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Mathematics · 2024 · 8 Apr · Shift 1

30 questions from this JEE Main paper

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2024 · 8 Apr · Shift 1
Mathematics

Mathematics · 2024 · 8 Apr · Shift 1

30 questions from this JEE Main paper

Matrices and Determinants2 questions Definite Integration1 questions Application of Derivatives3 questions Vector Algebra2 questions Circle1 questions Differential Equations2 questions Hyperbola1 questions Probability2 questions 3D Geometry2 questions Complex Numbers2 questions Quadratic Equation and Inequalities1 questions Straight Lines and Pair of Straight Lines2 questions Trigonometric Ratio and Identites1 questions Permutations and Combinations2 questions Indefinite Integrals1 questions Functions1 questions Sequences and Series2 questions Area Under the Curves1 questions Limits Continuity and Differentiability1 questions

Q31.Let $A = 210 a 35 01 b$ . If $A^{3} = 4 A^{2} - A - 21 I$ , where $I$ is the identity matrix of order $3 \times 3$ , then $2 a + 3 b$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q32.The value of $k \in N$ for which the integral $I_{n} = \int_{0}^{1} (1 - x^{k})^{n} d x, n \in N$ , satisfies $147 I_{20} = 148 I_{21}$ is
Mathematics · Definite Integration · MCQ
Q33.Let $f (x) = 4 cos^{3} x + 33 cos^{2} x - 10$ . The number of points of local maxima of $f$ in interval $(0, 2 π)$ is
Mathematics · Application of Derivatives · MCQ
Q34.The set of all $α$ , for which the vectors $a = α t \hat{i} + 6 \hat{j} - 3 \hat{k}$ and $b = t \hat{i} - 2 \hat{j} - 2 α t \hat{k}$ are inclined at an obtuse angle for all $t \in R$ , is
Mathematics · Vector Algebra · MCQ
Q35.Let the circles $C_{1} : (x - α)^{2} + (y - β)^{2} = r_{1}^{2}$ and $C_{2} : (x - 8)^{2} + (y - \frac{15}{2})^{2} = r_{2}^{2}$ touch each other externally at the point $(6, 6)$ . If the point $(6, 6)$ divides the line segment joining the centres of the circles…
Mathematics · Circle · MCQ
Q36.Let $f (x)$ be a positive function such that the area bounded by $y = f (x), y = 0$ from $x = 0$ to $x = a > 0$ is $e^{- a} + 4 a^{2} + a - 1$ . Then the differential equation, whose general solution is $y = c_{1} f (x) + c_{2}$ , where $c_{1}$ and $c_{2}$ are arbitrary…
Mathematics · Differential Equations · MCQ
Q37.Let $H : \frac{- x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ be the hyperbola, whose eccentricity is $3$ and the length of the latus rectum is $43$ . Suppose the point $(α, 6), α > 0$ lies on $H$ . If $β$ is the product of the…
Mathematics · Hyperbola · MCQ
Q38.The number of critical points of the function $f (x) = (x - 2)^{2/3} (2 x + 1)$ is
Mathematics · Application of Derivatives · MCQ
Q39.Let $y = y (x)$ be the solution of the differential equation $(1 + y^{2}) e^{t a n x} d x + cos^{2} x (1 + e^{2 t a n x}) d y = 0, y (0) = 1$ . Then $y (\frac{π}{4})$ is equal to
Mathematics · Differential Equations · MCQ
Q40.Let the sum of two positive integers be 24 . If the probability, that their product is not less than $\frac{3}{4}$ times their greatest possible product, is $\frac{m}{n}$ , where $gcd (m, n) = 1$ , then $n$ - $m$ equals
Mathematics · Probability · MCQ
Q41.For the function $f (x) = (cos x) - x + 1, x \in R$ , between the following two statements (S1) $f (x) = 0$ for only one value of $x$ in $[0, π]$ . (S2) $f (x)$ is decreasing in $[0, \frac{π}{2}]$ and increasing in $[\frac{π}{2}, π]$ …
Mathematics · Application of Derivatives · MCQ
Q42.Let $P (x, y, z)$ be a point in the first octant, whose projection in the $x y$ -plane is the point $Q$ . Let $O P = γ$ ; the angle between $O Q$ and the positive $x$ -axis be $θ$ ; and the angle between $O P$ and the positive $z$ -axis…
Mathematics · 3D Geometry · MCQ
