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 · 29 Jan · Shift 1

27 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 · 29 Jan · Shift 1
Mathematics

Mathematics · 2023 · 29 Jan · Shift 1

27 questions from this JEE Main paper

Quadratic Equation and Inequalities1 questions Straight Lines and Pair of Straight Lines2 questions Statistics1 questions Trigonometric Ratio and Identites1 questions Probability1 questions Circle1 questions Definite Integration1 questions Matrices and Determinants2 questions Complex Numbers1 questions Differential Equations1 questions Area Under the Curves3 questions Functions3 questions Vector Algebra1 questions Limits Continuity and Differentiability1 questions Sequences and Series1 questions Binomial Theorem2 questions Permutations and Combinations2 questions Differentiation1 questions 3D Geometry1 questions

Q22.Let $λ e 0$ be a real number. Let $14 x^{2} - 31 x + 3 λ = 0$ be the roots of the equation $14 x^{2} - 31 x + 3 λ = 0$ and $35 x^{2} - 53 x + 4 λ = 0$ be the roots of the equation $35 x^{2} - 53 x + 4 λ = 0$ . Then $\frac{3 α}{β}$ and $\frac{4 α}{γ}$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q23.Let $B$ and $C$ be the two points on the line $y + x = 0$ such that $B$ and $C$ are symmetric with respect to the origin. Suppose $A$ is a point on $y - 2 x = 2$ such that $△ A B C$ is an equilateral triangle. Then, the area of the $△ A B C$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q24.Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If $μ$ and $σ^{2}$ represent mean and variance of…
Mathematics · Statistics · MCQ
Q25.Let $f (θ) = 3 (sin^{4} (\frac{3 π}{2} - θ) + sin^{4} (3 π + θ)) - 2 (1 - sin^{2} 2 θ)$ and $$S = \left\{ {\theta \in [0,\pi ]:f'(\theta ) = - {{\sqrt 3 } \over 2}}…
Mathematics · Trigonometric Ratio and Identites · MCQ
Q26.Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is :
Mathematics · Probability · MCQ
Q27.Let the tangents at the points $A (4, - 11)$ and $B (8, - 5)$ on the circle $x^{2} + y^{2} - 3 x + 10 y - 15 = 0$ , intersect at the point $C$ . Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to :
Mathematics · Circle · MCQ
Q28.Let $f (x) = x + \frac{a}{π ^{2} - 4} sin x + \frac{b}{π ^{2} - 4} cos x, x \in R$ be a function which satisfies $f (x) = x + 0 \int π /2 sin (x + y) f (y) d y$ . then $(a + b)$ is equal to
Mathematics · Definite Integration · MCQ
Q29.Let $α$ and $β$ be real numbers. Consider a 3 $\times$ 3 matrix A such that $A^{2} = 3 A + α I$ . If $A^{4} = 21 A + β I$ , then
Mathematics · Matrices and Determinants · MCQ
Q30.A light ray emits from the origin making an angle 30 $^{\circ}$ with the positive $x$ -axis. After getting reflected by the line $x + y = 1$ , if this ray intersects $x$ -axis at Q, then the abscissa of Q is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.For two non-zero complex numbers $z_{1}$ and $z_{2}$ , if $Re (z_{1} z_{2}) = 0$ and $Re (z_{1} + z_{2}) = 0$ , then which of the following are possible? A. $Im (z_{1}) > 0$ …
Mathematics · Complex Numbers · MCQ
Q32.Let $y = f (x)$ be the solution of the differential equation $y (x + 1) d x - x^{2} d y = 0, y (1) = e$ . Then $x \to 0^{+} lim f (x)$ is equal to
Mathematics · Differential Equations · MCQ
