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Mathematics · 2023 · 11 Apr · Shift 2

20 questions from this JEE Main paper

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2023 · 11 Apr · Shift 2
Mathematics

Mathematics · 2023 · 11 Apr · Shift 2

20 questions from this JEE Main paper

Sequences and Series1 questions Binomial Theorem2 questions Matrices and Determinants2 questions Complex Numbers2 questions Permutations and Combinations1 questions Sets and Relations1 questions Statistics1 questions Definite Integration2 questions Limits Continuity and Differentiability1 questions Differential Equations1 questions Functions2 questions Vector Algebra1 questions Probability1 questions Area Under the Curves1 questions Quadratic Equation and Inequalities1 questions

Q23.Let $a, b, c$ and $d$ be positive real numbers such that $a + b + c + d = 11$ . If the maximum value of $a^{5} b^{3} c^{2} d$ is $3750 β$ , then the value of $β$ is
Mathematics · Sequences and Series · MCQ
Q24.The sum of the coefficients of three consecutive terms in the binomial expansion of $(1 + x)^{n + 2}$ , which are in the ratio $1 : 3 : 5$ , is equal to :
Mathematics · Binomial Theorem · MCQ
Q25.If the system of linear equations $7 x + 11 y + α z = 13 5 x + 4 y + 7 z = β 175 x + 194 y + 57 z = 361$ has infinitely many solutions, then $α + β + 2$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q26.For $a \in C$ , let $A = {z \in C : Re (a + \overset{z}{ˉ}) > Im (\overset{a}{ˉ} + z)}$ and $B = {z \in C : Re (a + \overset{z}{ˉ}) (S 1) : I f$ \operatorname{Re}(a),…
Mathematics · Complex Numbers · MCQ
Q27.If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is :
Mathematics · Permutations and Combinations · MCQ
Q28.Let $A = {1, 3, 4, 6, 9}$ and $B = {2, 4, 5, 8, 10}$ . Let $R$ be a relation defined on $A \times B$ such that $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) : a_{1} \leq b_{2}$ …
Mathematics · Sets and Relations · MCQ
Q29.If the $101 1^{th}$ term from the end in the binominal expansion of $(\frac{4 x}{5} - \frac{5}{2 x})^{2022}$ is 1024 times $101 1^{th}$ R term from the beginning, then $∣ x ∣$ is equal to
Mathematics · Binomial Theorem · MCQ
Q30. $x + 1 x x x x + λ x x x x + λ^{2} = \frac{9}{8} (103 x + 81)$ , then $λ, \frac{λ}{3}$ are the roots of the equation :
Mathematics · Matrices and Determinants · MCQ
Q31.Let the mean of 6 observations $1, 2, 4, 5, x$ and $y$ be 5 and their variance be 10 . Then their mean deviation about the mean is equal to :
Mathematics · Statistics · MCQ
Q32.If $f : R \to R$ be a continuous function satisfying $\int_{0}^{\frac{π}{2}} f (sin 2 x) sin x d x + α \int_{0}^{\frac{π}{4}} f (cos 2 x) cos x d x = 0$ , then the value of $α$ is :
Mathematics · Definite Integration · MCQ
Q33.Let $f$ and $g$ be two functions defined by $f (x) = {x + 1, ∣ x - 1∣, x < 0 x \geq 0$ and $g (x) = {x + 1, 1, x < 0 x \geq 0$ Then $(g \circ f) (x)$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q34.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + \frac{5}{x ( x ^{5} + 1 )} y = \frac{( x ^{5} + 1 ) ^{2}}{x ^{7}}, x > 0$ . If $y (1) = 2$ , then $y (2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q35.Let the function $f : [0, 2] \to R$ be defined as $f (x) = {e^{m i n {x^{2}, x - [x]},} e^{[x - l o g_{e} x]}, x \in [0, 1) x \in [1, 2]$ where $[t]$ denotes the greatest…
Mathematics · Definite Integration · MCQ
Q36.The domain of the function $f (x) = \frac{1}{[ x ] ^{2} - 3 [ x ] - 10}$ is : ( where $[x]$ denotes the greatest integer less than or equal to $x$ )
Mathematics · Functions · MCQ
Q37.Let $a = \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $b = \hat{i} + \hat{j} - \hat{k}$ . If $c$ is a vector such that $a \cdot c = 11, b \cdot (a \times c) = 27$ and $b \cdot c = - 3 ∣ b ∣$ , then…
Mathematics · Vector Algebra · Numerical
Q38.Let $A = {1, 2, 3, 4, 5}$ and $B = {1, 2, 3, 4, 5, 6}$ . Then the number of functions $f : A \to B$ satisfying $f (1) + f (2) = f (4) - 1$ is equal to .
Mathematics · Functions · Numerical
Q39.Let the probability of getting head for a biased coin be $\frac{1}{4}$ . It is tossed repeatedly until a head appears. Let $N$ be the number of tosses required. If the probability that the equation $64 x^{2} + 5 Nx + 1 = 0$ …
Mathematics · Probability · Numerical
Q40.If A is the area in the first quadrant enclosed by the curve $C : 2 x^{2} - y + 1 = 0$ , the tangent to $C$ at the point $(1, 3)$ and the line $x + y = 1$ , then the value of $60 A$ is …
Mathematics · Area Under the Curves · Numerical
Q41.Let $S = {z \in C - {i, 2 i} : \frac{z ^{2} + 8 i z - 15}{z ^{2} - 3 i z - 2} \in R}$ . If $α - \frac{13}{11} i \in S, α \in R - {0}$ , then $242 α^{2}$ is equal to …
Mathematics · Complex Numbers · Numerical
Q42.The number of points, where the curve $f (x) = e^{8 x} - e^{6 x} - 3 e^{4 x} - e^{2 x} + 1, x \in R$ cuts $x$ -axis, is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical