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Mathematics · 2025 · 29 Jan · Shift 1

25 questions from this JEE Main paper

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2025 · 29 Jan · Shift 1
Mathematics

Mathematics · 2025 · 29 Jan · Shift 1

25 questions from this JEE Main paper

3D Geometry1 questions Permutations and Combinations2 questions Matrices and Determinants3 questions Sequences and Series1 questions Ellipse1 questions Parabola1 questions Straight Lines and Pair of Straight Lines1 questions Quadratic Equation and Inequalities1 questions Binomial Theorem1 questions Limits Continuity and Differentiability2 questions Differential Equations1 questions Complex Numbers1 questions Statistics1 questions Vector Algebra2 questions Area Under the Curves1 questions Circle1 questions Sets and Relations1 questions Definite Integration2 questions Inverse Trigonometric Functions1 questions

Q26.Let $L_{1} : \frac{x - 1}{1} = \frac{y - 2}{- 1} = \frac{z - 1}{2}$ and $L_{2} : \frac{x + 1}{- 1} = \frac{y - 2}{2} = \frac{z}{1}$ be two lines. Let $L_{3}$ be a line passing through the point $(α, β, γ)$ and be perpendicular to both $L_{1}$ …
Mathematics · 3D Geometry · MCQ
Q27.Let $P$ be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in $P$ are formed by using the digits 1, 2 and 3 only, then the number of elements in the set $P$ is :
Mathematics · Permutations and Combinations · MCQ
Q28.Let $A = [a_{ij}] = [lo g_{5} 128 lo g_{5} 8 lo g_{4} 5 lo g_{4} 25]$ . If $A_{ij}$ is the cofactor of $a_{ij}$ , $C_{ij} = k = 1 \sum 2 a_{ik} A_{j k}, 1 \leq i, j \leq 2$ …
Mathematics · Matrices and Determinants · MCQ
Q29.Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is :
Mathematics · Sequences and Series · MCQ
Q30.Let the ellipse $E_{1} : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ , $a > b$ and $E_{2} : \frac{x ^{2}}{A ^{2}} + \frac{y ^{2}}{B ^{2}} = 1$ , $A < B$ have same eccentricity $\frac{1}{3}$ . Let the product of their lengths of latus rectums be $\frac{32}{3}$ …
Mathematics · Ellipse · MCQ
Q31.Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points A and B, then (AB)2 is equal to :
Mathematics · Parabola · MCQ
Q32.Let ΔABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y – 31 = 0 and 9x – 2y – 19 = 0. Let the point (h, k) be the image of the centroid of ΔABC in the line 3x + 6y – 53 = 0. Then h2 + k2 + hk is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.The number of solutions of the equation $(\frac{9}{x} - \frac{9}{x} + 2) (\frac{2}{x} - \frac{7}{x} + 3) = 0$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.The least value of n for which the number of integral terms in the Binomial expansion of $(37 + 1211)^{n}$ is 183, is :
Mathematics · Binomial Theorem · MCQ
Q35.The value of $n \to \infty lim (k = 1 \sum n \frac{k ^{3} + 6 k ^{2} + 11 k + 5}{( k + 3 )!})$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.Let y = y(x) be the solution of the differential equation : $cos x (lo g_{e} (cos x))^{2} d y + (sin x - 3 y sin x lo g_{e} (cos x)) d x = 0$ , x ∈ (0, $\frac{π}{2}$ ). If $y (\frac{π}{4})$ = $- \frac{1}{l o g _{e} 2}$ , then $y (\frac{π}{6})$ …
Mathematics · Differential Equations · MCQ
Q37.Let $∣ z_{1} - 8 - 2 i ∣ \leq 1$ and $∣ z_{2} - 2 + 6 i ∣ \leq 2$ , $z_{1}, z_{2} \in C$ . Then the minimum value of $∣ z_{1} - z_{2} ∣$ is :
Mathematics · Complex Numbers · MCQ
Q38.Let $x_{1}, x_{2}, ..., x_{10}$ be ten observations such that $i = 1 \sum 10 (x_{i} - 2) = 30$ , $i = 1 \sum 10 (x_{i} - β)^{2} = 98$ , $β > 2$ , and their variance is $\frac{4}{5}$ . If $μ$ and $σ^{2}$ are respectively…
Mathematics · Statistics · MCQ
Q39.Let $a = \hat{i} + 2 \hat{j} + \hat{k}$ and $b = 2 \hat{i} + 7 \hat{j} + 3 \hat{k}$ . Let $L_{1} : r = (- \hat{i} + 2 \hat{j} + \hat{k}) + λ a, λ \in R$ and $L_{2} : r = (\hat{j} + \hat{k}) + μ b, μ \in R$ …
Mathematics · Vector Algebra · MCQ
Q40.Let the area of the region $(x, y) : 2 y \leq x^{2} + 3, y + ∣ x ∣ \leq 3, y \geq ∣ x - 1∣$ be $A$ . Then $6 A$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q41.Let $a = 2 \hat{i} - \hat{j} + 3 \hat{k}, b = 3 \hat{i} - 5 \hat{j} + \hat{k}$ and $c$ be a vector such that $a \times c = a \times b = c \times b$ and $(a + c) \cdot (b + c) = 168$ …
Mathematics · Vector Algebra · MCQ
Q42.Let the line x+y=1 meet the circle $x^{2} + y^{2} = 4$ at the points A and B. If the line perpendicular to AB and passing through the mid-point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to :
Mathematics · Circle · MCQ
Q43.Define a relation R on the interval $[0, \frac{π}{2})$ by $x$ R $y$ if and only if $sec^{2} x - tan^{2} y = 1$ . Then R is :
Mathematics · Sets and Relations · MCQ
Q44.Let M and m respectively be the maximum and the minimum values of $f (x) = 1 + sin^{2} x sin^{2} x sin^{2} x cos^{2} x 1 + cos^{2} x cos^{2} x 4 sin 4 x 4 sin 4 x 1 + 4 sin 4 x, x \in R$ …
Mathematics · Matrices and Determinants · MCQ
Q45.The integral $80 0 \int \frac{π}{4} (\frac{s i n θ + c o s θ}{9 + 16 s i n 2 θ}) d θ$ is equal to :
Mathematics · Definite Integration · MCQ
Q46.Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which $x \to 0^{+} lim (x ([\frac{1}{x}] + [\frac{2}{x}] + \dots + [\frac{p}{x}]) - x^{2} ([\frac{1}{x ^{2}}] + [\frac{2 ^{2}}{x ^{2}}] + \dots + [\frac{9 ^{2}}{x ^{2}}]) \geq 1$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q47.Let $S = {m \in Z : A^{m^{2}} + A^{m} = 3 I - A^{- 6}}$ , where $A = [21 - 1 0]$ . Then $n (S)$ is equal to .
Mathematics · Matrices and Determinants · Numerical
Q48.Let S = ${x : cos^{- 1} x = π + sin^{- 1} x + sin^{- 1} [2 x + 1]}$ . Then $x \in S \sum (2 x - 1)^{2}$ is equal to .
Mathematics · Inverse Trigonometric Functions · Numerical
Q49.Let $f : (0, \infty) \to R$ be a twice differentiable function. If for some $a e 0, 0 \int 1 f (λ x) d λ = a f (x), f (1) = 1$ and $f (16) = \frac{1}{8}$ , then $16 - f^{'} (\frac{1}{16})$ …
Mathematics · Definite Integration · Numerical
Q50.The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is .
Mathematics · Permutations and Combinations · Numerical