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Mathematics · 2023 · 1 Feb · Shift 2

23 questions from this JEE Main paper

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2023 · 1 Feb · Shift 2
Mathematics

Mathematics · 2023 · 1 Feb · Shift 2

23 questions from this JEE Main paper

Statistics1 questions Sets and Relations1 questions Application of Derivatives1 questions Vector Algebra2 questions Matrices and Determinants2 questions Differentiation1 questions Definite Integration2 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Probability1 questions Inverse Trigonometric Functions1 questions Functions1 questions Differential Equations1 questions Parabola1 questions Binomial Theorem2 questions Sequences and Series1 questions Permutations and Combinations2 questions

Q24.Let $9 = x_{1} < x_{2} < \dots < x_{7}$ be in an A.P. with common difference d. If the standard deviation of $x_{1}, x_{2} ..., x_{7}$ is 4 and the mean is $\overset{x}{ˉ}$ , then $\overset{x}{ˉ} + x_{6}$ is equal to :
Mathematics · Statistics · MCQ
Q25.Let $P (S)$ denote the power set of $S = {1, 2, 3, \dots ., 10}$ . Define the relations $R_{1}$ and $R_{2}$ on $P (S)$ as $AR_{1} B$ if $(A \cap B^{c}) \cup (B \cap A^{c}) = \emptyset$ …
Mathematics · Sets and Relations · MCQ
Q26.The sum of the absolute maximum and minimum values of the function $f (x) = x^{2} - 5 x + 6 - 3 x + 2$ in the interval $[- 1, 3]$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q27.Let $a = 5 \hat{i} - \hat{j} - 3 \hat{k}$ and $b = \hat{i} + 3 \hat{j} + 5 \hat{k}$ be two vectors. Then which one of the following statements is TRUE ?
Mathematics · Vector Algebra · MCQ
Q28.For the system of linear equations $α x + y + z = 1, x + α y + z = 1, x + y + α z = β$ , which one of the following statements is NOT correct?
Mathematics · Matrices and Determinants · MCQ
Q29.If $y (x) = x^{x}, x > 0$ , then $y^{''} (2) - 2 y^{'} (2)$ is equal to
Mathematics · Differentiation · MCQ
Q30.The value of the integral $- \frac{π}{4} \int \frac{π}{4} \frac{x + \frac{π}{4}}{2 - c o s 2 x} d x$ is :
Mathematics · Definite Integration · MCQ
Q31.The area of the region given by ${(x, y) : x y \leq 8, 1 \leq y \leq x^{2}}$ is :
Mathematics · Area Under the Curves · MCQ
Q32.The number of integral values of k, for which one root of the equation $2 x^{2} - 8 x + k = 0$ lies in the interval (1, 2) and its other root lies in the interval (2, 3), is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.Let $a, b$ be two real numbers such that $ab < 0$ . IF the complex number $\frac{1 + ai}{b + i}$ is of unit modulus and $a + ib$ lies on the circle $∣ z - 1∣ = ∣2 z ∣$ , then a possible value of $\frac{1 + [ a ]}{4 b}$ , where $[t]$ is greatest integer…
Mathematics · Complex Numbers · MCQ
Q34.If $A = \frac{1}{2} [1 - 3 31]$ , then :
Mathematics · Matrices and Determinants · MCQ
Q35.Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{st}$ die is less than the number appeared on the $2^{nd}$ die, $B$ be the event that the number appeared on the…
Mathematics · Probability · MCQ
Q36.Let $a = 2 \hat{i} - 7 \hat{j} + 5 \hat{k}, b = \hat{i} + \hat{k}$ and $c = \hat{i} + 2 \hat{j} - 3 \hat{k}$ be three given vectors. If $r$ is a vector such that $r \times a = c \times a$ …
Mathematics · Vector Algebra · MCQ
Q37.Let $S = {x \in R : 0 < x < 1 and 2 tan^{- 1} (\frac{1 - x}{1 + x}) = cos^{- 1} (\frac{1 - x ^{2}}{1 + x ^{2}})}$ . If $n (S)$ denotes the number of elements in $S$ then :
Mathematics · Inverse Trigonometric Functions · MCQ
Q38.Let $f : R - 0, 1 \to R$ be a function such that $f (x) + f (\frac{1}{1 - x}) = 1 + x$ . Then $f (2)$ is equal to
Mathematics · Functions · MCQ
Q39.Let $α x = exp (x^{β} y^{γ})$ be the solution of the differential equation $2 x^{2} y d y - (1 - x y^{2}) d x = 0, x > 0, y (2) = lo g_{e} 2$ . Then $α + β - γ$ equals :
Mathematics · Differential Equations · MCQ
Q40.If the $x$ -intercept of a focal chord of the parabola $y^{2} = 8 x + 4 y + 4$ is 3, then the length of this chord is equal to .
Mathematics · Parabola · Numerical
Q41.If $0 \int π \frac{5 ^{c o s x} ( 1 + c o s x c o s 3 x + c o s ^{2} x + c o s ^{3} x c o s 3 x ) d x}{1 + 5 ^{c o s x}} = \frac{k π}{16}$ , then k is equal to .
Mathematics · Definite Integration · Numerical
Q42.Let the sixth term in the binomial expansion of $(2^{l o g_{2} (10 - 3^{x})} + 5 2^{(x - 2) l o g_{2} 3})^{m}$ in the increasing powers of $2^{(x - 2) l o g_{2} 3}$ , be 21 . If the…
Mathematics · Binomial Theorem · Numerical
Q43.The sum of the common terms of the following three arithmetic progressions. $3, 7, 11, 15, \dots ., 399$ , $2, 5, 8, 11, \dots ., 359$ and $2, 7, 12, 17, \dots ., 197$ , is equal to .
Mathematics · Sequences and Series · Numerical
Q44.Number of integral solutions to the equation $x + y + z = 21$ , where $x \geq 1, y \geq 3, z \geq 4$ , is equal to .
Mathematics · Permutations and Combinations · Numerical
Q45.If the term without $x$ in the expansion of $(x^{\frac{2}{3}} + \frac{α}{x ^{3}})^{22}$ is 7315 , then $∣ α ∣$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q46.The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is .
Mathematics · Permutations and Combinations · Numerical