Q43.Let $z$ be a complex number such that $∣ z + 2∣ = 1$ and $lm (\frac{z + 1}{z + 2}) = \frac{1}{5}$ . Then the value of $∣ Re (\overline{z + 2}) ∣$ is
Mathematics · Complex Numbers · MCQ
Q44.The sum of all the solutions of the equation $(8)^{2 x} - 16 \cdot (8)^{x} + 48 = 0$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q45.The equations of two sides $AB$ and $AC$ of a triangle $ABC$ are $4 x + y = 14$ and $3 x - 2 y = 5$ , respectively. The point $(2, - \frac{4}{3})$ divides the third side $BC$ internally in the ratio $2 : 1$ …
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q46.If $sin x = - \frac{3}{5}$ , where $π < x < \frac{3 π}{2}$ , then $80 (tan^{2} x - cos x)$ is equal to
Mathematics · Trigonometric Ratio and Identites · MCQ
Q47.Let $[t]$ be the greatest integer less than or equal to $t$ . Let $A$ be the set of all prime factors of 2310 and $f : A \to Z$ be the function $f (x) = [lo g_{2} (x^{2} + [\frac{x ^{3}}{5}])]$ . The…
Mathematics · Permutations and Combinations · MCQ
Q48.If the set $R = {(a, b) : a + 5 b = 42, a, b \in N}$ has $m$ elements and $\sum_{n = 1}^{m} (1 - i^{n!}) = x + i y$ , where $i = - 1$ , then the value of $m + x + y$ is
Mathematics · Complex Numbers · MCQ
Q49.If the shortest distance between the lines $L_{1} : r = (2 + λ) \hat{i} + (1 - 3 λ) \hat{j} + (3 + 4 λ) \hat{k}, L_{2} : r = 2 (1 + μ) \hat{i} + 3 (1 + μ) \hat{j} + (5 + μ) \hat{k}, λ \in R μ \in R$ …
Mathematics · 3D Geometry · MCQ
Q50.Let $I (x) = \int \frac{6}{s i n ^{2} x ( 1 - c o t x ) ^{2}} d x$ . If $I (0) = 3$ , then $I (\frac{π}{12})$ is equal to
Mathematics · Indefinite Integrals · MCQ
Q51.If the orthocentre of the triangle formed by the lines $2 x + 3 y - 1 = 0, x + 2 y - 1 = 0$ and $a x + b y - 1 = 0$ , is the centroid of another triangle, whose circumcentre and orthocentre respectively are $(3, 4)$ and $(- 6, - 8)$ , then the value of $∣ a - b ∣$ is…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q52.If the range of $f (θ) = \frac{s i n ^{4} θ + 3 c o s ^{2} θ}{s i n ^{4} θ + c o s ^{2} θ}, θ \in R$ is $[α, β]$ , then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{α}{β}$ …
Mathematics · Functions · Numerical
Q53.Let $a = 9 \hat{i} - 13 \hat{j} + 25 \hat{k}, b = 3 \hat{i} + 7 \hat{j} - 13 \hat{k}$ and $c = 17 \hat{i} - 2 \hat{j} + \hat{k}$ be three given vectors. If $r$ is a vector such that $r \times a = (b + c) \times a$ …
Mathematics · Vector Algebra · Numerical
Q54.Let the positive integers be written in the form : If the $k^{th}$ row contains exactly $k$ numbers for every natural number $k$ , then the row in which the number 5310 will be, is . Includes diagram
Mathematics · Sequences and Series · Numerical
Q55.The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to .
Mathematics · Permutations and Combinations · Numerical
Q56.Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\overset{ˉ}{X}$ and $\overset{ˉ}{Y}$ are the means of $X$ and $Y$ …
Mathematics · Probability · Numerical
Q57.Let $α = \sum_{r = 0}^{n} (4 r^{2} + 2 r + 1)^{n} C_{r}$ and $β = (\sum_{r = 0}^{n} \frac{^{n} C _{r}}{r + 1}) + \frac{1}{n + 1}$ . If $140 < \frac{2 α}{β} < 281$ , then the value of $n$ is .
Mathematics · Sequences and Series · Numerical
Q58.Let $A = [21 - 1 1]$ . If the sum of the diagonal elements of $A^{13}$ is $3^{n}$ , then $n$ is equal to .
Mathematics · Matrices and Determinants · Numerical
Q59.Let the area of the region enclosed by the curve $y = min {sin x, cos x}$ and the $x$ axis between $x = - π$ to $x = π$ be $A$ . Then $A^{2}$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q60.The value of $lim_{x \to 0} 2 (\frac{1 - c o s x c o s 2 x 3 c o s 3 x \dots\dots . 10 c o s 10 x}{x ^{2}})$ is .
Mathematics · Limits Continuity and Differentiability · Numerical