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Mathematics · 2023 · 13 Apr · Shift 1

22 questions from this JEE Main paper

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2023 · 13 Apr · Shift 1
Mathematics

Mathematics · 2023 · 13 Apr · Shift 1

22 questions from this JEE Main paper

Area Under the Curves1 questions Parabola1 questions Vector Algebra2 questions Matrices and Determinants3 questions Differential Equations1 questions Probability1 questions Quadratic Equation and Inequalities1 questions Definite Integration2 questions Sequences and Series1 questions Binomial Theorem2 questions Functions1 questions Differentiation1 questions Application of Derivatives1 questions Statistics1 questions Complex Numbers1 questions Permutations and Combinations1 questions Inverse Trigonometric Functions1 questions

Q23.The area of the region enclosed by the curve $f (x) = max {sin x, cos x}, - π \leq x \leq π$ and the $x$ -axis is
Mathematics · Area Under the Curves · MCQ
Q24.Let $PQ$ be a focal chord of the parabola $y^{2} = 36 x$ of length 100 , making an acute angle with the positive $x$ -axis. Let the ordinate of $P$ be positive and $M$ be the point on the line segment PQ such that…
Mathematics · Parabola · MCQ
Q25.Let $a = \hat{i} + 4 \hat{j} + 2 \hat{k}, b = 3 \hat{i} - 2 \hat{j} + 7 \hat{k}$ and $c = 2 \hat{i} - \hat{j} + 4 \hat{k}$ . If a vector $d$ satisfies $d \times b = c \times b$ and $d \cdot a = 24$ ,…
Mathematics · Vector Algebra · MCQ
Q26.For the system of linear equations $2 x + 4 y + 2 a z = b x + 2 y + 3 z = 42 x - 5 y + 2 z = 8$ which of the following is NOT correct?
Mathematics · Matrices and Determinants · MCQ
Q27.Let $y = y_{1} (x)$ and $y = y_{2} (x)$ be the solution curves of the differential equation $\frac{d y}{d x} = y + 7$ with initial conditions $y_{1} (0) = 0$ and $y_{2} (0) = 1$ respectively. Then the curves $y = y_{1} (x)$ and $y = y_{2} (x)$ intersect at
Mathematics · Differential Equations · MCQ
Q28.A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin, then the mean of $X$ is :
Mathematics · Probability · MCQ
Q29.The set of all $a \in R$ for which the equation $x ∣ x - 1∣ + ∣ x + 2∣ + a = 0$ has exactly one real root, is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q30. $\int_{0}^{\infty} \frac{6}{e ^{3 x} + 6 e ^{2 x} + 11 e ^{x} + 6} d x =$
Mathematics · Definite Integration · MCQ
Q31.Let $s_{1}, s_{2}, s_{3}, \dots, s_{10}$ respectively be the sum to 12 terms of 10 A.P. s whose first terms are $1, 2, 3, \dots .10$ and the common differences are $1, 3, 5, \dots\dots, 19$ respectively. Then $\sum_{i = 1}^{10} s_{i}$ is…
Mathematics · Sequences and Series · MCQ
Q32.Let $B = 11 α 32 α α 34, α > 2$ be the adjoint of a matrix $A$ and $∣ A ∣ = 2$ . Then $[α - 2 α α] B α - 2 α α$ …
Mathematics · Matrices and Determinants · MCQ
Q33.Fractional part of the number $\frac{4 ^{2022}}{15}$ is equal to
Mathematics · Binomial Theorem · MCQ
Q34.For $x \in R$ , two real valued functions $f (x)$ and $g (x)$ are such that, $g (x) = x + 1$ and $f \circ g (x) = x + 3 - x$ . Then $f (0)$ is equal to
Mathematics · Functions · MCQ
Q35.For the differentiable function $f : R - {0} \to R$ , let $3 f (x) + 2 f (\frac{1}{x}) = \frac{1}{x} - 10$ , then $f (3) + f^{'} (\frac{1}{4})$ is equal to
Mathematics · Differentiation · MCQ
Q36. $max_{0 \leq x \leq π} {x - 2 sin x cos x + \frac{1}{3} sin 3 x} =$
Mathematics · Application of Derivatives · MCQ
Q37.The number of symmetric matrices of order 3, with all the entries from the set ${0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$ is :
Mathematics · Matrices and Determinants · MCQ
Q38.Let the mean of the data be 5. If $m$ and $σ^{2}$ are respectively the mean deviation about the mean and the variance of the data, then $\frac{3 α}{m + σ ^{2}}$ is equal to Includes table
Mathematics · Statistics · Numerical
Q39.Let $w = z \overset{z}{ˉ} + k_{1} z + k_{2} i z + λ (1 + i), k_{1}, k_{2} \in R$ . Let $Re (w) = 0$ be the circle $C$ of radius 1 in the first quadrant touching the line $y = 1$ and the $y$ -axis. If the curve $Im (w) = 0$ …
Mathematics · Complex Numbers · Numerical
Q40.The number of seven digit positive integers formed using the digits $1, 2, 3$ and $4$ only and sum of the digits equal to $12$ is .
Mathematics · Permutations and Combinations · Numerical
Q41.If $S = {x \in R : sin^{- 1} (\frac{x + 1}{x ^{2} + 2 x + 2}) - sin^{- 1} (\frac{x}{x ^{2} + 1}) = \frac{π}{4}}$ , then $\sum_{x \in s} (sin ((x^{2} + x + 5) \frac{π}{2}) - cos ((x^{2} + x + 5) π))$ …
Mathematics · Inverse Trigonometric Functions · Numerical
Q42.Let for $x \in R, S_{0} (x) = x, S_{k} (x) = C_{k} x + k \int_{0}^{x} S_{k - 1} (t) d t$ , where $C_{0} = 1, C_{k} = 1 - \int_{0}^{1} S_{k - 1} (x) d x, k = 1, 2, 3, \dots$ Then $S_{2} (3) + 6 C_{3}$ is equal to .
Mathematics · Definite Integration · Numerical
Q43.Let $a = 3 \hat{i} + \hat{j} - \hat{k}$ and $c = 2 \hat{i} - 3 \hat{j} + 3 \hat{k}$ . If $b$ is a vector such that $a = b \times c$ and $∣ b ∣^{2} = 50$ , then $∣72 - ∣ b + c ∣^{2} ∣$ is equal…
Mathematics · Vector Algebra · Numerical
Q44.Let $α$ be the constant term in the binomial expansion of $(x - \frac{6}{x ^{\frac{3}{2}}})^{n}, n \leq 15$ . If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of…
Mathematics · Binomial Theorem · Numerical