinants1 questions Permutations and Combinations2 questions Statistics1 questions Sequences and Series1 questions Limits Continuity and Differentiability1 questions Area Under the Curves2 questions Application of Derivatives1 questions Parabola1 questions Vector Algebra1 questions Functions2 questions Differential Equations1 questions Binomial Theorem2 questions Quadratic Equation and Inequalities1 questions Circle1 questions 3D Geometry1 questions Probability1 questions Indefinite Integrals1 questions

Q23.Let $a_{1} = 1, a_{2}, a_{3}, a_{4}, \dots .$ . be consecutive natural numbers. Then $tan^{- 1} (\frac{1}{1 + a _{1} a _{2}}) + tan^{- 1} (\frac{1}{1 + a _{2} a _{3}}) + \dots .. + tan^{- 1} (\frac{1}{1 + a _{2021} a _{2022}})$ …
Mathematics · Inverse Trigonometric Functions · Multiple correct
Q24.For $α, β \in R$ , suppose the system of linear equations $x - y + z = 5 2 x + 2 y + α z = 8 3 x - y + 4 z = β$ has infinitely many solutions. Then $α$ and $β$ are…
Mathematics · Matrices and Determinants · MCQ
Q25.The number of ways of selecting two numbers $a$ and $b, a \in {2, 4, 6, \dots ., 100}$ and $b \in {1, 3, 5, \dots .., 99}$ such that 2 is the remainder when $a + b$ is divided by 23 is :
Mathematics · Permutations and Combinations · MCQ
Q26.Let $S$ be the set of all values of $a_{1}$ for which the mean deviation about the mean of 100 consecutive positive integers $a_{1}, a_{2}, a_{3}, \dots ., a_{100}$ is 25 . Then $S$ is :
Mathematics · Statistics · MCQ
Q27.Let $a, b, c > 1, a^{3}, b^{3}$ and $c^{3}$ be in A.P., and $lo g_{a} b, lo g_{c} a$ and $lo g_{b} c$ be in G.P. If the sum of first 20 terms of an A.P., whose first term is $\frac{a + 4 b + c}{3}$ and the common difference is $\frac{a - 8 b + c}{10}$ is $- 444$ …
Mathematics · Sequences and Series · MCQ
Q28.Let $h$ and $h$ be the real valued functions defined on $R$ as $f (x) = {\frac{x}{∣ x ∣}, 1, x e q 0 x = 0 g (x) = {\frac{s i n ( x + 1 )}{( x + 1 )}, 1, x e q - 1 x = - 1$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.Let $q$ be the maximum integral value of $p$ in $[0, 10]$ for which the roots of the equation $x^{2} - p x + \frac{5}{4} p = 0$ are rational. Then the area of the region ${(x, y) : 0 \leq y \leq (x - q)^{2}, 0 \leq x \leq q}$ is :
Mathematics · Area Under the Curves · MCQ
Q30.If the functions $f (x) = \frac{x ^{3}}{3} + 2 b x + \frac{a x ^{2}}{2}$ and $g (x) = \frac{x ^{3}}{3} + a x + b x^{2}, a e q 2 b$ have a common extreme point, then $a + 2 b + 7$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q31.The parabolas : $a x^{2} + 2 b x + cy = 0$ and $d x^{2} + 2 e x + f y = 0$ intersect on the line $y = 1$ . If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in G.P., then :
Mathematics · Parabola · MCQ
Q32.Let $a$ and $b$ be two vectors, Let $∣ a ∣ = 1, ∣ b ∣ = 4$ and $a \cdot b = 2$ . If $c = (2 a \times b) - 3 b$ , then the value of $b \cdot c$ is :
Mathematics · Vector Algebra · MCQ
Q33.The range of the function $f (x) = 3 - x + 2 + x$ is :
Mathematics · Functions · MCQ
Q34.The solution of the differential equation $\frac{d y}{d x} = - (\frac{x ^{2} + 3 y ^{2}}{3 x ^{2} + y ^{2}}), y (1) = 0$ is :
Mathematics · Differential Equations · MCQ
Q35.Let $x = (83 + 13)^{13}$ and $y = (72 + 9)^{9}$ . If $[t]$ denotes the greatest integer $\leq t$ , then :
Mathematics · Binomial Theorem · MCQ
Q36.Let $A = {1, 2, 3, 5, 8, 9}$ . Then the number of possible functions $f : A \to A$ such that $f (m \cdot n) = f (m) \cdot f (n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to .
Mathematics · Functions · Numerical
Q37.The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is .
Mathematics · Permutations and Combinations · Numerical
Q38.Let $A$ be the area of the region ${(x, y) : y \geq x^{2}, y \geq (1 - x)^{2}, y \leq 2 x (1 - x)}$ . Then $540 A$ is equal to :
Mathematics · Area Under the Curves · Numerical
Q39.If the value of real number $a > 0$ for which $x^{2} - 5 a x + 1 = 0$ and $x^{2} - a x - 5 = 0$ have a common real root is $\frac{3}{2 β}$ then $β$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q40.Let $P (a_{1}, b_{1})$ and $Q (a_{2}, b_{2})$ be two distinct points on a circle with center $C (2, 3)$ . Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$ . If…
Mathematics · Circle · Numerical
Q41.Let a line $L$ pass through the point $P (2, 3, 1)$ and be parallel to the line $x + 3 y - 2 z - 2 = 0 = x - y + 2 z$ . If the distance of $L$ from the point $(5, 3, 8)$ is $α$ , then $3 α^{2}$ is equal to :
Mathematics · 3D Geometry · Numerical
Q42.A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the…
Mathematics · Probability · Numerical
Q43.If $\int sec 2 x - 1 d x = α lo g_{e} cos 2 x + β + cos 2 x (1 + cos \frac{1}{β} x) +$ constant, then $β - α$ is equal to .
Mathematics · Indefinite Integrals · Numerical
Q44. $5 0^{th}$ root of a number $x$ is 12 and $5 0^{th}$ root of another number $y$ is 18 . Then the remainder obtained on dividing $(x + y)$ by 25 is .
Mathematics · Binomial Theorem · Numerical