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Mathematics · 2022 · 25 Jul · Shift 2

23 questions from this JEE Main paper

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2022 · 25 Jul · Shift 2
Mathematics

Mathematics · 2022 · 25 Jul · Shift 2

23 questions from this JEE Main paper

Complex Numbers1 questions Matrices and Determinants2 questions Functions2 questions Binomial Theorem1 questions Limits Continuity and Differentiability1 questions Probability1 questions Definite Integration3 questions Straight Lines and Pair of Straight Lines1 questions Ellipse1 questions Hyperbola1 questions 3D Geometry1 questions Vector Algebra1 questions Statistics1 questions Trigonometric Ratio and Identites1 questions Sets and Relations1 questions Application of Derivatives1 questions Differential Equations1 questions Area Under the Curves1 questions Inverse Trigonometric Functions1 questions

Q23.For $z \in C$ if the minimum value of $(∣ z - 32 ∣ + ∣ z - p 2 i ∣)$ is $52$ , then a value Question: of $p$ is .
Mathematics · Complex Numbers · MCQ
Q24.The number of real values of $λ$ , such that the system of linear equations 2x $-$ 3y + 5z = 9 x + 3y $-$ z = $-$ 18 3x $-$ y + ( $λ$ 2 $-$ | $λ$ |)z = 16 has no solutions, is
Mathematics · Matrices and Determinants · MCQ
Q25.The number of bijective functions $f : {1, 3, 5, 7, \dots, 99} \to {2, 4, 6, 8, \dots .100}$ , such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \dots .. f (99)$ , is .
Mathematics · Functions · MCQ
Q26.The remainder when $(11)^{1011} + (1011)^{11}$ is divided by 9 is
Mathematics · Binomial Theorem · MCQ
Q27. $x \to \frac{π}{4} lim \frac{8 2 - ( c o s x + s i n x ) ^{7}}{2 - 2 s i n 2 x}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.If $A$ and $B$ are two events such that $P (A) = \frac{1}{3}, P (B) = \frac{1}{5}$ and $P (A \cup B) = \frac{1}{2}$ , then $P (A ∣ B^{'}) + P (B ∣ A^{'})$ is equal to :
Mathematics · Probability · MCQ
Q29.Let $[t]$ denote the greatest integer less than or equal to $t$ . Then the value of the integral $\int_{- 3}^{101} ([sin (π x)] + e^{[c o s (2 π x)]}) d x$ is equal to
Mathematics · Definite Integration · MCQ
Q30.Let the point $P (α, β)$ be at a unit distance from each of the two lines $L_{1} : 3 x - 4 y + 12 = 0$ , and $L_{2} : 8 x + 6 y + 11 = 0$ . If $P$ lies below $L_{1}$ and above $L_{2}$ , then $100 (α + β)$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.If the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ meets the line $\frac{x}{7} + \frac{y}{2 6} = 1$ on the $x$ -axis and the line $\frac{x}{7} - \frac{y}{2 6} = 1$ on the $y$ -axis, then the eccentricity of the ellipse is :
Mathematics · Ellipse · MCQ
Q32.Let the foci of the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{7} = 1$ and the hyperbola $\frac{x ^{2}}{144} - \frac{y ^{2}}{α} = \frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is :
Mathematics · Hyperbola · MCQ
Q33.The shortest distance between the lines $\frac{x + 7}{- 6} = \frac{y - 6}{7} = z$ and $\frac{7 - x}{2} = y - 2 = z - 6$ is :
Mathematics · 3D Geometry · MCQ
Q34.Let $a = \hat{i} - \hat{j} + 2 \hat{k}$ and let $b$ be a vector such that $a \times b = 2 \hat{i} - \hat{k}$ and $a \cdot b = 3$ . Then the projection of $b$ on the vector $a - b$ is :
Mathematics · Vector Algebra · MCQ
Q35.If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :
Mathematics · Statistics · MCQ
Q36. $2 sin (\frac{π}{22}) sin (\frac{3 π}{22}) sin (\frac{5 π}{22}) sin (\frac{7 π}{22}) sin (\frac{9 π}{22})$ is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q37.Let $A = {1, 2, 3, 4, 5, 6, 7}$ . Define $B = {T \subseteq A$ : either $1 o t in T$ or $2 \in T}$ and $C = {T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $}$ . Then the number of elements in the set $B \cup C$ is …
Mathematics · Sets and Relations · Numerical
Q38.Let $f (x)$ be a quadratic polynomial with leading coefficient 1 such that $f (0) = p, p e q 0$ , and $f (1) = \frac{1}{3}$ . If the equations $f (x) = 0$ and $f \circ f \circ f \circ f (x) = 0$ have a common real root, then $f (- 3)$ is equal to …
Mathematics · Functions · Numerical
Q39.Let $A = 100 a 10 a b 1, a, b \in R$ . If for some $n \in N, A^{n} = 10048102160961$ …
Mathematics · Matrices and Determinants · Numerical
Q40.The sum of the maximum and minimum values of the function $f (x) = ∣5 x - 7∣ + [x^{2} + 2 x]$ in the interval $[\frac{5}{4}, 2]$ , where $[t]$ is the greatest integer , is .
Mathematics · Application of Derivatives · Numerical
Q41.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = \frac{4 y ^{3} + 2 y x ^{2}}{3 x y ^{2} + x ^{3}}, y (1) = 1$ . If for some $n \in N, y (2) \in [n - 1, n)$ , then $n$ is equal to .
Mathematics · Differential Equations · Numerical
Q42.Let $f$ be a twice differentiable function on $R$ . If $f^{'} (0) = 4$ and $f (x) + 0 \int x (x - t) f^{'} (t) d t = (e^{2 x} + e^{- 2 x}) cos 2 x + \frac{2}{a} x$ , then $(2 a + 1)^{5} a^{2}$ is equal to …
Mathematics · Definite Integration · Numerical
Q43.Let $a_{n} = - 1 \int n (1 + \frac{x}{2} + \frac{x ^{2}}{3} + ..... + \frac{x ^{n - 1}}{n}) d x$ for every n $\in$ N. Then the sum of all the elements of the set {n} $\in$ N : an $\in$ (2, 30)} is …
Mathematics · Definite Integration · Numerical
Q44.Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve $4 x^{3} - 3 x y^{2} + 6 x^{2} - 5 x y - 8 y^{2} + 9 x + 14 = 0$ at the point ( $-$ 2, 3) be A. Then 8A is equal to .
Mathematics · Area Under the Curves · Numerical
Q45.Let $x = sin (2 tan^{- 1} α)$ and $y = sin (\frac{1}{2} tan^{- 1} \frac{4}{3})$ . If $S = {a \in R : y^{2} = 1 - x}$ , then $α \in S \sum 16 α^{3}$ is equal to …
Mathematics · Inverse Trigonometric Functions · Numerical