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Mathematics · 2025 · 29 Jan · Shift 2

25 questions from this JEE Main paper

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2025 · 29 Jan · Shift 2
Mathematics

Mathematics · 2025 · 29 Jan · Shift 2

25 questions from this JEE Main paper

Sets and Relations1 questions Matrices and Determinants3 questions 3D Geometry2 questions Functions1 questions Vector Algebra1 questions Quadratic Equation and Inequalities1 questions Straight Lines and Pair of Straight Lines1 questions Probability1 questions Binomial Theorem1 questions Ellipse1 questions Circle1 questions Differential Equations1 questions Trigonometric Ratio and Identites1 questions Definite Integration3 questions Area Under the Curves1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability1 questions Parabola1 questions Complex Numbers1 questions Sequences and Series1 questions

Q26.Let $S = N \cup {0}$ . Define a relation R from S to $R$ by : $R = {(x, y) : lo g_{e} y = x lo g_{e} (\frac{2}{5}), x \in S, y \in R} .$ Then, the…
Mathematics · Sets and Relations · MCQ
Q27.Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} \in {0, 1}$ for all $i$ and $j$ . Let the random variable $X$ denote the possible values of the determinant of the matrix $A$ . Then, the variance of $X$ is:
Mathematics · Matrices and Determinants · MCQ
Q28.Let a straight line $L$ pass through the point $P (2, - 1, 3)$ and be perpendicular to the lines $\frac{x - 1}{2} = \frac{y + 1}{1} = \frac{z - 3}{- 2}$ and $\frac{x - 3}{1} = \frac{y - 2}{3} = \frac{z + 2}{4}$ . If the line $L$ intersects the…
Mathematics · 3D Geometry · MCQ
Q29.If the domain of the function $lo g_{5} (18 x - x^{2} - 77)$ is $(α, β)$ and the domain of the function $lo g_{(x - 1)} (\frac{2 x ^{2} + 3 x - 2}{x ^{2} - 3 x - 4})$ is $(γ, δ)$ , then $α^{2} + β^{2} + γ^{2}$ is…
Mathematics · Functions · MCQ
Q30.Let $\overset{a}{^}$ be a unit vector perpendicular to the vectors $b = \hat{i} - 2 \hat{j} + 3 \hat{k}$ and $c = 2 \hat{i} + 3 \hat{j} - \hat{k}$ , and $\overset{a}{^}$ makes an angle of $cos^{- 1} (- \frac{1}{3})$ with the vector $\hat{i} + \hat{j} + \hat{k}$ …
Mathematics · Vector Algebra · MCQ
Q31.Let $α, β (α e q β)$ be the values of $m$ , for which the equations $x + y + z = 1$ , $x + 2 y + 4 z = m$ and $x + 4 y + 10 z = m^{2}$ have infinitely many solutions. Then the value of $n = 1 \sum 10 (n^{α} + n^{β})$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q32.If the set of all $a \in R$ , for which the equation $2 x^{2} + (a - 5) x + 15 = 3 a$ has no real root, is the interval ( $X = ∣ x \in Z; α < x < β ∣$ ), and $X = ∣ x \in Z; α < x < β ∣$ , then $x \in X \sum x^{2}$ is equal to:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball…
Mathematics · Probability · MCQ
Q35.The remainder, when $7^{103}$ is divided by 23, is equal to:
Mathematics · Binomial Theorem · MCQ
Q36.If $α x + β y = 109$ is the equation of the chord of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ , whose mid point is $(\frac{5}{2}, \frac{1}{2})$ . then $α + β$ is equal to :
Mathematics · Ellipse · MCQ
