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 · 30 Jan · Shift 1

17 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 · 30 Jan · Shift 1
Mathematics

Mathematics · 2023 · 30 Jan · Shift 1

17 questions from this JEE Main paper

Differential Equations1 questions Sets and Relations1 questions Matrices and Determinants1 questions Definite Integration2 questions Binomial Theorem1 questions Limits Continuity and Differentiability1 questions Logarithm1 questions Trigonometric Ratio and Identites1 questions Vector Algebra1 questions Probability1 questions Permutations and Combinations1 questions Complex Numbers1 questions Area Under the Curves1 questions Functions1 questions Differentiation1 questions Statistics1 questions

Q23.Let the solution curve $y = y (x)$ of the differential equation $\frac{d y}{d x} - \frac{3 x ^{5} t a n ^{- 1} ( x ^{3} )}{( 1 + x ^{6} ) ^{3/2}} y = 2 x exp {\frac{x ^{3} - t a n ^{- 1} x ^{3}}{( 1 + x ^{6} )}} pass through the origin. Then y (1) is equal to :$ …
Mathematics · Differential Equations · MCQ
Q24.The minimum number of elements that must be added to the relation $R = {(a, b), (b, c)}$ on the set ${a, b, c}$ so that it becomes symmetric and transitive is :
Mathematics · Sets and Relations · MCQ
Q25.Let the system of linear equations $x + y + k z = 22 x + 3 y - z = 13 x + 4 y + 2 z = k$ have infinitely many solutions. Then the system $(k + 1) x + (2 k - 1) y = 7 (2 k + 1) x + (k + 5) y = 10$ has :
Mathematics · Matrices and Determinants · MCQ
Q26.If [t] denotes the greatest integer $\frac{3 ( e - 1 )}{e} 1 \int 2 x^{2} e^{[x] + [x^{3}]} d x$ , then the value of $\frac{3 ( e - 1 )}{e} 1 \int 2 x^{2} e^{[x] + [x^{3}]} d x$ is :
Mathematics · Definite Integration · MCQ
Q27.If the coefficient of $x^{15}$ in the expansion of $(a x^{3} + \frac{1}{b x ^{1/3}})^{15}$ is equal to the coefficient of $x^{- 15}$ in the expansion of $(a x^{1/3} - \frac{1}{b x ^{3}})^{15}$ ,…
Mathematics · Binomial Theorem · MCQ
Q28.Suppose $f : R \to (0, \infty)$ be a differentiable function such that $5 f (x + y) = f (x) \cdot f (y), \forall x, y \in R$ . If $f (3) = 320$ , then $\sum_{n = 0}^{5} f (n)$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.If the solution of the equation $lo g_{c o s x} cot x + 4 lo g_{s i n x} tan x = 1, x \in (0, \frac{π}{2})$ , is $sin^{- 1} (\frac{α + β}{2})$ , where $α$ , $β$ are integers, then $α + β$ …
Mathematics · Logarithm · MCQ
Q30.If $tan 1 5^{\circ} + \frac{1}{t a n 7 5 ^{\circ}} + \frac{1}{t a n 10 5 ^{\circ}} + tan 19 5^{\circ} = 2 a$ , then the value of $(a + \frac{1}{a})$ is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q31.Let a unit vector $O P$ make angles $α, β, γ$ with the positive directions of the co-ordinate axes $OX$ , $OY, OZ$ respectively, where $β \in (0, \frac{π}{2})$ . If $OP$ …
Mathematics · Vector Algebra · MCQ
Q32.If an unbiased die, marked with $- 2, - 1, 0, 1, 2, 3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :
Mathematics · Probability · MCQ
Q33. $lim_{x \to 0} \frac{48}{x ^{4}} \int_{0}^{x} \frac{t ^{3}}{t ^{6} + 1} d t$ is equal to .
Mathematics · Definite Integration · Numerical
Q34.Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to .
Mathematics · Permutations and Combinations · Numerical
Q35.Let $z = 1 + i$ and $z_{1} = \frac{1 + i z ˉ}{z ˉ ( 1 - z ) + \frac{1}{z}}$ . Then $\frac{12}{π} ar g (z_{1})$ is equal to .
Mathematics · Complex Numbers · Numerical
Q36.Let $α$ be the area of the larger region bounded by the curve $y^{2} = 8 x$ and the lines $y = x$ and $x = 2$ , which lies in the first quadrant. Then the value of $3 α$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q37.Let $S = {1, 2, 3, 4, 5, 6}$ . Then the number of one-one functions $f : S \to P (S)$ , where $P (S)$ denote the power set of $S$ , such that $f (n) \subset f (m)$ where $n \lt…
Mathematics · Functions · Numerical
Q38.Let $f^{1} (x) = \frac{3 x + 2}{2 x + 3}, x \in R - {\frac{- 3}{2}}$ For $n \geq 2$ , define $f^{n} (x) = f^{1} o f^{n - 1} (x)$ . If $f^{5} (x) = \frac{a x + b}{b x + a}, gcd (a, b) = 1$ …
Mathematics · Differentiation · Numerical
Q39.The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observation, then $a + 3b - 5$ is equal to .
Mathematics · Statistics · Numerical