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Mathematics · 2022 · 29 Jun · Shift 1

22 questions from this JEE Main paper

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2022 · 29 Jun · Shift 1
Mathematics

Mathematics · 2022 · 29 Jun · Shift 1

22 questions from this JEE Main paper

Probability1 questions Differential Equations2 questions Definite Integration2 questions Vector Algebra1 questions Area Under the Curves1 questions Matrices and Determinants2 questions Complex Numbers2 questions Sets and Relations1 questions Straight Lines and Pair of Straight Lines1 questions Application of Derivatives1 questions Inverse Trigonometric Functions2 questions Binomial Theorem1 questions Parabola1 questions Statistics1 questions Functions1 questions Hyperbola1 questions Permutations and Combinations1 questions

Q20.The probability that a randomly chosen 2 $\times$ 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :
Mathematics · Probability · MCQ
Q21.Let the solution curve of the differential equation $x \frac{d y}{d x} - y = y^{2} + 16 x^{2}$ , $y (1) = 3$ be $y = y (x)$ . Then y(2) is equal to:
Mathematics · Differential Equations · MCQ
Q22.Let $f : R \to R$ be a function defined by : $f (x) = {max {t^{3} - 3 t} t \leq x x^{2} + 2 x - 6;; x \leq 2 25$ where [t] is the greatest integer…
Mathematics · Definite Integration · MCQ
Q23.Let $a = α i + 3 j - k$ , $b = 3 i - β j + 4 k$ and $c = i + 2 j - 2 k$ where $\alpha ,\,\beta \in…
Mathematics · Vector Algebra · MCQ
Q24.The area enclosed by y2 = 8x and y = $2$ x that lies outside the triangle formed by y = $2$ x, x = 1, y = 2 $2$ , is equal to:
Mathematics · Area Under the Curves · MCQ
Q25.If the system of linear equations 2x + y $-$ z = 7 x $-$ 3y + 2z = 1 x + 4y + $δ$ z = k, where $δ$ , k $\in$ R has infinitely many solutions, then $δ$ + k is equal to:
Mathematics · Matrices and Determinants · MCQ
Q26.Let $α$ and $β$ be the roots of the equation x2 + (2i $-$ 1) = 0. Then, the value of | $α$ 8 + $β$ 8| is equal to :
Mathematics · Complex Numbers · MCQ
Q27.Let $A = [a_{ij}]$ be a square matrix of order 3 such that $a_{ij} = 2^{j - i}$ , for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ...... + A10 is equal to :
Mathematics · Matrices and Determinants · MCQ
Q28.Let a set A = A1 $\cup$ A2 $\cup$ ..... $\cup$ Ak, where Ai $\cap$ Aj = $ϕ$ for i $e$ j, 1 $\leq$ j, j $\leq$ k. Define the relation R from A to A by R = {(x, y) : y $\in$ Ai if and only if x $\in$ Ai, 1 $\leq$ i $\leq$ k}. Then, R is :
Mathematics · Sets and Relations · MCQ
Q29.The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle $\frac{π}{4}$ at the origin, is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square…
Mathematics · Application of Derivatives · MCQ
Q31.The domain of the function $cos^{- 1} (\frac{2 s i n ^{- 1} ( \frac{1}{4 x ^{2} - 1} )}{π})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.If the constant term in the expansion of $(3 x^{3} - 2 x^{2} + \frac{5}{x ^{5}})^{10}$ is 2k.l, where l is an odd integer, then the value of k is equal to:
Mathematics · Binomial Theorem · MCQ
Q33. $\int_{0}^{5} cos (π (x - [\frac{x}{2}])) d x$ , where [t] denotes greatest integer less than or equal to t, is equal to:
Mathematics · Definite Integration · MCQ
Q34.Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of $\frac{π}{2}$ at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} =…
Mathematics · Parabola · MCQ
Q35.Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first 4 observation are $\frac{7}{2}$ and a respectively, then (4a + x5) is equal to:
Mathematics · Statistics · MCQ
Q36.Let $S = {z \in C : ∣ z - 2∣ \leq 1, z (1 + i) + \overline{z} (1 - i) \leq 2}$ . Let $∣ z - 4 i ∣$ attains minimum and maximum values, respectively, at z1 $\in$ S and z2 $\in$ S. If $5 (∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2}) = α + β 5$ ,…
Mathematics · Complex Numbers · Numerical
Q37.Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} + {{\sqrt 2 y} \over {2{{\cos }^4}x - {{\cos }^2}x}} = x{e^{{{\tan }^{ - 1}}(\sqrt 2 \cot 2x)}},\,0 2 is equal to $\underline{\hspace{2cm}}$.
Mathematics · Differential Equations · Numerical
Q38. $50 tan (3 tan^{- 1} (\frac{1}{2}) + 2 cos^{- 1} (\frac{1}{5})) + 42 tan (\frac{1}{2} tan^{- 1} (22))$ is equal to …
Mathematics · Inverse Trigonometric Functions · Numerical
Q39.Let c, k $\in$ R. If $f (x) = (c + 1) x^{2} + (1 - c^{2}) x + 2 k$ and $f (x + y) = f (x) + f (y) - x y$ , for all x, y $\in$ R, then the value of $∣2 (f (1) + f (2) + f (3) + ...... + f (20)) ∣$ is equal to .
Mathematics · Functions · Numerical
Q40.Let $H : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ , a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4 (22 + 14)$ . If the eccentricity H is $\frac{11}{2}$ …
Mathematics · Hyperbola · Numerical
Q41.Let b1b2b3b4 be a 4-element permutation with bi $\in$ {1, 2, 3, ........, 100} for 1 $\leq$ i $\leq$ 4 and bi $e$ bj for i $e$ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of…
Mathematics · Permutations and Combinations · Numerical