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Mathematics · 2025 · 23 Jan · Shift 1

25 questions from this JEE Main paper

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2025 · 23 Jan · Shift 1
Mathematics

Mathematics · 2025 · 23 Jan · Shift 1

25 questions from this JEE Main paper

Differential Equations1 questions 3D Geometry1 questions Permutations and Combinations1 questions Functions1 questions Vector Algebra2 questions Inverse Trigonometric Functions1 questions Probability1 questions Trigonometric Ratio and Identites1 questions Limits Continuity and Differentiability1 questions Matrices and Determinants2 questions Definite Integration1 questions Statistics1 questions Complex Numbers1 questions Indefinite Integrals1 questions Parabola1 questions Sequences and Series1 questions Properties of Triangle1 questions Sets and Relations1 questions Binomial Theorem1 questions Application of Derivatives1 questions Quadratic Equation and Inequalities1 questions Circle1 questions Area Under the Curves1 questions

Q26.Let a curve $y = f (x)$ pass through the points $(0, 5)$ and $(lo g_{e} 2, k)$ . If the curve satisfies the differential equation $2 (3 + y) e^{2 x} d x - (7 + e^{2 x}) d y = 0$ , then $k$ is equal to
Mathematics · Differential Equations · MCQ
Q27.Let P be the foot of the perpendicular from the point $Q (10, - 3, - 1)$ on the line $\frac{x - 3}{7} = \frac{y - 2}{- 1} = \frac{z + 1}{- 2}$ . Then the area of the right angled triangle $P QR$ , where $R$ is the point $(3, - 2, 1)$ , is
Mathematics · 3D Geometry · MCQ
Q28.The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :
Mathematics · Permutations and Combinations · MCQ
Q29.Let $f (x) = lo g_{e} x$ and $g (x) = \frac{x ^{4} - 2 x ^{3} + 3 x ^{2} - 2 x + 2}{2 x ^{2} - 2 x + 1}$ . Then the domain of $f \circ g$ is
Mathematics · Functions · MCQ
Q30.Let the position vectors of the vertices $\hat{i} + 2 \hat{j} + \hat{k}, \hat{i} + 3 \hat{j} - 2 \hat{k}$ and C of a tetrahedron ABCD be $\hat{i} + 2 \hat{j} + \hat{k}, \hat{i} + 3 \hat{j} - 2 \hat{k}$ and $2 \hat{i} + \hat{j} - \hat{k}$ …
Mathematics · Vector Algebra · MCQ
Q31.If $\frac{π}{2} \leq x \leq \frac{3 π}{4}$ , then $cos^{- 1} (\frac{12}{13} cos x + \frac{5}{13} sin x)$ is equal to
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of…
Mathematics · Probability · MCQ
Q33.The value of $(sin 7 0^{\circ}) (cot 1 0^{\circ} cot 7 0^{\circ} - 1)$ is
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.If the function $f (x) = {\frac{2}{x} {sin (k_{1} + 1) x + sin (k_{2} - 1) x}, x 0$ is continuous at $x = 0$ , then $k_{1}^{2} + k_{2}^{2}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.If the system of equations $(λ - 1) x + (λ - 4) y + λ z = 5 λ x + (λ - 1) y + (λ - 4) z = 7 (λ + 1) x + (λ + 2) y - (λ + 2) z = 9$ has infinitely many solutions,…
Mathematics · Matrices and Determinants · MCQ
Q36.The value of $\int_{e^{2}}^{e^{4}} \frac{1}{x} (\frac{e ^{((l o g_{e} x)^{2} + 1)^{- 1}}}{e ^{((l o g_{e} x)^{2} + 1)^{- 1}} + e ^{((6 - l o g_{e} x)^{2} + 1)^{- 1}}}) d x$ is
Mathematics · Definite Integration · MCQ
Q37.Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of…
Mathematics · Statistics · MCQ
Q38.Let $\frac{z ˉ - i}{2 z ˉ + i} = \frac{1}{3}, z \in C$ , be the equation of a circle with center at $C$ . If the area of the triangle, whose vertices are at the points $(0, 0), C$ and $(α, 0)$ is 11 square units, then $α^{2}$ …
Mathematics · Complex Numbers · MCQ
Q39.Let $I (x) = \int \frac{d x}{( x - 11 ) ^{\frac{11}{13}} ( x + 15 ) ^{\frac{15}{13}}}$ . If $I (37) - I (24) = \frac{1}{4} (\frac{1}{b ^{\frac{1}{13}}} - \frac{1}{c ^{\frac{1}{13}}}), b, c \in N$ …
Mathematics · Indefinite Integrals · MCQ
Q40.If the line $3 x - 2 y + 12 = 0$ intersects the parabola $4 y = 3 x^{2}$ at the points $A$ and $B$ , then at the vertex of the parabola, the line segment AB subtends an angle equal to
Mathematics · Parabola · MCQ
Q41.If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to
Mathematics · Sequences and Series · MCQ
Q42.Let the arc $A C$ of a circle subtend a right angle at the centre $O$ . If the point $B$ on the arc $A C$ , divides the arc $A C$ such that $\frac{length of arc A B}{length of arc B C} = \frac{1}{5}$ …
Mathematics · Vector Algebra · MCQ
Q43.Let the area of a $△ P QR$ with vertices $P (5, 4), Q (- 2, 4)$ and $R (a, b)$ be 35 square units. If its orthocenter and centroid are $O (2, \frac{14}{5})$ and $C (c, d)$ respectively, then $c + 2 d$ is equal to
Mathematics · Properties of Triangle · MCQ
Q44.If $A, B, and (adj (A^{- 1}) + adj (B^{- 1}))$ are non-singular matrices of same order, then the inverse of $A (adj (A^{- 1}) + adj (B^{- 1}))^{- 1} B$ …
Mathematics · Matrices and Determinants · MCQ
Q45.Let $R = {(1, 2), (2, 3), (3, 3)}$ be a relation defined on the set ${1, 2, 3, 4}$ . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:
Mathematics · Sets and Relations · MCQ
Q46.The sum of all rational terms in the expansion of $(1 + 2^{1/3} + 3^{1/2})^{6}$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q47.If the set of all values of $a$ , for which the equation $5 x^{3} - 15 x - a = 0$ has three distinct real roots, is the interval $(α, β)$ , then $β - 2 α$ is equal to .
Mathematics · Application of Derivatives · Numerical
Q48.If the equation $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ has equal roots, where $a + c = 15$ and $b = \frac{36}{5}$ , then $a^{2} + c^{2}$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q49.Let the circle $C$ touch the line $x - y + 1 = 0$ , have the centre on the positive $x$ -axis, and cut off a chord of length $\frac{4}{13}$ along the line $- 3 x + 2 y = 1$ . Let H be the hyperbola $\frac{x ^{2}}{α ^{2}} - \frac{y ^{2}}{β ^{2}} = 1$ ,…
Mathematics · Circle · Numerical
Q50.If the area of the larger portion bounded between the curves $x^{2} + y^{2} = 25$ and $y = ∣ x - 1∣$ is $\frac{1}{4} (b π + c), b, c \in N$ , then $b + c$ is equal to …
Mathematics · Area Under the Curves · Numerical