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 · 2023 · 25 Jan · Shift 1

23 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
2023 · 25 Jan · Shift 1
Mathematics

Mathematics · 2023 · 25 Jan · Shift 1

23 questions from this JEE Main paper

Vector Algebra1 questions Definite Integration1 questions Application of Derivatives2 questions Statistics1 questions Limits Continuity and Differentiability1 questions Probability1 questions Indefinite Integrals1 questions 3D Geometry2 questions Differentiation1 questions Circle1 questions Complex Numbers1 questions Matrices and Determinants2 questions Differential Equations1 questions Binomial Theorem1 questions Sets and Relations1 questions Permutations and Combinations1 questions Functions1 questions Logarithm1 questions Area Under the Curves1 questions Inverse Trigonometric Functions1 questions

Q24.The vector $a = - i + 2 j + k$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $b$ . Then the projection of $3 a + 2 b$ …
Mathematics · Vector Algebra · MCQ
Q25.The minimum value of the function $f (x) = 0 \int 2 e^{∣ x - t ∣} d t$ is :
Mathematics · Definite Integration · MCQ
Q26.Let $x = 2$ be a local minima of the function $f (x) = 2 x^{4} - 18 x^{2} + 8 x + 12, x \in (- 4, 4)$ . If M is local maximum value of the function $f$ in ( $- 4, 4)$ , then M =
Mathematics · Application of Derivatives · MCQ
Q27.The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :
Mathematics · Statistics · MCQ
Q28.The value of $n \to \infty lim \frac{1 + 2 - 3 + 4 + 5 - 6 + ..... + ( 3 n - 2 ) + ( 3 n - 1 ) - 3 n}{2 n ^{4} + 4 n + 3 - n ^{4} + 5 n + 4}$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S = {x \in Z : x (66 - x) \geq \frac{5}{9} M}$ and the event $A = {x \in S : x is a multiple of 3}$ …
Mathematics · Probability · MCQ
Q30.Let $f (x) = \int \frac{2 x}{( x ^{2} + 1 ) ( x ^{2} + 3 )} d x$ . If $f (3) = \frac{1}{2} (lo g_{e} 5 - lo g_{e} 6)$ , then $f (4)$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q31.The distance of the point P(4, 6, $-$ 2) from the line passing through the point ( $-$ 3, 2, 3) and parallel to a line with direction ratios 3, 3, $-$ 1 is equal to :
Mathematics · 3D Geometry · MCQ
Q32.Let $y (x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) (1 + x^{16})$ . Then $y^{'} - y^{''}$ at $x = - 1$ is equal to
Mathematics · Differentiation · MCQ
Q33.Consider the lines $L_{1}$ and $L_{2}$ given by $L_{1} : \frac{x - 1}{2} = \frac{y - 3}{1} = \frac{z - 2}{2} L_{2} : \frac{x - 2}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}$ . A line $L_{3}$ having direction ratios 1, $-$ 1, $-$ 2,…
Mathematics · 3D Geometry · MCQ
Q34.The points of intersection of the line $a x + b y = 0, (a e b)$ and the circle $x^{2} + y^{2} - 2 x = 0$ are $A (α, 0)$ and $B (1, β)$ . The image of the circle with AB as a diameter in the line $x + y + 2 = 0$ is :
Mathematics · Circle · MCQ
Q35.Let $z_{1} = 2 + 3i$ and $z_{2} = 3 + 4i$ . The set $S = {z \in C : ∣ z - z_{1} ∣^{2} - ∣ z - z_{2} ∣^{2} = ∣ z_{1} - z_{2} ∣^{2}}$ represents a
Mathematics · Complex Numbers · MCQ
Q36.Let S $_{1}$ and S $_{2}$ be respectively the sets of all $a \in R - {0}$ for which the system of linear equations $a x + 2 a y - 3 a z = 1 (2 a + 1) x + (2 a + 3) y + (a + 1) z = 2 (3 a + 5) x + (a + 5) y + (a + 2) z = 3$ has unique solution and…
Mathematics · Matrices and Determinants · MCQ
Q37.Let $y = y (x)$ be the solution curve of the differential equation $\frac{d y}{d x} = \frac{y}{x} (1 + x y^{2} (1 + lo g_{e} x)), x > 0, y (1) = 3$ . Then $\frac{y ^{2} ( x )}{9}$ is equal to :
Mathematics · Differential Equations · MCQ
Q38.Let $f : (0, 1) \to R$ be a function defined $f (x) = \frac{1}{1 - e ^{- x}}$ , and $g (x) = (f (- x) - f (x))$ . Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,
Mathematics · Application of Derivatives · MCQ
Q39.The constant term in the expansion of $(2 x + \frac{1}{x ^{7}} + 3 x^{2})^{5}$ is .
Mathematics · Binomial Theorem · Numerical
Q40.Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is .
Mathematics · Sets and Relations · Numerical
Q41.Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$ . Then, the number of ways of choosing $x$ and $y$ , such that $x + y$ is divisible by 5, is .
Mathematics · Permutations and Combinations · Numerical
Q42.For some a, b, c $f (x) = a x - 3$ , let $f (x) = a x - 3$ and $g (x) = x^{b} + c, x \in R$ . If $(f o g)^{- 1} (x) = (\frac{x - 7}{2})^{1/3}$ , then $(f o g) (a c) + (g o f) (b)$ is equal to .
Mathematics · Functions · Numerical
Q43.Let $S = {α : lo g_{2} (9^{2 α - 4} + 13) - lo g_{2} (\frac{5}{2} . 3^{2 α - 4} + 1) = 2}$ . Then the maximum value of $β$ for which the equation $x^{2} - 2 (α \in s \sum α)^{2} x + α \in s \sum (α + 1)^{2} β = 0$ …
Mathematics · Logarithm · Numerical
Q44.Let $A_{1}, A_{2}, A_{3}$ be the three A.P. with the same common difference d and having their first terms as $A, A + 1, A + 2$ , respectively. Let a, b, c be the $7^{th}, 9^{th}, 1 7^{th}$ terms of $A_{1}, A_{2}, A_{3}$ ,…
Mathematics · Matrices and Determinants · Numerical
Q45.If the area enclosed by the parabolas $P_{1} : 2y = 5 x^{2}$ and $P_{2} : x^{2} - y + 6 = 0$ is equal to the area enclosed by $P_{1}$ and $y = α x, α > 0$ , then $α^{3}$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q46.If the sum of all the solutions of $tan^{- 1} (\frac{2 x}{1 - x ^{2}}) + cot^{- 1} (\frac{1 - x ^{2}}{2 x}) = \frac{π}{3}, - 1 < x < 1, x e 0$ , is $α - \frac{4}{3}$ , then $α$ …
Mathematics · Inverse Trigonometric Functions · Numerical