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Mathematics · 2024 · 27 Jan · Shift 2

30 questions from this JEE Main paper

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2024 · 27 Jan · Shift 2
Mathematics

Mathematics · 2024 · 27 Jan · Shift 2

30 questions from this JEE Main paper

Inverse Trigonometric Functions1 questions Vector Algebra2 questions Limits Continuity and Differentiability2 questions Probability1 questions 3D Geometry2 questions Sets and Relations1 questions Quadratic Equation and Inequalities1 questions Hyperbola1 questions Sequences and Series1 questions Functions1 questions Differential Equations2 questions Trigonometric Functions and Equations1 questions Application of Derivatives1 questions Straight Lines and Pair of Straight Lines2 questions Permutations and Combinations1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions Definite Integration2 questions Statistics1 questions Binomial Theorem1 questions Area Under the Curves1 questions Circle1 questions Complex Numbers1 questions

Q31.Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $tan^{- 1} (x) + tan^{- 1} (2 x) = \frac{π}{4}$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.Let the position vectors of the vertices $C$ and $C$ of a triangle be $2 \hat{i} + 2 \hat{j} + \hat{k}, \hat{i} + 2 \hat{j} + 2 \hat{k}$ and $2 \hat{i} + \hat{j} + 2 \hat{k}$ respectively. Let $l_{1}, l_{2}$ and $l_{3}$ be…
Mathematics · Vector Algebra · MCQ
Q33.Consider the function $f : (0, 2) \to R$ defined by $f (x) = \frac{x}{2} + \frac{2}{x}$ and the function $g (x)$ defined by $g (x) = {min ⌊ f (t)}, \frac{3}{2} + x, 0 < t \leq x and 0 < x \leq 1 1 < x < 2 . Then,$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q34.An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :
Mathematics · Probability · MCQ
Q35.Let the image of the point $(1, 0, 7)$ in the line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$ be the point $(α, β, γ)$ . Then which one of the following points lies on the line passing through $(α, β, γ)$ and making…
Mathematics · 3D Geometry · MCQ
Q36.Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B$ . Then the distance of the point $P (m, n)$ from the point $Q (- 2, - 3)$ is…
Mathematics · Sets and Relations · MCQ
Q37.If $x^{2} - x - 1 = 0$ are the roots of the equation, $x^{2} - x - 1 = 0$ and $S_{n} = 2023 α^{n} + 2024 β^{n}$ , then :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.Let $e_{1}$ be the eccentricity of the hyperbola $\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1$ and $e_{2}$ be the eccentricity of the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ , which passes through the foci of the hyperbola.…
Mathematics · Hyperbola · MCQ
Q39. $The 2 0^{th} term from the end of the progression 20, 19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \dots, - 129 \frac{1}{4} is :$
Mathematics · Sequences and Series · MCQ
Q40.Let $f : R - {\frac{- 1}{2}} \to R$ and $g : R - {\frac{- 5}{2}} \to R$ be defined as $f (x) = \frac{2 x + 3}{2 x + 1}$ and $g (x) = \frac{∣ x ∣ + 1}{2 x + 5}$ . Then, the domain of…
Mathematics · Functions · MCQ
Q41. $If lim_{x \to 0} \frac{3 + α s i n x + β c o s x + l o g _{e} ( 1 - x )}{3 t a n ^{2} x} = \frac{1}{3}, then 2 α - β is equal to :$
Mathematics · Limits Continuity and Differentiability · MCQ
Q42.If $y = y (x)$ is the solution curve of the differential equation $(x^{2} - 4) d y - (y^{2} - 3 y) d x = 0, x > 2, y (4) = \frac{3}{2}$ and the slope of the curve is never zero, then the value of $y (10)$ equals :
Mathematics · Differential Equations · MCQ
Q43.If $2 tan^{2} θ - 5 sec θ = 1$ has exactly 7 solutions in the interval $[0, \frac{nπ}{2}]$ , for the least value of $n \in N$ , then $\sum_{k = 1}^{n} \frac{k}{2 ^{k}}$ is equal to:
