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 · 24 Jan · Shift 2

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
2023 · 24 Jan · Shift 2
Mathematics

Mathematics · 2023 · 24 Jan · Shift 2

22 questions from this JEE Main paper

Functions2 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations2 questions Vector Algebra2 questions Matrices and Determinants1 questions Limits Continuity and Differentiability1 questions Circle1 questions Differential Equations1 questions Statistics1 questions Complex Numbers1 questions Differentiation1 questions Definite Integration2 questions Sets and Relations1 questions 3D Geometry1 questions Binomial Theorem1 questions Straight Lines and Pair of Straight Lines1 questions Area Under the Curves1 questions Probability1 questions

Q23.Let $f (x)$ be a function such that $f (x + y) = f (x) . f (y)$ for all $x, y \in N$ . If $f (1) = 3$ and $k = 1 \sum n f (k) = 3279$ , then the value of n is
Mathematics · Functions · MCQ
Q24.The number of real solutions of the equation $3 (x^{2} + \frac{1}{x ^{2}}) - 2 (x + \frac{1}{x}) + 5 = 0$ , is
Mathematics · Quadratic Equation and Inequalities · MCQ
Q25.The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :
Mathematics · Permutations and Combinations · MCQ
Q26.Let $α = 4 i + 3 j + 5 k$ and $β = i + 2 j - 4 k$ . Let $β_{1}$ be parallel to $α$ and $β_{2}$ …
Mathematics · Vector Algebra · MCQ
Q27.If the system of equations $x + 2 y + 3 z = 34 x + 3 y - 4 z = 48 x + 4 y - λ z = 9 + μ$ has infinitely many solutions, then the ordered pair ( $λ, μ$ ) is equal to :
Mathematics · Matrices and Determinants · MCQ
Q28.The set of all values of $a$ for which $x \to a lim ([x - 5] - [2 x + 2]) = 0$ , where [ $α$ ] denotes the greatest integer less than or equal to $α$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.The locus of the mid points of the chords of the circle $C_{1} : (x - 4)^{2} + (y - 5)^{2} = 4$ which subtend an angle $θ_{i}$ at the centre of the circle $C_{1}$ , is a circle of radius $r_{i}$ . If $θ_{1} = \frac{π}{3}, θ_{3} = \frac{2 π}{3}$ …
Mathematics · Circle · MCQ
Q30.Let $y = y (x)$ be the solution of the differential equation $(x^{2} - 3 y^{2}) d x + 3 x y d y = 0, y (1) = 1$ . Then $6 y^{2} (e)$ is equal to
Mathematics · Differential Equations · MCQ
Q31.If $f (x) = \frac{2 ^{2 x}}{2 ^{2 x} + 2}, x \in R$ , then $f (\frac{1}{2023}) + f (\frac{2}{2023}) + ... + f (\frac{2022}{2023})$ is equal to
Mathematics · Functions · MCQ
Q32.The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is :
Mathematics · Permutations and Combinations · MCQ
Q33.Let the six numbers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}$ , be in A.P. and $a_{1} + a_{3} = 10$ . If the mean of these six numbers is $\frac{19}{2}$ and their variance is $σ^{2}$ , then 8 $σ^{2}$ is equal to :
Mathematics · Statistics · MCQ
Q34.The value of $(\frac{1 + s i n \frac{2 π}{9} + i c o s \frac{2 π}{9}}{1 + s i n \frac{2 π}{9} - i c o s \frac{2 π}{9}})^{3}$ is
Mathematics · Complex Numbers · MCQ
Q35.If $f (x) = x^{3} - x^{2} f^{'} (1) + x f^{''} (2) - f^{'''} (3), x \in R$ , then
Mathematics · Differentiation · MCQ
Q36. $\frac{3 2}{4} \int \frac{3 3}{4} \frac{48}{9 - 4 x ^{2}} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q37.The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is .
Mathematics · Sets and Relations · Numerical
Q38.If the shortest between the lines $\frac{x + 6}{2} = \frac{y - 6}{3} = \frac{z - 6}{4}$ and $\frac{x - λ}{3} = \frac{y - 2 6}{4} = \frac{z + 2 6}{5}$ is 6, then the square of sum of…
Mathematics · 3D Geometry · Numerical
Q39.Let $a = i + 2 j + λ k, b = 3 i - 5 j - λ k, a . c = 7, 2 b . c + 43 = 0, a \times c = b \times c$ …
Mathematics · Vector Algebra · Numerical
Q40.Let the sum of the coefficients of the first three terms in the expansion of $(x - \frac{3}{x ^{2}})^{n}, x e 0. n \in N$ , be 376. Then the coefficient of $x^{4}$ is .
Mathematics · Binomial Theorem · Numerical
Q41.The equations of the sides AB, BC and CA of a triangle ABC are : $2 x + y = 0, x + p y = 21 a, (a \pm 0)$ and $x - y = 3$ respectively. Let P(2, a) be the centroid of $Δ$ ABC. Then (BC) $^{2}$ is equal to .
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q42.Let $f$ be $a$ differentiable function defined on $[0, \frac{π}{2}]$ such that $f (x) > 0$ and $f (x) + \int_{0}^{x} f (t) 1 - (lo g_{e} f (t))^{2} d t = e, \forall x \in [0, \frac{π}{2}]$ . Then $(6 lo g_{e} f (\frac{π}{6}))^{2}$ …
Mathematics · Definite Integration · Numerical
Q43.If the area of the region bounded by the curves $y^{2} - 2 y = - x, x + y = 0$ is A, then 8 A is equal to
Mathematics · Area Under the Curves · Numerical
Q44.Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and $λ$ red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn…
Mathematics · Probability · Numerical