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Mathematics · 2025 · 7 Apr · Shift 1

25 questions from this JEE Main paper

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2025 · 7 Apr · Shift 1
Mathematics

Mathematics · 2025 · 7 Apr · Shift 1

25 questions from this JEE Main paper

Permutations and Combinations1 questions Circle1 questions Parabola1 questions Statistics1 questions Straight Lines and Pair of Straight Lines1 questions Limits Continuity and Differentiability2 questions Differential Equations1 questions Matrices and Determinants3 questions Binomial Theorem1 questions Trigonometric Ratio and Identites1 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Definite Integration1 questions 3D Geometry2 questions Area Under the Curves1 questions Application of Derivatives1 questions Vector Algebra1 questions Sequences and Series1 questions Sets and Relations2 questions Hyperbola1 questions

Q26.From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be…
Mathematics · Permutations and Combinations · MCQ
Q27.Let $C_{1}$ be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let $C_{2}$ be the circle with centre $(1, 3)$ that touches $C_{1}$ externally at the point $(α, β)$ . If $(β - α)^{2} = \frac{m}{n}$ …
Mathematics · Circle · MCQ
Q28.Let P be the parabola, whose focus is $(- 2, 1)$ and directrix is $2 x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose abscissa is $-$ 2, is
Mathematics · Parabola · MCQ
Q29.The mean and standard deviation of 100 observations are 40 and 5.1 , respectively. By mistake one observation is taken as 50 instead of 40 . If the correct mean and the correct standard deviation are $μ$ and $σ$ respectively, then $10 (μ + σ)$ …
Mathematics · Statistics · MCQ
Q30.Let ABC be the triangle such that the equations of lines AB and AC be $3 y - x = 2$ and $x + y = 2$ , respectively, and the points B and C lie on $x$ -axis. If P is the orthocentre of the triangle ABC , then the area of the triangle PBC is equal to
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31. $lim_{x \to 0^{+}} \frac{t a n ( 5 ( x ) ^{\frac{1}{3}} ) l o g _{e} ( 1 + 3 x ^{2} )}{( t a n ^{- 1} 3 x ) ^{2} ( e ^{5 (x)^{\frac{4}{3}}} - 1 )}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Let $y = y (x)$ be the solution curve of the differential equation $x (x^{2} + e^{x}) d y + (e^{x} (x - 2) y - x^{3}) d x = 0, x > 0$ , passing through the point $(1, 0)$ . Then $y (2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q33.Let $A$ be a $3 \times 3$ matrix such that $∣ adj (adj (adj A)) ∣ = 81$ . If $S = {n \in Z : (∣ adj (adj A) ∣)^{\frac{( n - 1 ) ^{2}}{2}} = ∣ A ∣^{(3 n^{2} - 5 n - 4)}}$ …
Mathematics · Matrices and Determinants · MCQ
Q34.The remainder when $((64)^{(64)})^{(64)}$ is divided by 7 is equal to
Mathematics · Binomial Theorem · MCQ
Q35.If for $θ \in [- \frac{π}{3}, 0]$ , the points $(x, y) = (3 tan (θ + \frac{π}{3}), 2 tan (θ + \frac{π}{6}))$ lie on $x y + α x + β y + γ = 0$ , then $α^{2} + β^{2} + γ^{2}$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q36.Let the system of equations : $2 x + 3 y + 5 z = 9 7 x + 3 y - 2 z = 8 12 x + 3 y - (4 + λ) z = 16 - μ$ have infinitely many solutions. Then the radius of the circle centred at $(λ, μ)$ and…
Mathematics · Matrices and Determinants · MCQ
Q37.Let the set of all values of $p \in R$ , for which both the roots of the equation $x^{2} - (p + 2) x + (2 p + 9) = 0$ are negative real numbers, be the interval $(α, β]$ . Then $β - 2 α$ is equal to
Mathematics · Quadratic Equation and Inequalities · MCQ
Q38.Among the statements (S1) : The set ${z \in C - {- i} : ∣ z ∣ = 1$ and $\frac{z - i}{z + i}$ is purely real $}$ contains exactly two elements, and (S2) : The set ${z \in C - {- 1} : ∣ z ∣ = 1$ and $\frac{z - 1}{z + 1}$ …
Mathematics · Complex Numbers · MCQ
Q39.The integral $\int_{0}^{π} \frac{( x + 3 ) s i n x}{1 + 3 c o s ^{2} x} d x$ is equal to
Mathematics · Definite Integration · MCQ
Q40.Let the line L pass through $(1, 1, 1)$ and intersect the lines $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}$ and $\frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z}{1}$ . Then, which of the following points lies on the line $L$ ?
Mathematics · 3D Geometry · MCQ
Q41.If the area of the region bounded by the curves $y = 4 - \frac{x ^{2}}{4}$ and $y = \frac{x - 4}{2}$ is equal to $α$ , then $6 α$ . equals
Mathematics · Area Under the Curves · MCQ
Q42.If the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x}{1} = \frac{y}{α} = \frac{z - 5}{1}$ is $\frac{5}{6}$ , then the sum of all possible values of $α$ is
Mathematics · 3D Geometry · MCQ
Q43.Let $x = - 1$ and $x = 2$ be the critical points of the function $f (x) = x^{3} + a x^{2} + b lo g_{e} ∣ x ∣ + 1, x e q 0$ . Let $m$ and M respectively be the absolute minimum and the absolute maximum values of $f$ in the interval $[- 2, - \frac{1}{2}]$ …
Mathematics · Application of Derivatives · MCQ
Q44.Let the angle $θ, 0 < θ < \frac{π}{2}$ between two unit vectors $\overset{a}{^}$ and $\hat{b}$ be $sin^{- 1} (\frac{65}{9})$ . If the vector $c = 3 \overset{a}{^} + 6 \hat{b} + 9 (\overset{a}{^} \times \hat{b})$ , then the value of…
Mathematics · Vector Algebra · MCQ
Q45.Let $x_{1}, x_{2}, x_{3}, x_{4}$ be in a geometric progression. If $2, 7, 9, 5$ are subtracted respectively from $x_{1}, x_{2}, x_{3}, x_{4}$ , then the resulting numbers are in an arithmetic progression. Then the value of $\frac{1}{24} (x_{1} x_{2} x_{3} x_{4})$ …
Mathematics · Sequences and Series · MCQ
Q46.The number of singular matrices of order 2 , whose elements are from the set ${2, 3, 6, 9}$ , is .
Mathematics · Matrices and Determinants · Numerical
Q47.The number of relations on the set $A = {1, 2, 3}$ , containing at most 6 elements including $(1, 2)$ , which are reflexive and transitive but not symmetric, is .
Mathematics · Sets and Relations · Numerical
Q48.The number of points of discontinuity of the function $f (x) = [\frac{x ^{2}}{2}] - [x], x \in [0, 4]$ , where $[\cdot]$ denotes the greatest integer function, is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q49.For $n \geq 2$ , let $S_{n}$ denote the set of all subsets of ${1, 2, \dots, n}$ with no two consecutive numbers. For example ${1, 3, 5} \in S_{6}$ , but ${1, 2, 4} \in / S_{6}$ . Then $n (S_{5})$ is equal to
Mathematics · Sets and Relations · Numerical
Q50.Consider the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ having one of its focus at $P (- 3, 0)$ . If the latus ractum through its other focus subtends a right angle at P and $a^{2} b^{2} = α 2 - β, α, β \in N$ …
Mathematics · Hyperbola · Numerical