New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematics · 2022 · 24 Jun · Shift 1

22 questions from this JEE Main paper

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Papers
2022 · 24 Jun · Shift 1
Mathematics

Mathematics · 2022 · 24 Jun · Shift 1

22 questions from this JEE Main paper

Complex Numbers1 questions Binomial Theorem1 questions Application of Derivatives3 questions Probability1 questions Matrices and Determinants1 questions Quadratic Equation and Inequalities1 questions Inverse Trigonometric Functions2 questions Sequences and Series1 questions Differential Equations1 questions Vector Algebra1 questions Functions1 questions Permutations and Combinations1 questions Straight Lines and Pair of Straight Lines1 questions 3D Geometry2 questions Limits Continuity and Differentiability1 questions Definite Integration2 questions Area Under the Curves1 questions

Q22.Let $A = {z \in C : 1 \leq ∣ z - (1 + i) ∣ \leq 2}$ and $B = {z \in A : ∣ z - (1 - i) ∣ = 1}$ . Then, B :
Mathematics · Complex Numbers · MCQ
Q23.The remainder when 32022 is divided by 5 is :
Mathematics · Binomial Theorem · MCQ
Q24.The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :
Mathematics · Application of Derivatives · MCQ
Q25.Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls…
Mathematics · Probability · MCQ
Q26.The number of values of $α$ for which the system of equations : x + y + z = $α α$ x + 2 $α$ y + 3z = $-$ 1 x + 3 $α$ y + 5z = 4 is inconsistent, is
Mathematics · Matrices and Determinants · MCQ
Q27.If the sum of the squares of the reciprocals of the roots $α$ and $β$ of the equation 3x2 + $λ$ x $-$ 1 = 0 is 15, then 6( $α$ 3 + $β$ 3)2 is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q28.The set of all values of k for which $(tan^{- 1} x)^{3} + (cot^{- 1} x)^{3} = k π^{3}, x \in R$ , is the interval :
Mathematics · Inverse Trigonometric Functions · MCQ
Q29.For the function $f (x) = 4 lo g_{e} (x - 1) - 2 x^{2} + 4 x + 5, x > 1$ , which one of the following is NOT correct?
Mathematics · Application of Derivatives · MCQ
Q30.The sum of absolute maximum and absolute minimum values of the function $f (x) = ∣2 x^{2} + 3 x - 2∣ + sin x cos x$ in the interval [0, 1] is :
Mathematics · Application of Derivatives · MCQ
Q31.If ${a_{i}}_{i = 1}^{n}$ , where n is an even integer, is an arithmetic progression with common difference 1, and $i = 1 \sum n a_{i} = 192, i = 1 \sum n /2 a_{2 i} = 120$ , then n is equal to :
Mathematics · Sequences and Series · MCQ
Q32.If x = x(y) is the solution of the differential equation $y \frac{d x}{d y} = 2 x + y^{3} (y + 1) e^{y}, x (1) = 0$ ; then x(e) is equal to :
Mathematics · Differential Equations · MCQ
Q33.Let $a$ , $b$ be unit vectors. If $c$ be a vector such that the angle between $a$ and $c$ is $\frac{π}{12}$ , and $b = c + 2 (c \times a)$ …
Mathematics · Vector Algebra · MCQ
Q34.The domain of the function $f (x) = \frac{c o s ^{- 1} ( \frac{x ^{2} - 5 x + 6}{x ^{2} - 9} )}{l o g _{e} ( x ^{2} - 3 x + 2 )}$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q35.The number of one-one functions f : {a, b, c, d} $\to$ {0, 1, 2, ......, 10} such that 2f(a) $-$ f(b) + 3f(c) + f(d) = 0 is .
Mathematics · Functions · Numerical
Q36.In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, $-$ 2 marks for each wrong answer and 0 mark if the question is not attempted. Then,…
Mathematics · Permutations and Combinations · Numerical
Q37.Let $A (\frac{3}{a}, a), a > 0$ , be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If $D (3 cos θ, a sin θ)$ is a point in the fourth quadrant…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q38.Let a line having direction ratios, 1, $-$ 4, 2 intersect the lines $\frac{x - 7}{3} = \frac{y - 1}{- 1} = \frac{z + 2}{1}$ and $\frac{x}{2} = \frac{y - 7}{3} = \frac{z}{1}$ at the points A and B. Then (AB)2 is equal to …
Mathematics · 3D Geometry · Numerical
Q39.The number of points where the function $f (x) = ⎩ ⎨ ⎧ ∣2 x^{2} - 3 x - 7∣ [4 x^{2} - 1] ∣ x + 1∣ + ∣ x - 2∣ if if if x \leq - 1 - 1 < x < 1 x \geq 1$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q40.Let $f (θ) = sin θ + - π /2 \int π /2 (sin θ + t cos θ) f (t) d t$ . Then the value of $\int_{0}^{π /2} f (θ) d θ$ is .
Mathematics · Definite Integration · Numerical
Q41.Let $0 \leq x \leq 2 M a x {\frac{9 - x ^{2}}{5 - x}} = α$ and $0 \leq x \leq 2 M in {\frac{9 - x ^{2}}{5 - x}} = β$ . If $β - \frac{8}{3} \int 2 α - 1 M a x {\frac{9 - x ^{2}}{5 - x}, x} d x = α_{1} + α_{2} lo g_{e} (\frac{8}{15})$ …
Mathematics · Definite Integration · Numerical
Q42.Let S be the region bounded by the curves y = x3 and y2 = x. The curve y = 2|x| divides S into two regions of areas R1, R2. If max {R1, R2} = R2, then $\frac{R _{2}}{R _{1}}$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q43.If the shortest distance between the lines $r = (- i + 3 k) + λ (i - a j)$ and $r = (- j + 2 k) + μ (i - j + k)$ …
Mathematics · 3D Geometry · Numerical