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 · 8 Apr · Shift 1

26 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 · 8 Apr · Shift 1
Mathematics

Mathematics · 2023 · 8 Apr · Shift 1

26 questions from this JEE Main paper

Permutations and Combinations3 questions Differentiation1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability1 questions Probability1 questions 3D Geometry1 questions Parabola1 questions Area Under the Curves1 questions Straight Lines and Pair of Straight Lines1 questions Indefinite Integrals1 questions Quadratic Equation and Inequalities1 questions Sequences and Series1 questions Complex Numbers1 questions Vector Algebra2 questions Definite Integration1 questions Sets and Relations1 questions Differential Equations1 questions Statistics1 questions Application of Derivatives1 questions Binomial Theorem2 questions Circle1 questions

Q22.The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is :
Mathematics · Permutations and Combinations · MCQ
Q23.Let $f (x) = \frac{s i n x + c o s x - 2}{s i n x - c o s x}, x \in [0, π] - {\frac{π}{4}}$ . Then $f (\frac{7 π}{12}) f^{''} (\frac{7 π}{12})$ is equal to
Mathematics · Differentiation · MCQ
Q24.Let $A = 210 12 - 1 0 - 1 2$ . If $∣ adj (adj (adj 2 A)) ∣ = (16)^{n}$ , then $n$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q25. $lim_{x \to 0} ((\frac{( 1 - c o s ^{2} ( 3 x )}{c o s ^{3} ( 4 x )}) (\frac{s i n ^{3} ( 4 x )}{( l o g _{e} ( 2 x + 1 ) ) ^{5}}))$ is equal to .
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.In a bolt factory, machines $C$ and $C$ manufacture respectively $50%$ and $50%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt…
Mathematics · Probability · MCQ
Q27.The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :
Mathematics · Permutations and Combinations · MCQ
Q28.The shortest distance between the lines $\frac{x - 4}{4} = \frac{y + 2}{5} = \frac{z + 3}{3}$ and $\frac{x - 1}{3} = \frac{y - 3}{4} = \frac{z - 4}{2}$ is :
Mathematics · 3D Geometry · MCQ
Q29.Let $R$ be the focus of the parabola $y^{2} = 20 x$ and the line $y = m x + c$ intersect the parabola at two points $P$ and $Q$ . Let the point $G (10, 10)$ be the centroid of the triangle $P QR$ . If $c - m = 6$ , then $(P Q)^{2}$ is :
Mathematics · Parabola · MCQ
Q30.The area of the region ${(x, y) : x^{2} \leq y \leq 8 - x^{2}, y \leq 7}$ is :
Mathematics · Area Under the Curves · MCQ
Q31.Let $C (α, β)$ be the circumcenter of the triangle formed by the lines $4 x + 3 y = 694 y - 3 x = 17$ , and $x + 7 y = 61$ . Then $(α - β)^{2} + α + β$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q32.Let $I (x) = \int \frac{( x + 1 )}{x ( 1 + x e ^{x} ) ^{2}} d x, x > 0$ . If $lim_{x \to \infty} I (x) = 0$ , then $I (1)$ is equal to :
Mathematics · Indefinite Integrals · MCQ
Q33.Let $α, β, γ$ be the three roots of the equation $x^{3} + b x + c = 0$ . If $β γ = 1 = - α$ , then $b^{3} + 2 c^{3} - 3 α^{3} - 6 β^{3} - 8 γ^{3}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is :
Mathematics · Permutations and Combinations · MCQ
Q35.Let $S_{K} = \frac{1 + 2 + \dots + K}{K}$ and $\sum_{j = 1}^{n} S_{j}^{2} = \frac{n}{A} (B n^{2} + C n + D)$ , where $A, B, C, D \in N$ and $A$ has least value. Then
Mathematics · Sequences and Series · MCQ
Q36.Let $P = [\frac{3}{2} - \frac{1}{2} \frac{1}{2} \frac{3}{2}], A = [1011]$ and $Q = P A P^{T}$ . If $P^{T} Q^{2007} P = [a c b d]$ …
Mathematics · Matrices and Determinants · MCQ
Q37.If for $z = α + i β, ∣ z + 2∣ = z + 4 (1 + i)$ , then $α + β$ and $α β$ are the roots of the equation :
Mathematics · Complex Numbers · MCQ
Q38.If the points with position vectors $α \hat{i} + 10 \hat{j} + 13 \hat{k}, 6 \hat{i} + 11 \hat{j} + 11 \hat{k}, \frac{9}{2} \hat{i} + β \hat{j} - 8 \hat{k}$ are collinear, then $(19 α - 6 β)^{2}$ is equal to :
Mathematics · Vector Algebra · MCQ
Q39.Let $[t]$ denote the greatest integer $\frac{2}{π} \int_{π /6}^{5 π /6} (8 [cosec x] - 5 [cot x]) d x$ . Then $\frac{2}{π} \int_{π /6}^{5 π /6} (8 [cosec x] - 5 [cot x]) d x$ is equal to .
Mathematics · Definite Integration · Numerical
Q40.Let $A = {0, 3, 4, 6, 7, 8, 9, 10}$ and $R$ be the relation defined on $A$ such that $R = {(x, y) \in A \times A : x - y$ is odd positive integer or $x - y = 2}$ . The minimum number of elements that must be added to the relation $R$ , so that it is a…
Mathematics · Sets and Relations · Numerical
Q41.If the solution curve of the differential equation $(y - 2 lo g_{e} x) d x + (x lo g_{e} x^{2}) d y = 0, x > 1$ passes through the points $(e, \frac{4}{3})$ and $(e^{4}, α)$ , then $α$ …
Mathematics · Differential Equations · Numerical
Q42.Let the mean and variance of 8 numbers $x, y, 10, 12, 6, 12, 4, 8$ be $9$ and $9.25$ respectively. If $x > y$ , then $3 x - 2 y$ is equal to .
Mathematics · Statistics · Numerical
Q43.Let $a = 6 \hat{i} + 9 \hat{j} + 12 \hat{k}, b = α \hat{i} + 11 \hat{j} - 2 \hat{k}$ and $c$ be vectors such that $a \times c = a \times b$ . If $a \cdot c = - 12, c \cdot (\hat{i} - 2 \hat{j} + \hat{k}) = 5$ …
Mathematics · Vector Algebra · Numerical
Q44.If $a_{α}$ is the greatest term in the sequence $α_{n} = \frac{n ^{3}}{n ^{4} + 147}, n = 1, 2, 3, \dots$ , then $α$ is equal to .
Mathematics · Application of Derivatives · Numerical
Q45.Let $[t]$ denote the greatest integer $(3 x^{2} - \frac{1}{2 x ^{5}})^{7}$ . If the constant term in the expansion of $(3 x^{2} - \frac{1}{2 x ^{5}})^{7}$ is $α$ , then $[α]$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q46.Consider a circle $C_{1} : x^{2} + y^{2} - 4 x - 2 y = α - 5$ . Let its mirror image in the line $y = 2 x + 1$ be another circle $C_{2} : 5 x^{2} + 5 y^{2} - 10 f x - 10 g y + 36 = 0$ . Let $r$ be the radius of $C_{2}$ . Then $α + r$ is equal to …
Mathematics · Circle · Numerical
Q47.The largest natural number $n$ such that $3^{n}$ divides $66!$ is .
Mathematics · Binomial Theorem · Numerical