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 · 28 Jun · Shift 1

19 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 · 28 Jun · Shift 1
Mathematics

Mathematics · 2022 · 28 Jun · Shift 1

19 questions from this JEE Main paper

Functions1 questions Matrices and Determinants1 questions Permutations and Combinations1 questions Sequences and Series2 questions Definite Integration1 questions Limits Continuity and Differentiability1 questions Area Under the Curves1 questions Differential Equations2 questions Application of Derivatives1 questions Probability1 questions Sets and Relations1 questions Quadratic Equation and Inequalities1 questions Statistics1 questions Vector Algebra1 questions Straight Lines and Pair of Straight Lines1 questions Binomial Theorem1 questions Complex Numbers1 questions

Q24.Let a function f : N $\to$ N be defined by $f (n) = 2 n, n - 1, \frac{n + 1}{2}, n = 2, 4, 6, 8, ...... n = 3, 7, 11, 15, ...... n = 1, 5, 9, 13, ......$ then, f is
Mathematics · Functions · MCQ
Q25.If the system of linear equations $2 x + 3 y - z = - 2 x + y + z = 4 x - y + ∣ λ ∣ z = 4 λ - 4$ where, $λ \in$ R, has no solution, then
Mathematics · Matrices and Determinants · MCQ
Q26.The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :
Mathematics · Permutations and Combinations · MCQ
Q27.Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = $\frac{1}{1296}$ and A2 + A4 = $\frac{7}{36}$ , then the value of A6 + A8 + A10 is equal to
Mathematics · Sequences and Series · MCQ
Q28.Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral $0 \int 1 [- 8 x^{2} + 6 x - 1] d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q29.Let f : R $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ [e^{x}], a e^{x} + [x - 1], b + [sin (π x)], [e^{- x}] - c, x < 0 0 \leq x < 1 1 \leq x < 2 x \geq 2$ where a, b, c $\in$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q30.The area of the region S = {(x, y) : y2 $\leq$ 8x, y $\geq 2$ x, x $\geq$ 1} is
Mathematics · Area Under the Curves · MCQ
Q31.Let the solution curve $y = y (x)$ of the differential equation $[\frac{x}{x ^{2} - y ^{2}} + e^{\frac{y}{x}}] x \frac{d y}{d x} = x + [\frac{x}{x ^{2} - y ^{2}} + e^{\frac{y}{x}}] y$ …
Mathematics · Differential Equations · MCQ
Q32.Let y = y(x) be the solution of the differential equation $x (1 - x^{2}) \frac{d y}{d x} + (3 x^{2} y - y - 4 x^{3}) = 0$ , $x > 1$ , with $y (2) = - 2$ . Then y(3) is equal to :
Mathematics · Differential Equations · MCQ
Q33.The number of real solutions of $x^{7} + 5 x^{3} + 3 x + 1 = 0$ is equal to .
Mathematics · Application of Derivatives · MCQ
Q34.The probability, that in a randomly selected 3-digit number at least two digits are odd, is :
Mathematics · Probability · MCQ
Q35.Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\geq$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is …
Mathematics · Sets and Relations · Numerical
Q36.The number of real solutions of the equation $e^{4 x} + 4 e^{3 x} - 58 e^{2 x} + 4 e^{x} + 1 = 0$ is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q37.The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to .
Mathematics · Statistics · Numerical
Q38.If $a = 2 i + j + 3 k$ , $b = 3 i + 3 j + k$ and $c = c_{1} i + c_{2} j + c_{3} k$ are coplanar vectors and $a . c = 5$ …
Mathematics · Vector Algebra · Numerical
Q39.A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q40.Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 1 2 18 1 + a2 + ...... + a18 is equal to .
Mathematics · Sequences and Series · Numerical
Q41.The number of positive integers k such that the constant term in the binomial expansion of $(2 x^{3} + \frac{3}{x ^{k}})^{12}$ , x $e$ 0 is 28 . l, where l is an odd integer, is .
Mathematics · Binomial Theorem · Numerical
Q42.The number of elements in the set {z = a + ib $\in$ C : a, b $\in$ Z and 1 < | z $-$ 3 + 2i | < 4} is .
Mathematics · Complex Numbers · Numerical