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Mathematics · 2023 · 29 Jan · Shift 2

21 questions from this JEE Main paper

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2023 · 29 Jan · Shift 2
Mathematics

Mathematics · 2023 · 29 Jan · Shift 2

21 questions from this JEE Main paper

Differential Equations1 questions Sets and Relations1 questions Permutations and Combinations3 questions Vector Algebra2 questions Probability1 questions Functions1 questions Trigonometric Ratio and Identites1 questions Area Under the Curves1 questions Definite Integration2 questions Binomial Theorem1 questions 3D Geometry1 questions Differentiation1 questions Statistics1 questions Complex Numbers1 questions Quadratic Equation and Inequalities1 questions Sequences and Series1 questions Matrices and Determinants1 questions

Q24.Let $y = y (x)$ be the solution of the differential equation $x lo g_{e} x \frac{d y}{d x} + y = x^{2} lo g_{e} x, (x > 1)$ . If $y (2) = 2$ , then $y (e)$ is equal to
Mathematics · Differential Equations · MCQ
Q25.Let R be a relation defined on $N$ as $a R b$ if $2 a + 3 b$ is a multiple of $5, a, b \in N$ . Then R is
Mathematics · Sets and Relations · MCQ
Q26.The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :
Mathematics · Permutations and Combinations · MCQ
Q27.If $a = i + 2 k, b = i + j + k, c = 7 i - 3 j + 4 k, r \times b + b \times c = 0$ …
Mathematics · Vector Algebra · MCQ
Q28.The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :
Mathematics · Permutations and Combinations · MCQ
Q29.Let $S = {w_{1}, w_{2}, ......}$ be the sample space associated to a random experiment. Let $P (w_{n}) = \frac{P ( w _{n - 1} )}{2}, n \geq 2$ . Let $A = {2 k + 3 l : k, l \in N}$ and $B = {w_{n} : n \in A}$ . Then P(B) is equal to :
Mathematics · Probability · MCQ
Q30.Consider a function $f : N \to R$ , satisfying $f (1) + 2 f (2) + 3 f (3) + .... + x f (x) = x (x + 1) f (x); x \geq 2$ with $f (1) = 1$ . Then $\frac{1}{f ( 2022 )} + \frac{1}{f ( 2028 )}$ is equal to
Mathematics · Functions · MCQ
Q31.The set of all values of $λ$ for which the equation $cos^{2} 2 x - 2 sin^{4} x - 2 cos^{2} x = λ$ has a real solution $x$ , is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q32.The area of the region $A = {(x, y) : ∣ cos x - sin x ∣ \leq y \leq sin x, 0 \leq x \leq \frac{π}{2}}$ is
Mathematics · Area Under the Curves · MCQ
Q33.Let $a = 4 i + 3 j$ and $b = 3 i - 4 j + 5 k$ . If $c$ is a vector such that $c . (a \times b) + 25 = 0, c . (i + j + k) = 4$ …
Mathematics · Vector Algebra · MCQ
Q34.The value of the integral $\int_{1}^{2} (\frac{t ^{4} + 1}{t ^{6} + 1}) d t$ is
Mathematics · Definite Integration · MCQ
Q35.Let K be the sum of the coefficients of the odd powers of $x$ in the expansion of $(1 + x)^{99}$ . Let $a$ be the middle term in the expansion of $(2 + \frac{1}{2})^{200}$ . If $\frac{^{200} C _{99} K}{a} = \frac{2 ^{l} m}{n}$ …
Mathematics · Binomial Theorem · MCQ
Q36.The value of the integral $1/2 \int 2 \frac{t a n ^{- 1} x}{x} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q37.The shortest distance between the lines $\frac{x - 1}{2} = \frac{y + 8}{- 7} = \frac{z - 4}{5}$ and $\frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 6}{- 3}$ is :
Mathematics · 3D Geometry · MCQ
Q38.Let $f$ and $g$ be the twice differentiable functions on $R$ such that $f^{''} (x) = g^{''} (x) + 6 x f^{'} (1) = 4 g^{'} (1) - 3 = 9 f (2) = 3 g (2) = 12$ . Then which of the following is NOT true?
Mathematics · Differentiation · MCQ
Q39.The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is .
Mathematics · Permutations and Combinations · Numerical
Q40.Let $X = {11, 12, 13, ...., 40, 41}$ and $Y = {61, 62, 63, ...., 90, 91}$ be the two sets of observations. If $\overline{x}$ and $\overline{y}$ are their respective means and $σ^{2}$ is the variance of all the observations in $X \cup Y$ ,…
Mathematics · Statistics · Numerical
Q41.Let $α = 8 - 14 i, A = {z \in c : \frac{α z - α z}{z ^{2} - ( z ) ^{2} - 112 i} = 1}$ and $B = {z \in c : ∣ z + 3 i ∣ = 4}$ . Then $z \in A \cap B \sum (Re o l imi t s z - Im o l imi t s z)$ …
Mathematics · Complex Numbers · Numerical
Q42.Let $α_{1}, α_{2}, ...., α_{7}$ be the roots of the equation $x^{7} + 3 x^{5} - 13 x^{3} - 15 x = 0$ and $∣ α_{1} ∣ \geq ∣ α_{2} ∣ \geq ... \geq ∣ α_{7} ∣$ . Then $α_{1} α_{2} - α_{3} α_{4} + α_{5} α_{6}$ is…
Mathematics · Quadratic Equation and Inequalities · Numerical
Q43.Let ${a_{k}}$ and ${b_{k}}, k \in N$ , be two G.P.s with common ratios $r_{1}$ and $r_{2}$ respectively such that $a_{1} = b_{1} = 4$ and $r_{1} < r_{2}$ . Let $c_{k} = a_{k} + b_{k}, k \in N$ . If $c_{2} = 5$ and $c_{3} = \frac{13}{4}$ …
Mathematics · Sequences and Series · Numerical
Q44.Let A be a symmetric matrix such that $∣A∣ = 2$ and $[23 1 \frac{3}{2}] A = [1 α 2 β]$ . If the…
Mathematics · Matrices and Determinants · Numerical