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Mathematics · 2024 · 6 Apr · Shift 2

30 questions from this JEE Main paper

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2024 · 6 Apr · Shift 2
Mathematics

Mathematics · 2024 · 6 Apr · Shift 2

30 questions from this JEE Main paper

Functions2 questions Complex Numbers1 questions Sets and Relations1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants2 questions Probability2 questions Vector Algebra2 questions Area Under the Curves1 questions 3D Geometry2 questions Sequences and Series3 questions Differential Equations2 questions Circle1 questions Permutations and Combinations2 questions Differentiation1 questions Indefinite Integrals1 questions Straight Lines and Pair of Straight Lines1 questions Properties of Triangle1 questions Definite Integration1 questions Hyperbola1 questions Quadratic Equation and Inequalities1 questions

Q30.If the function $f (x) = (\frac{1}{x})^{2 x}; x > 0$ attains the maximum value at $x = \frac{1}{e}$ then :
Mathematics · Functions · MCQ
Q31.If $z_{1}, z_{2}$ are two distinct complex number such that $\frac{z _{1} - 2 z _{2}}{\frac{1}{2} - z _{1} z ˉ _{2}} = 2$ , then
Mathematics · Complex Numbers · MCQ
Q32.Let $A = {1, 2, 3, 4, 5}$ . Let $R$ be a relation on $A$ defined by $x R y$ if and only if $4 x \leq 5 y$ . Let $m$ be the number of elements in $R$ and $n$ be the minimum…
Mathematics · Sets and Relations · MCQ
Q33.Let $f (x) = \frac{1}{7 - s i n 5 x}$ be a function defined on $R$ . Then the range of the function $f (x)$ is equal to :
Mathematics · Functions · MCQ
Q34. $lim_{n \to \infty} \frac{( 1 ^{2} - 1 ) ( n - 1 ) + ( 2 ^{2} - 2 ) ( n - 2 ) + \dots + ( ( n - 1 ) ^{2} - ( n - 1 ) ) \cdot 1}{( 1 ^{3} + 2 ^{3} + \dots\dots + n ^{3} ) - ( 1 ^{2} + 2 ^{2} + \dots\dots + n ^{2} )}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.If $A$ is a square matrix of order 3 such that $det (A) = 3$ and $det (adj (- 4 adj (- 3 adj (3 adj ((2 A)^{- 1}))))) = 2^{m} 3^{n}$ …
Mathematics · Matrices and Determinants · MCQ
Q36.If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :
Mathematics · Probability · MCQ
Q37.Let $a = 2 \hat{i} + \hat{j} - \hat{k}, b = ((a \times (\hat{i} + \hat{j})) \times \hat{i}) \times \hat{i}$ . Then the square of the projection of $a$ on $b$ is:
Mathematics · Vector Algebra · MCQ
Q38.Let $a = 6 \hat{i} + \hat{j} - \hat{k}$ and $b = \hat{i} + \hat{j}$ . If $c$ is a is vector such that $∣ c ∣ \geq 6, a \cdot c = 6∣ c ∣, ∣ c - a ∣ = 22$ …
Mathematics · Vector Algebra · MCQ
Q39.If the area of the region ${(x, y) : \frac{a}{x ^{2}} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2, 0 < a < 1}$ is $(lo g_{e} 2) - \frac{1}{7}$ then the value of $7 a - 3$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q40.Let $P (α, β, γ)$ be the image of the point $Q (3, - 3, 1)$ in the line $\frac{x - 0}{1} = \frac{y - 3}{1} = \frac{z - 1}{- 1}$ and $R$ be the point $(2, 5, - 1)$ . If the area of the triangle $PQR$ is $λ$ …
Mathematics · 3D Geometry · MCQ
Q41.Let $A B C$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $A B C$ and the same process is repeated infinitely many times. If $P$ is the sum of perimeters and $Q$ is…
Mathematics · Sequences and Series · MCQ
Q42.Suppose the solution of the differential equation $\frac{d y}{d x} = \frac{( 2 + α ) x - β y + 2}{β x - 2 α y - ( β γ - 4 α )}$ represents a circle passing through origin. Then the radius of this circle is :
Mathematics · Differential Equations · MCQ
