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 · 2024 · 29 Jan · Shift 2

30 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
2024 · 29 Jan · Shift 2
Mathematics

Mathematics · 2024 · 29 Jan · Shift 2

30 questions from this JEE Main paper

Permutations and Combinations1 questions Straight Lines and Pair of Straight Lines2 questions Indefinite Integrals1 questions Vector Algebra2 questions Application of Derivatives2 questions Sets and Relations1 questions Statistics1 questions 3D Geometry2 questions Differentiation1 questions Sequences and Series2 questions Differential Equations1 questions Probability1 questions Complex Numbers2 questions Trigonometric Functions and Equations1 questions Inverse Trigonometric Functions1 questions Matrices and Determinants2 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions Definite Integration2 questions Parabola1 questions Binomial Theorem1 questions Limits Continuity and Differentiability1 questions

Q31.Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
Mathematics · Permutations and Combinations · MCQ
Q32.Let $A$ be the point of intersection of the lines $3 x + 2 y = 14, 5 x - y = 6$ and $B$ be the point of intersection of the lines $4 x + 3 y = 8, 6 x + y = 5$ . The distance of the point $P (5, - 2)$ from the line $AB$ is
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.If $\int \frac{s i n ^{\frac{3}{2}} x + c o s ^{\frac{3}{2}} x}{s i n ^{3} x c o s ^{3} x s i n ( x - θ )} d x = A cos θ tan x - sin θ + B cos θ - sin θ cot x + C$ , where $C$ is the integration constant, then $A B$ …
Mathematics · Indefinite Integrals · MCQ
Q34.The distance of the point $(2, 3)$ from the line $2 x - 3 y + 28 = 0$ , measured parallel to the line $3 x - y + 1 = 0$ , is equal to
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.Let a unit vector $\overset{u}{^} = x \hat{i} + y \hat{j} + z \hat{k}$ make angles $\frac{π}{2}, \frac{π}{3}$ and $\frac{2 π}{3}$ with the vectors $\frac{1}{2} \hat{i} + \frac{1}{2} \hat{k}, \frac{1}{2} \hat{j} + \frac{1}{2} \hat{k}$ …
Mathematics · Vector Algebra · MCQ
Q36.The function $f (x) = \frac{x}{x ^{2} - 6 x - 16}, x \in R - {- 2, 8}$
Mathematics · Application of Derivatives · MCQ
Q37.If R is the smallest equivalence relation on the set ${1, 2, 3, 4}$ such that ${(1, 2), (1, 3)} \subset R$ , then the number of elements in $R$ is .
Mathematics · Sets and Relations · MCQ
Q38.If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of the first four observations is $\frac{7}{2}$ , then the variance of the first four observations in equal to
Mathematics · Statistics · MCQ
Q39.Let $P (3, 2, 3), Q (4, 6, 2)$ and $R (7, 3, 2)$ be the vertices of $△ PQR$ . Then, the angle $∠ QPR$ is
Mathematics · 3D Geometry · MCQ
Q40. $Let y = lo g_{e} (\frac{1 - x ^{2}}{1 + x ^{2}}), - 1 < x < 1 . Then at x = \frac{1}{2}, the value of 225 (y^{'} - y^{''}) is equal to$
Mathematics · Differentiation · MCQ
Q41.If $lo g_{e} a, lo g_{e} b, lo g_{e} c$ are in an A.P. and $lo g_{e} a - lo g_{e} 2 b, lo g_{e} 2 b - lo g_{e} 3 c, lo g_{e} 3 c - lo g_{e}$ a are also in an A.P, then $a : b : c$ …
Mathematics · Sequences and Series · MCQ
Q42.If $sin (\frac{y}{x}) = lo g_{e} ∣ x ∣ + \frac{α}{2}$ is the solution of the differential equation $x cos (\frac{y}{x}) \frac{d y}{d x} = y cos (\frac{y}{x}) + x$ and $y (1) = \frac{π}{3}$ , then $α^{2}$ …
Mathematics · Differential Equations · MCQ
Q43.An integer is chosen at random from the integers $1, 2, 3, \dots, 50$ . The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is
Mathematics · Probability · MCQ
Q44.Let $O A = a, O B = 12 a + 4 b and O C = b$ , where O is the origin. If S is the parallelogram with adjacent sides OA and OC, then $\frac{area of the quadrilateral OA BC}{area of S}$ …