Q37.Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord, of the circle C, whose mid-point is (1, 2), is:
Mathematics · Circle · MCQ
Q38.If for the solution curve $y = f (x)$ of the differential equation $\frac{d y}{d x} + (tan x) y = \frac{2 + s e c x}{( 1 + 2 s e c x ) ^{2}}$ , $x \in (\frac{- π}{2}, \frac{π}{2}), f (\frac{π}{3}) = \frac{3}{10}$ , then $f (\frac{π}{4})$ …
Mathematics · Differential Equations · MCQ
Q39.Let $A = [a_{ij}]$ be a matrix of order $3 \times 3$ , with $a_{ij} = (2)^{i + j}$ . If the sum of all the elements in the third row of $A^{2}$ is $α + β 2, α, β \in Z$ , then…
Mathematics · Matrices and Determinants · MCQ
Q40.If $sin x + sin^{2} x = 1$ , $x \in (0, \frac{π}{2})$ , then $(cos^{12} x + tan^{12} x) + 3 (cos^{10} x + tan^{10} x + cos^{8} x + tan^{8} x) + (cos^{6} x + tan^{6} x)$ is equal to:
Mathematics · Trigonometric Ratio and Identites · MCQ
Q41.Let $f (x) = 0 \int x t (t^{2} - 9 t + 20) dt, 1 \leq x \leq 5$ . If the range of $f$ is $[α, β]$ , then $4 (α + β)$ equals :
Mathematics · Definite Integration · MCQ
Q42.Let the area enclosed between the curves $∣ y ∣ = 1 - x^{2}$ and $x^{2} + y^{2} = 1$ be $α$ . If $9 α = β π + γ; β, γ$ are integers, then the value of $∣ β - γ ∣$ equals:
Mathematics · Area Under the Curves · MCQ
Q43.Let P be the foot of the perpendicular from the point $(1, 2, 2)$ on the line $L : \frac{x - 1}{1} = \frac{y + 1}{- 1} = \frac{z - 2}{2}$ . Let the line $r = (- \hat{i} + \hat{j} - 2 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}), λ \in R$ …
Mathematics · 3D Geometry · MCQ
Q44.If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is :
Mathematics · Permutations and Combinations · MCQ
Q45.Let the function $f (x) = (x^{2} - 1) x^{2} - a x + 2 + cos ∣ x ∣$ be not differentiable at the two points $x = α = 2$ and $x = β$ . Then the distance of the point $(α, β)$ from the line $12 x + 5 y + 10 = 0$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.If $24 0 \int \frac{π}{4} [sin 4 x - \frac{π}{12} + [2 sin x]] d x = 2 π + α$ , where $[\cdot]$ denotes the greatest integer function, then $α$ is equal to .
Mathematics · Definite Integration · Numerical
Q47.Let $y^{2} = 12 x$ be the parabola and $S$ be its focus. Let $P Q$ be a focal chord of the parabola such that $(S P) (S Q) = \frac{147}{4}$ . Let $C$ be the circle described taking $P Q$ as a diameter. If the equation of a circle $C$ is $64 x^{2} + 64 y^{2} - α x - 643 y = β$ …
Mathematics · Parabola · Numerical
Q48.Let integers $a, b \in [- 3, 3]$ be such that $a + b e q 0$ . Then the number of all possible ordered pairs (a, b), for which $\frac{z - a}{z + b} = 1$ and $z + 1 ω ω^{2} ω z + ω^{2} 1 ω^{2} 1 z + ω = 1, z \in C$ …
Mathematics · Complex Numbers · Numerical
Q49.If $t \to 0 lim (0 \int 1 (3 x + 5)^{t} d x)^{\frac{1}{t}} = \frac{α}{5 e} (\frac{8}{5})^{\frac{2}{3}}$ , then $α$ is equal to .
Mathematics · Definite Integration · Numerical
Q50.Let $a_{1}, a_{2}, \dots, a_{2024}$ be an Arithmetic Progression such that $a_{1} + (a_{5} + a_{10} + a_{15} + \dots + a_{2020}) + a_{2024} = 2233$ . Then $a_{1} + a_{2} + a_{3} + \dots + a_{2024}$ is equal to .
Mathematics · Sequences and Series · Numerical