Q43.A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took…
Mathematics · Sequences and Series · MCQ
Q44.If $P (6, 1)$ be the orthocentre of the triangle whose vertices are $A (5, - 2), B (8, 3)$ and $C (h, k)$ , then the point $C$ lies on the circle :
Mathematics · Circle · MCQ
Q45.If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $31 5^{th}$ position in this arrangement is :
Mathematics · Permutations and Combinations · MCQ
Q46.Suppose for a differentiable function $h, h (0) = 0, h (1) = 1$ and $h^{'} (0) = h^{'} (1) = 2$ . If $g (x) = h (e^{x}) e^{h (x)}$ , then $g^{'} (0)$ is equal to:
Mathematics · Differentiation · MCQ
Q47.Let $0 \leq r \leq n$ . If $^{n + 1} C_{r + 1} :^{n} C_{r} :^{n - 1} C_{r - 1} = 55 : 35 : 21$ , then $2 n + 5 r$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q48.If $\int \frac{1}{a ^{2} s i n ^{2} x + b ^{2} c o s ^{2} x} d x = \frac{1}{12} tan^{- 1} (3 tan x) +$ constant, then the maximum value of $a sin x + b cos x$ , is :
Mathematics · Indefinite Integrals · MCQ
Q49.If the locus of the point, whose distances from the point $(2, 1)$ and $(1, 3)$ are in the ratio $5 : 4$ , is $a x^{2} + b y^{2} + c x y + d x + ey + 170 = 0$ , then the value of $a^{2} + 2 b + 3 c + 4 d + e$ is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q50.Let $[t]$ denote the greatest integer less than or equal to $t$ . Let $f : [0, \infty) \to R$ be a function defined by $f (x) = [\frac{x}{2} + 3] - [x]$ . Let $S$ be the set of all points in the…
Mathematics · Limits Continuity and Differentiability · Numerical
Q51.In a triangle $ABC, BC = 7, AC = 8, AB = α \in N$ and $cos A = \frac{2}{3}$ . If $49 cos (3 C) + 42 = \frac{m}{n}$ , where $gcd (m, n) = 1$ , then $m + n$ …
Mathematics · Properties of Triangle · Numerical
Q52.Let $[t]$ denote the largest integer less than or equal to $t$ . If $0 \int 3 ([x^{2}] + [\frac{x ^{2}}{2}]) d x = a + b 2 - 3 - 5 + c 6 - 7$ , where $a, b, c \in Z$ …
Mathematics · Definite Integration · Numerical
Q53.If the solution $y (x)$ of the given differential equation $(e^{y} + 1) cos x d x + e^{y} sin x d y = 0$ passes through the point $(\frac{π}{2}, 0)$ , then the value of $e^{y (\frac{π}{6})}$ …
Mathematics · Differential Equations · Numerical
Q54.If the shortest distance between the lines $\frac{x - λ}{3} = \frac{y - 2}{- 1} = \frac{z - 1}{1}$ and $\frac{x + 2}{- 3} = \frac{y + 5}{2} = \frac{z - 4}{4}$ is $\frac{44}{30}$ , then the largest possible value of $∣ λ ∣$ is equal to …
Mathematics · 3D Geometry · Numerical
Q55.The length of the latus rectum and directrices of hyperbola with eccentricity e are 9 and $x = \pm \frac{4}{3}$ , respectively. Let the line $y - 3 x + 3 = 0$ touch this hyperbola at $(x_{0}, y_{0})$ . If $m$ …
Mathematics · Hyperbola · Numerical
Q56.Let $x^{2} + 2 x - 8 = 0$ be roots of $x^{2} + 2 x - 8 = 0$ . If $U_{n} = α^{n} + β^{n}$ , then $\frac{U _{10} + 2 U _{9}}{2 U _{8}}$ is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q57.If the system of equations $2 x + 7 y + λ z = 3 3 x + 2 y + 5 z = 4 x + μ y + 32 z = - 1$ has infinitely many solutions, then $(λ - μ)$ is equal to :
Mathematics · Matrices and Determinants · Numerical
Q58.If $S (x) = (1 + x) + 2 (1 + x)^{2} + 3 (1 + x)^{3} + \dots + 60 (1 + x)^{60}, x e q 0$ , and $(60)^{2} S (60) = a (b)^{b} + b$ , where $a, b \in N$ , then $(a + b)$ equal to .
Mathematics · Sequences and Series · Numerical
Q59.From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If…
Mathematics · Probability · Numerical