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Mathematics · 2022 · 29 Jul · Shift 2

21 questions from this JEE Main paper

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2022 · 29 Jul · Shift 2
Mathematics

Mathematics · 2022 · 29 Jul · Shift 2

21 questions from this JEE Main paper

Complex Numbers2 questions Matrices and Determinants3 questions Limits Continuity and Differentiability2 questions Definite Integration1 questions Indefinite Integrals1 questions Differential Equations2 questions Straight Lines and Pair of Straight Lines2 questions Probability1 questions Vector Algebra2 questions Inverse Trigonometric Functions1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Circle2 questions

Q23.If $z e q 0$ be a complex number such that $z - \frac{1}{z} = 2$ , then the maximum value of $∣ z ∣$ is :
Mathematics · Complex Numbers · MCQ
Q24.Which of the following matrices can NOT be obtained from the matrix $[- 1 1 2 - 1]$ by a single elementary row operation ?
Mathematics · Matrices and Determinants · MCQ
Q25.If the system of equations $x + y + z = 6 2 x + 5 y + α z = β x + 2 y + 3 z = 14$ has infinitely many solutions, then $α + β$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q26. $Let the function f (x) = {\frac{l o g _{e} ( 1 + 5 x ) - l o g _{e} ( 1 + α x )}{x} 10; if x e q 0; if x = 0 be continuous at x = 0.$ Then $α$ is…
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.If $[t]$ denotes the greatest integer $\int_{0}^{1} [2 x - 3 x^{2} - 5 x + 2 + 1] d x$ , then the value of $\int_{0}^{1} [2 x - 3 x^{2} - 5 x + 2 + 1] d x$ is :
Mathematics · Definite Integration · MCQ
Q28.For $I (x) = \int \frac{s e c ^{2} x - 2022}{s i n ^{2022} x} d x$ , if $I (\frac{π}{4}) = 2^{1011}$ , then
Mathematics · Indefinite Integrals · MCQ
Q29.If the solution curve of the differential equation $\frac{d y}{d x} = \frac{x + y - 2}{x - y}$ passes through the points $(2, 1)$ and $(k + 1, 2), k > 0$ , then
Mathematics · Differential Equations · MCQ
Q30.Let $y = y (x)$ be the solution curve of the differential equation $\frac{d y}{d x} + (\frac{2 x ^{2} + 11 x + 13}{x ^{3} + 6 x ^{2} + 11 x + 6}) y = \frac{( x + 3 )}{x + 1}, x > - 1$ , which passes through the point $(0, 1)$ . Then $y (1)$ is equal to :
Mathematics · Differential Equations · MCQ
Q31.Let $m_{1}, m_{2}$ be the slopes of two adjacent sides of a square of side a such that $a^{2} + 11 a + 3 (m_{1}^{2} + m_{2}^{2}) = 220$ . If one vertex of the square is $(10 (cos α - sin α), 10 (sin α + cos α))$ ,…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q32.Let $A (α, - 2), B (α, 6)$ and $C (\frac{α}{4}, - 2)$ be vertices of a $△ ABC$ . If $(5, \frac{α}{4})$ is the circumcentre of $△ ABC$ , then…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then…
Mathematics · Probability · MCQ
Q34.Let $S = {z = x + i y : ∣ z - 1 + i ∣ \geq ∣ z ∣, ∣ z ∣ < 2, ∣ z + i ∣ = ∣ z - 1∣}$ . Then the set of all values of $x$ , for which $w = 2 x + i y \in S$ for some $y \in R$ , is :
Mathematics · Complex Numbers · MCQ
Q35.Let $a, b, c$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and $(a \times b) \cdot (b \times c) + (b \times c) \cdot (c \times a) + (c \times a) \cdot (a \times b) = 168$ …
Mathematics · Vector Algebra · MCQ
Q36.The domain of the function $f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q37.Let $α, β (α > β)$ be the roots of the quadratic equation $x^{2} - x - 4 = 0.$ If $P_{n} = α^{n} - β^{n}$ , $n \in N$ , then $\frac{P _{15} P _{16} - P _{14} P _{16} - P _{15}^{2} + P _{14} P _{15}}{P _{13} P _{14}}$ is equal…
Mathematics · Quadratic Equation and Inequalities · Numerical
Q38.Let $X = 111$ and $A = - 1 00 210 36 - 1$ . For $k \in N$ , if $X^{'} A^{k} X = 33$ , then $k$ …
Mathematics · Matrices and Determinants · Numerical
Q39.The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $2, 3, 4, 5, 6$ (repetition of digits is not allowed) and divisible by 55 is .
Mathematics · Permutations and Combinations · Numerical
Q40.If $[t]$ denotes the greatest integer $f (x) = 4∣2 x + 3∣ + 9 [x + \frac{1}{2}] - 12 [x + 20]$ , then the number of points, at which the function $f (x) = 4∣2 x + 3∣ + 9 [x + \frac{1}{2}] - 12 [x + 20]$ is not differentiable in the open interval $(- 20, 20)$ , is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q41.Let $A B$ be a chord of length 12 of the circle $(x - 2)^{2} + (y + 1)^{2} = \frac{169}{4}$ . If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$ , then five times the distance of point $P$ from chord $A B$ is equal to …
Mathematics · Circle · Numerical
Q42.Let $a$ and $b$ be two vectors such that $∣ a + b ∣^{2} = ∣ a ∣^{2} + 2∣ b ∣^{2}, a \cdot b = 3$ and $∣ a \times b ∣^{2} = 75$ . Then $∣ a ∣^{2}$ is equal to .
Mathematics · Vector Algebra · Numerical
Q43. $Let S = {(x, y) \in N \times N : 9 (x - 3)^{2} + 16 (y - 4)^{2} \leq 144}$ and $T = {(x, y) \in R \times R : (x - 7)^{2} + (y - 4)^{2} \leq 36}$ . Then $n (S \cap T)$ is equal to …
Mathematics · Circle · Numerical