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Mathematics · 2024 · 27 Jan · Shift 1

30 questions from this JEE Main paper

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2024 · 27 Jan · Shift 1
Mathematics

Mathematics · 2024 · 27 Jan · Shift 1

30 questions from this JEE Main paper

Definite Integration2 questions Complex Numbers2 questions Sets and Relations1 questions Parabola1 questions Differential Equations2 questions 3D Geometry2 questions Ellipse1 questions Limits Continuity and Differentiability2 questions Matrices and Determinants2 questions Circle1 questions Straight Lines and Pair of Straight Lines1 questions Binomial Theorem2 questions Sequences and Series2 questions Statistics1 questions Vector Algebra2 questions Functions1 questions Differentiation1 questions Trigonometric Ratio and Identites1 questions Application of Derivatives1 questions Area Under the Curves1 questions Probability1 questions

Q31.If $0 \int 1 \frac{1}{3 + x + 1 + x} d x = a + b 2 + c 3$ , where $a, b, c$ are rational numbers, then $2 a + 3 b - 4 c$ is equal…
Mathematics · Definite Integration · MCQ
Q32.If $S = {z \in C : ∣ z - i ∣ = ∣ z + i ∣ = ∣ z - 1∣}$ , then, $n (S)$ is :
Mathematics · Complex Numbers · MCQ
Q33.Let $S = {1, 2, 3, \dots, 10}$ . Suppose $M$ is the set of all the subsets of $S$ , then the relation $R = {(A, B) : A \cap B e q ϕ; A, B \in M}$ is :
Mathematics · Sets and Relations · MCQ
Q34.If the shortest distance of the parabola $y^{2} = 4 x$ from the centre of the circle $x^{2} + y^{2} - 4 x - 16 y + 64 = 0$ is $d$ , then $d^{2}$ is equal to :
Mathematics · Parabola · MCQ
Q35.If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2), (2, 3)$ and $(3, 1)$ , and $I_{1} = a \int b x sin (4 x - x^{2}) d x, I_{2} = a \int b sin (4 x - x^{2}) d x$ …
Mathematics · Definite Integration · MCQ
Q36.Let $x = x (t)$ and $y = y (t)$ be solutions of the differential equations $\frac{d x}{dt} + a x = 0$ and $\frac{d y}{dt} + by = 0$ respectively, $a, b \in R$ …
Mathematics · Differential Equations · MCQ
Q37.The distance, of the point $(7, - 2, 11)$ from the line $\frac{x - 6}{1} = \frac{y - 4}{0} = \frac{z - 8}{3}$ along the line $\frac{x - 5}{2} = \frac{y - 1}{- 3} = \frac{z - 5}{6}$ , is :
Mathematics · 3D Geometry · MCQ
Q38.The length of the chord of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ , whose mid point is $(1, \frac{2}{5})$ , is equal to :
Mathematics · Ellipse · MCQ
Q39.Consider the function. $f (x) = ⎩ ⎨ ⎧ \frac{a ( 7 x - 12 - x ^{2} )}{b ∣ x ^{2} - 7 x + 12 ∣} b, x 3, x = 3,$ where $[x]$ denotes the greatest integer less…
Mathematics · Limits Continuity and Differentiability · MCQ
Q40.If $a = x \to 0 lim \frac{1 + 1 + x ^{4} - 2}{x ^{4}}$ and $b = x \to 0 lim \frac{s i n ^{2} x}{2 - 1 + c o s x}$ , then the value of $a b^{3}$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q41.Consider the matrix $f (x) = cos x sin x 0 - sin x cos x 0 001$ . Given below are two statements : Statement I : $f (- x)$ is the inverse of the matrix $f (x)$ …
Mathematics · Matrices and Determinants · MCQ
Q42.Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for $k$ equal to :
Mathematics · Circle · MCQ
Q43.If the shortest distance between the lines $\frac{x - 4}{1} = \frac{y + 1}{2} = \frac{z}{- 3}$ and $\frac{x - λ}{2} = \frac{y + 1}{4} = \frac{z - 2}{- 5}$ is $\frac{6}{5}$ , then the sum of all possible values of $λ$ is :
Mathematics · 3D Geometry · MCQ
