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Mathematics · 2023 · 31 Jan · Shift 2

22 questions from this JEE Main paper

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2023 · 31 Jan · Shift 2
Mathematics

Mathematics · 2023 · 31 Jan · Shift 2

22 questions from this JEE Main paper

Vector Algebra2 questions Functions2 questions Quadratic Equation and Inequalities1 questions Inverse Trigonometric Functions1 questions Definite Integration2 questions Statistics1 questions Sequences and Series1 questions Complex Numbers1 questions Sets and Relations1 questions Hyperbola1 questions Limits Continuity and Differentiability1 questions Differential Equations1 questions Circle1 questions Area Under the Curves1 questions Binomial Theorem2 questions Permutations and Combinations2 questions Probability1 questions

Q23.Let $a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = \hat{i} - \hat{j} + 2 \hat{k}$ and $c = 5 \hat{i} - 3 \hat{j} + 3 \hat{k}$ be three vectors. If $r$ is a vector such that, $r \times b = c \times b$ and $r \cdot a = 0$ …
Mathematics · Vector Algebra · MCQ
Q24.Let $f : R - {2, 6} \to R$ be real valued function defined as $f (x) = \frac{x ^{2} + 2 x + 1}{x ^{2} - 8 x + 12}$ . Then range of $f$ is
Mathematics · Functions · MCQ
Q25.The equation $e^{4 x} + 8 e^{3 x} + 13 e^{2 x} - 8 e^{x} + 1 = 0, x \in R$ has :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q26.Let (a, b) $\subset (0, 2 π)$ be the largest interval for which $sin^{- 1} (sin θ) - cos^{- 1} (sin θ) > 0, θ \in (0, 2 π)$ , holds. If $α x^{2} + β x + sin^{- 1} (x^{2} - 6 x + 10) + cos^{- 1} (x^{2} - 6 x + 10) = 0$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q27.Let $α > 0$ . If $0 \int α \frac{x}{x + α - x} d x = \frac{16 + 20 2}{15}$ , then $α$ is equal to :
Mathematics · Definite Integration · MCQ
Q28.Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $α (>$ 0 ), and the mean and standard deviation of marks of class $B$ of $n$ students be respectively 55 and 30 $- α$ . If the mean and…
Mathematics · Statistics · MCQ
Q29.Let $a_{1}, a_{2}, a_{3}, \dots$ be an A.P. If $a_{7} = 3$ , the product $a_{1} a_{4}$ is minimum and the sum of its first $n$ terms is zero, then $n! - 4 a_{n (n + 2)}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q30.The complex number $z = \frac{i - 1}{c o s \frac{π}{3} + i s i n \frac{π}{3}}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q31.Among the relations $S = {(a, b) : a, b \in R - {0}, 2 + \frac{a}{b} > 0}$ and $T = {(a, b) : a, b \in R, a^{2} - b^{2} \in Z}$ …
Mathematics · Sets and Relations · MCQ
Q32.The absolute minimum value, of the function $f (x) = x^{2} - x + 1 + [x^{2} - x + 1]$ , where $[t]$ denotes the greatest integer function, in the interval $[- 1, 2]$ , is :
Mathematics · Functions · MCQ
Q33.If $ϕ (x) = \frac{1}{x} \frac{π}{4} \int x (42 sin t - 3 ϕ^{'} (t)) d t, x > 0$ , then $\emptyset^{'} (\frac{π}{4})$ is equal to :
Mathematics · Definite Integration · MCQ
Q34.Let $H$ be the hyperbola, whose foci are $(1 \pm 2, 0)$ and eccentricity is $2$ . Then the length of its latus rectum is :
Mathematics · Hyperbola · MCQ
Q35. $x \to \infty lim \frac{( 3 x + 1 + 3 x - 1 ) ^{6} + ( 3 x + 1 - 3 x - 1 ) ^{6}}{( x + x ^{2} - 1 ) ^{6} + ( x - x ^{2} - 1 ) ^{6}} x^{3}$
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.Let $y = y (x)$ be the solution of the differential equation $(3 y^{2} - 5 x^{2}) y d x + 2 x (x^{2} - y^{2}) d y = 0$ such that $y (1) = 1$ . Then $(y (2))^{3} - 12 y (2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q37.The set of all values of $a^{2}$ for which the line $x + y = 0$ bisects two distinct chords drawn from a point $P (\frac{1 + a}{2}, \frac{1 - a}{2})$ on the circle $2 x^{2} + 2 y^{2} - (1 + a) x - (1 - a) y = 0$ , is equal to :
Mathematics · Circle · MCQ
Q38.Let the area of the region ${(x, y) : ∣2 x - 1∣ \leq y \leq x^{2} - x, 0 \leq x \leq 1}$ be $A$ . Then $(6 A + 11)^{2}$ is equal to
Mathematics · Area Under the Curves · Numerical
Q39.The coefficient of $x^{- 6}$ , in the expansion of $(\frac{4 x}{5} + \frac{5}{2 x ^{2}})^{9}$ , is
Mathematics · Binomial Theorem · Numerical
Q40.Let $A = [a_{ij}], a_{ij} \in Z \cap [0, 4], 1 \leq i, j \leq 2$ . The number of matrices A such that the sum of all entries is a prime number $p \in (2, 13)$ is .
Mathematics · Permutations and Combinations · Numerical
Q41.If $^{2 n + 1} P_{n - 1} :^{2 n - 1} P_{n} = 11 : 21$ , then $n^{2} + n + 15$ is equal to :
Mathematics · Permutations and Combinations · Numerical
Q42.Let $a, b, c$ be three vectors such that $∣ a ∣ = 31, 4∣ b ∣ = ∣ c ∣ = 2$ and $2 (a \times b) = 3 (c \times a)$ . If the angle between $b$ and $c$ is $\frac{2 π}{3}$ , then $(\frac{a \times c}{a \cdot b})^{2}$ …
Mathematics · Vector Algebra · Numerical
Q43.Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0, 60]$ is less than or equal to a . If $P (A) = \frac{11}{36}$ , then $a$ is equal to …
Mathematics · Probability · Numerical
Q44.If the constant term in the binomial expansion of $(\frac{x ^{\frac{5}{2}}}{2} - \frac{4}{x ^{l}})^{9}$ is $- 84$ and the coefficient of $x^{- 3 l}$ is $2^{α} β$ , where $β < 0$ is an odd number, then $∣ α l - β ∣$ …
Mathematics · Binomial Theorem · Numerical