Q33.Let $Δ$ be the area of the region ${(x, y) \in R^{2} : x^{2} + y^{2} \leq 21, y^{2} \leq 4 x, x \geq 1}$ . Then $\frac{1}{2} (Δ - 21 sin^{- 1} \frac{2}{7})$ is equal to
Mathematics · Area Under the Curves · MCQ
Q34.The domain of $f (x) = \frac{l o g _{(x + 1)} ( x - 2 )}{e ^{2 l o g_{e} x} - ( 2 x + 3 )}, x \in R$ is
Mathematics · Functions · MCQ
Q35.Let $f : R \to R$ be a function such that $f (x) = \frac{x ^{2} + 2 x + 1}{x ^{2} + 1}$ . Then
Mathematics · Functions · MCQ
Q36.Let $[x]$ denote the greatest integer $f (x) = max {x^{2}, 1 + [x]}$ . Consider the function $f (x) = max {x^{2}, 1 + [x]}$ . Then the value of the integral $0 \int 2 f (x) d x$ is
Mathematics · Area Under the Curves · MCQ
Q37.Let $A = {(x, y) \in R^{2} : y \geq 0, 2 x \leq y \leq 4 - (x - 1)^{2}}$ and $B = {(x, y) \in R \times R : 0 \leq y \leq min {2 x, 4 - (x - 1)^{2}}} .$ . Then…
Mathematics · Area Under the Curves · MCQ
Q38.Consider the following system of equations $α x + 2 y + z = 12 α x + 3 y + z = 13 x + α y + 2 z = β$ for some $α, β \in R$ . Then which of the following is NOT correct.
Mathematics · Matrices and Determinants · MCQ
Q39.If the vectors $a = λ i + μ j + 4 k$ , $b = - 2 i + 4 j - 2 k$ and $c = 2 i + 3 j + k$ are coplanar and…
Mathematics · Vector Algebra · MCQ
Q40.Let $x = 2$ be a root of the equation $x^{2} + p x + q = 0$ and $f (x) = {\frac{1 - c o s ( x ^{2} - 4 p x + q ^{2} + 8 q + 16 )}{( x - 2 p ) ^{4}}, 0, x e 2 p x = 2 p$ Then $x \to 2 p^{+} lim [f (x)]$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q41.Let $a_{1}, a_{2}, a_{3}, ...$ be a $GP$ of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then $a_{1} a_{9} + a_{2} a_{4} a_{9} + a_{5} + a_{7}$ is equal to .
Mathematics · Sequences and Series · Numerical
Q42.Suppose $f$ is a function satisfying $f (x + y) = f (x) + f (y)$ for all $x, y \in N$ and $f (1) = \frac{1}{5}$ . If $n = 1 \sum m \frac{f ( n )}{n ( n + 1 ) ( n + 2 )} = \frac{1}{12}$ , then $m$ is equal to .
Mathematics · Functions · Numerical
Q43.Let the coefficients of three consecutive terms in the binomial expansion of $(1 + 2 x)^{n}$ be in the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of those three terms, is .
Mathematics · Binomial Theorem · Numerical
Q44.If the co-efficient of $x^{9}$ in $(α x^{3} + \frac{1}{β x})^{11}$ and the co-efficient of $x^{- 9}$ in $(α x - \frac{1}{β x ^{3}})^{11}$ are equal, then $(α β)^{2}$ is equal to…
Mathematics · Binomial Theorem · Numerical
Q45.If all the six digit numbers $x_{1} x_{2} x_{3} x_{4} x_{5} x_{6}$ with $0 < x_{1} < x_{2} < x_{3} < x_{4} < x_{5} < x_{6}$ are arranged in the increasing order, then the sum of the digits in the $7 2^{th}$ number is …
Mathematics · Permutations and Combinations · Numerical
Q46.Let $f : R \to R$ be a differentiable function that satisfies the relation $f (x + y) = f (x) + f (y) - 1, \forall x, y \in R$ . If $f^{'} (0) = 2$ , then $∣ f (- 2) ∣$ is equal to .
Mathematics · Differentiation · Numerical
Q47.Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is …
Mathematics · Permutations and Combinations · Numerical
Q48.Let the co-ordinates of one vertex of $Δ A B C$ be $A (0, 2, α)$ and the other two vertices lie on the line $\frac{x + α}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ . For $α \in Z$ , if the area of $Δ A B C$ …
Mathematics · 3D Geometry · Numerical