Q44.The portion of the line $4 x + 5 y = 20$ in the first quadrant is trisected by the lines $L_{1}$ and $L_{2}$ passing through the origin. The tangent of an angle between the lines $L_{1}$ and $L_{2}$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q45. $^{n - 1} C_{r} = (k^{2} - 8)^{n} C_{r + 1}$ if and only if :
Mathematics · Binomial Theorem · MCQ
Q46.The number of common terms in the progressions $4, 9, 14, 19, \dots\dots$ , up to $2 5^{th}$ term and $3, 6, 9, 12, \dots\dots$ , up to $3 7^{th}$ term is :
Mathematics · Sequences and Series · MCQ
Q47.Let $a_{1}, a_{2}, \dots a_{10}$ be 10 observations such that $k = 1 \sum 10 a_{k} = 50$ and $\forall k < j \sum a_{k} \cdot a_{j} = 1100$ …
Mathematics · Statistics · MCQ
Q48.Let $a = \hat{i} + 2 \hat{j} + \hat{k}, b = 3 (\hat{i} - \hat{j} + \hat{k})$ . Let $c$ be the vector such that $a \times c = b$ …
Mathematics · Vector Algebra · MCQ
Q49.If A denotes the sum of all the coefficients in the expansion of $(1 - 3 x + 10 x^{2})^{n}$ and B denotes the sum of all the coefficients in the expansion of $(1 + x^{2})^{n}$ , then :
Mathematics · Binomial Theorem · MCQ
Q50.The function $f : N - {1} \to N$ ; defined by $f (n) =$ the highest prime factor of $n$ , is :
Mathematics · Functions · MCQ
Q51.If $8 = 3 + \frac{1}{4} (3 + p) + \frac{1}{4 ^{2}} (3 + 2 p) + \frac{1}{4 ^{3}} (3 + 3 p) + \dots\dots \infty$ , then the value of $p$ is .
Mathematics · Sequences and Series · Numerical
Q52.If the solution of the differential equation $(2 x + 3 y - 2) d x + (4 x + 6 y - 7) d y = 0, y (0) = 3$ , is $α x + β y + 3 lo g_{e} ∣2 x + 3 y - γ ∣ = 6$ , then $α + 2 β + 3 γ$ is equal to .
Mathematics · Differential Equations · Numerical
Q53.Let $f (x) = x^{3} + x^{2} f^{'} (1) + x f^{''} (2) + f^{'''} (3), x \in R$ . Then $f^{'} (10)$ is equal to .
Mathematics · Differentiation · Numerical
Q54.Let the set of all $a \in R$ such that the equation $cos 2 x + a sin x = 2 a - 7$ has a solution be $[p, q]$ and $r = tan 9^{\circ} - tan 2 7^{\circ} - \frac{1}{c o t 6 3 ^{\circ}} + tan 8 1^{\circ}$ , then pqr is equal to …
Mathematics · Trigonometric Ratio and Identites · Numerical
Q55.Let for a differentiable function $f : (0, \infty) \to R, f (x) - f (y) ⩾ lo g_{e} (\frac{x}{y}) + x - y, \forall x, y \in (0, \infty)$ . Then $n = 1 \sum 20 f^{'} (\frac{1}{n ^{2}})$ …
Mathematics · Application of Derivatives · Numerical
Q56.Let the area of the region ${(x, y) : x - 2 y + 4 ⩾ 0, x + 2 y^{2} ⩾ 0, x + 4 y^{2} \leq 8, y ⩾ 0}$ be $\frac{m}{n}$ , where $m$ and $n$ are coprime numbers. Then $m + n$ …
Mathematics · Area Under the Curves · Numerical
Q57.Let $A = 211010101, B = [B_{1}, B_{2}, B_{3}]$ , where $B_{1}, B_{2}, B_{3}$ are column matrics, and $AB_{1} = 100, AB_{2} = 230, AB_{3} = 321$ …
Mathematics · Matrices and Determinants · Numerical
Q58.The least positive integral value of $α$ , for which the angle between the vectors $α \hat{i} - 2 \hat{j} + 2 \hat{k}$ and $α \hat{i} + 2 α \hat{j} - 2 \hat{k}$ is acute, is .
Mathematics · Vector Algebra · Numerical
Q59.If $α$ satisfies the equation $x^{2} + x + 1 = 0$ and $(1 + α)^{7} = A + B α + C α^{2}, A, B, C ⩾ 0$ , then $5 (3 A - 2 B - C)$ is equal to .
Mathematics · Complex Numbers · Numerical
Q60.A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let $a = P (X = 3), b = P (X ⩾ 3)$ and $c = P (X ⩾ 6 ∣ X > 3)$ . Then $\frac{b + c}{a}$ is equal to .
Mathematics · Probability · Numerical