Mathematics · Vector Algebra · MCQ
Q45.The function $f (x) = 2 x + 3 (x)^{\frac{2}{3}}, x \in R$ , has
Mathematics · Application of Derivatives · MCQ
Q46.If each term of a geometric progression $a_{1}, a_{2}, a_{3}, \dots$ with $a_{1} = \frac{1}{8}$ and $a_{2} e q a_{1}$ , is the arithmetic mean of the next two terms and $S_{n} = a_{1} + a_{2} + \dots .. + a_{n}$ , then $S_{20} - S_{18}$ is equal to
Mathematics · Sequences and Series · MCQ
Q47.Let $r$ and $θ$ respectively be the modulus and amplitude of the complex number $z = 2 - i (2 tan \frac{5 π}{8})$ , then $(r, θ)$ is equal to
Mathematics · Complex Numbers · MCQ
Q48.The sum of the solutions $x \in R$ of the equation $\frac{3 c o s 2 x + c o s ^{3} 2 x}{c o s ^{6} x - s i n ^{6} x} = x^{3} - x^{2} + 6$ is
Mathematics · Trigonometric Functions and Equations · MCQ
Q49.Let $x = \frac{m}{n}$ ( $cos (2 sin^{- 1} x) = \frac{1}{9}$ are co-prime natural numbers) be a solution of the equation $cos (2 sin^{- 1} x) = \frac{1}{9}$ and let $α, β (α > β)$ be the roots of the equation $m x^{2} - n x - m + n = 0$ . Then the…
Mathematics · Inverse Trigonometric Functions · MCQ
Q50.Let $A = 2631232112$ and $P = 157201025$ . The sum of…
Mathematics · Matrices and Determinants · MCQ
Q51.Let O be the origin, and M and $N$ be the points on the lines $\frac{x - 5}{4} = \frac{y - 4}{1} = \frac{z - 5}{3}$ and $\frac{x + 8}{12} = \frac{y + 2}{5} = \frac{z + 11}{9}$ respectively such that $MN$ is the shortest distance between the…
Mathematics · 3D Geometry · Numerical
Q52.Let the area of the region ${(x, y) : 0 \leq x \leq 3, 0 \leq y \leq min {x^{2} + 2, 2 x + 2}}$ be A. Then is equal to .
Mathematics · Area Under the Curves · Numerical
Q53.Let the set $C = {(x, y) ∣ x^{2} - 2^{y} = 2023, x, y \in N}$ . Then $\sum_{(x, y) \in C} (x + y)$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q54.Let the slope of the line $45 x + 5 y + 3 = 0$ be $27 r_{1} + \frac{9 r _{2}}{2}$ for some $r_{1}, r_{2} \in R$ . Then $lim_{x \to 3} (\int_{3}^{x} \frac{8 t ^{2}}{\frac{3 r _{2} x}{2} - r _{2} x ^{2} - r _{1} x ^{3} - 3 x} d t)$ is equal to …
Mathematics · Definite Integration · Numerical
Q55.Let $x^{2} - 6 x + 3 = 0$ be the roots of the equation $x^{2} - 6 x + 3 = 0$ such that $Im (α) > Im (β)$ . Let $n$ be integers not divisible by 3 and $n$ be a natural number such that $\frac{α ^{99}}{β} + α^{98} = 3^{n} (a + ib), i = - 1$ …
Mathematics · Complex Numbers · Numerical
Q56.Let for any three distinct consecutive terms $a, b, c$ of an A.P, the lines $a x + b y + c = 0$ be concurrent at the point $P$ and $Q (α, β)$ be a point such that the system of equations $x + y + z = 6, 2 x + 5 y + α z = β and$ …
Mathematics · Matrices and Determinants · Numerical
Q57.Let $P (α, β)$ be a point on the parabola $y^{2} = 4 x$ . If $P$ also lies on the chord of the parabola $x^{2} = 8 y$ whose mid point is $(1, \frac{5}{4})$ , then $(α - 28) (β - 8)$ is equal to .
Mathematics · Parabola · Numerical
Q58.Remainder when $6 4^{3 2^{32}}$ is divided by 9 is equal to .
Mathematics · Binomial Theorem · Numerical
Q59.Let $f (x) = lim_{r \to x} {\frac{2 r ^{2} [ ( f ( r ) ) ^{2} - f ( x ) f ( r ) ]}{r ^{2} - x ^{2}} - r^{3} e^{\frac{f ( r )}{r}}}$ be differentiable in $(- \infty, 0) \cup (0, \infty)$ and $f (1) = 1$ . Then the value of ea, such that…
Mathematics · Limits Continuity and Differentiability · Numerical
Q60.If $\int_{\frac{π}{6}}^{\frac{π}{3}} 1 - sin 2 x d x = α + β 2 + γ 3$ , where $γ$ and $γ$ are rational numbers, then $3 α + 4 β - γ$ is equal to .
Mathematics · Definite Integration · Numerical