Mathematics · Trigonometric Functions and Equations · MCQ
Q44.Let $g (x) = 3 f (\frac{x}{3}) + f (3 - x)$ and $f^{''} (x) > 0$ for all $x \in (0, 3)$ . If $g$ is decreasing in $(0, α)$ and increasing in $(α, 3)$ , then $8 α$ is :
Mathematics · Application of Derivatives · MCQ
Q45.Let $R$ be the interior region between the lines $3 x - y + 1 = 0$ and $x + 2 y - 5 = 0$ containing the origin. The set of all values of $a$ , for which the points $(a^{2}, a + 1)$ lie in $R$ , is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q46.Let $α = \frac{( 4 !)!}{( 4 ! ) ^{3!}}$ and $β = \frac{( 5 !)!}{( 5 ! ) ^{4!}}$ . Then :
Mathematics · Permutations and Combinations · MCQ
Q47. $The integral \int \frac{( x ^{8} - x ^{2} ) d x}{( x ^{12} + 3 x ^{6} + 1 ) t a n ^{- 1} ( x ^{3} + \frac{1}{x ^{3}} )} is equal to :$
Mathematics · Indefinite Integrals · MCQ
Q48.The values of $α$ , for which $11 2 α + 3 \frac{3}{2} \frac{1}{3} 3 α + 1 α + \frac{3}{2} α + \frac{1}{3} 0 = 0$ , lie in the interval
Mathematics · Matrices and Determinants · MCQ
Q49.For $0 < a < 1$ , the value of the integral $0 \int π \frac{d x}{1 - 2 a c o s x + a ^{2}}$ is :
Mathematics · Definite Integration · MCQ
Q50.The position vectors of the vertices $C$ and $C$ of a triangle are $2 \hat{i} - 3 \hat{j} + 3 \hat{k}, 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $- \hat{i} + \hat{j} + 3 \hat{k}$ respectively. Let $l$ denotes the length of…
Mathematics · Vector Algebra · MCQ
Q51.The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If $μ$ and $σ^{2}$ denote the mean and variance of the correct…
Mathematics · Statistics · Numerical
Q52.The coefficient of $x^{2012}$ in the expansion of $(1 - x)^{2008} (1 + x + x^{2})^{2007}$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q53.The lines $\frac{x - 2}{2} = \frac{y}{- 2} = \frac{z - 7}{16}$ and $\frac{x + 3}{4} = \frac{y + 2}{3} = \frac{z + 2}{1}$ intersect at the point $P$ . If the distance of $P$ from the line $\frac{x + 1}{2} = \frac{y - 1}{3} = \frac{z - 1}{1}$ is $l$ , then $14 l^{2}$ …
Mathematics · 3D Geometry · Numerical
Q54.Let $f (x) = 0 \int x g (t) lo g_{e} (\frac{1 - t}{1 + t}) dt$ , where $g$ is a continuous odd function. If $\int_{- π /2}^{π /2} (f (x) + \frac{x ^{2} c o s x}{1 + e ^{x}}) d x = (\frac{π}{α})^{2} - α$ …
Mathematics · Definite Integration · Numerical
Q55.If the area of the region ${(x, y) : 0 \leq y \leq min {2 x, 6 x - x^{2}}}$ is $A$ , then is equal to .
Mathematics · Area Under the Curves · Numerical
Q56.If the sum of squares of all real values of $α$ , for which the lines $2 x - y + 3 = 0, 6 x + 3 y + 1 = 0$ and $α x + 2 y - 2 = 0$ do not form a triangle is $p$ , then the greatest integer less than or equal to $p$ is .
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q57.Let $A$ be a $2 \times 2$ real matrix and $I$ be the identity matrix of order 2. If the roots of the equation $∣ A - x I ∣ = 0$ be $- 1$ and 3, then the sum of the diagonal elements of the matrix $A^{2}$ is
Mathematics · Matrices and Determinants · Numerical
Q58.Consider a circle $(x - α)^{2} + (y - β)^{2} = 50$ , where $α, β > 0$ . If the circle touches the line $y + x = 0$ at the point $P$ , whose distance from the origin is $42$ , then $(α + β)^{2}$ is equal to …
Mathematics · Circle · Numerical
Q59.Let the complex numbers $α$ and $\frac{1}{α ˉ}$ lie on the circles $∣ z - z_{0} ∣^{2} = 4$ and $∣ z - z_{0} ∣^{2} = 16$ respectively, where $z_{0} = 1 + i$ . Then, the value of $100∣ α ∣^{2}$ is .
Mathematics · Complex Numbers · Numerical
Q60.If the solution curve, of the differential equation $\frac{d y}{d x} = \frac{x + y - 2}{x - y}$ passing through the point $(2, 1)$ is $tan^{- 1} (\frac{y - 1}{x - 1}) - \frac{1}{β} lo g_{e} (α + (\frac{y - 1}{x - 1})^{2}) = lo g_{e} ∣ x - 1∣$ …
Mathematics · Differential Equations · Numerical