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Mathematics · 2024 · 1 Feb · Shift 1

30 questions from this JEE Main paper

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2024 · 1 Feb · Shift 1
Mathematics

Mathematics · 2024 · 1 Feb · Shift 1

30 questions from this JEE Main paper

Probability1 questions Definite Integration2 questions Matrices and Determinants2 questions Trigonometric Ratio and Identites1 questions Permutations and Combinations2 questions Complex Numbers2 questions Statistics1 questions Vector Algebra1 questions Quadratic Equation and Inequalities1 questions Area Under the Curves1 questions Functions1 questions Hyperbola1 questions Differential Equations2 questions Limits Continuity and Differentiability2 questions Ellipse1 questions Sequences and Series2 questions Circle1 questions Application of Derivatives1 questions 3D Geometry2 questions Binomial Theorem1 questions Parabola1 questions Sets and Relations1 questions

Q31.A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of…
Mathematics · Probability · MCQ
Q32.The value of the integral $0 \int π /4 \frac{x d x}{s i n ^{4} ( 2 x ) + c o s ^{4} ( 2 x )}$ equals :
Mathematics · Definite Integration · MCQ
Q33.If $A = [2 - 1 12], B = [1101], C = ABA^{T}$ and $X = A^{T} C^{2} A$ …
Mathematics · Matrices and Determinants · MCQ
Q34.If $tan A = \frac{1}{x ( x ^{2} + x + 1 )}, tan B = \frac{x}{x ^{2} + x + 1}$ and $tan C = (x^{- 3} + x^{- 2} + x^{- 1})^{1/2}, 0 < A, B, C < \frac{π}{2}$ , then $A + B$ …
Mathematics · Trigonometric Ratio and Identites · MCQ
Q35.If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $n$ is equal to :
Mathematics · Permutations and Combinations · MCQ
Q36.Let $S = ∣ z \in C : ∣ z - 1 ∣= 1$ and $(2 - 1) (z + \overset{z}{ˉ}) - i (z - \overset{z}{ˉ}) = 22 ∣$ . Let $z_{1}, z_{2} \in S$ be such that $∣ z_{1} ∣ = z \in s max ∣ z ∣$ and $∣ z_{2} ∣ = z \in S min ∣ z ∣$ …
Mathematics · Complex Numbers · MCQ
Q37.Let the median and the mean deviation about the median of 7 observation $170, 125, 230, 190, 210$ , a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :
Mathematics · Statistics · MCQ
Q38.Let $a = - 5 \hat{i} + \hat{j} - 3 \hat{k}, b = \hat{i} + 2 \hat{j} - 4 \hat{k}$ and $c = (((a \times b) \times \hat{i}) \times \hat{i}) \times \hat{i}$ …
Mathematics · Vector Algebra · MCQ
Q39.Let $S = {x \in R : (3 + 2)^{x} + (3 - 2)^{x} = 10}$ . Then the number of elements in $S$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q40.The area enclosed by the curves $x y + 4 y = 16$ and $x + y = 6$ is equal to :
Mathematics · Area Under the Curves · MCQ
Q41.Let $f : R \to R$ and $g : R \to R$ be defined as $f (x) = {lo g_{e} x, e^{- x}, x > 0 x \leq 0$ and $g (x) = {x, e^{x}, x ⩾ 0 x < 0$ …
Mathematics · Functions · MCQ
Q42.If the system of equations $2 x + 3 y - z = 5 x + α y + 3 z = - 4 3 x - y + β z = 7$ has infinitely many solutions, then $13 α β$ is equal to :
Mathematics · Matrices and Determinants · MCQ
Q43.For $0 < θ < π /2$ , if the eccentricity of the hyperbola $x^{2} - y^{2} cosec^{2} θ = 5$ is $7$ times eccentricity of the ellipse $x^{2} cosec^{2} θ + y^{2} = 5$ , then the value of $θ$ is :
Mathematics · Hyperbola · MCQ
Q44.Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = 2 x (x + y)^{3} - x (x + y) - 1, y (0) = 1$ . Then, $(\frac{1}{2} + y (\frac{1}{2}))^{2}$ equals :
Mathematics · Differential Equations · MCQ
Q45.Let $f : R \to R$ be defined as : $f (x) = {\frac{a - b c o s 2 x}{x ^{2}}; x 1$ If $f$ is continuous everywhere in $R$ and $m$ is the number of points where $f$ is NOT differential…
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.Let $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ be an ellipse, whose eccentricity is $\frac{1}{2}$ and the length of the latusrectum is $14$ . Then the square of the eccentricity of $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ …
Mathematics · Ellipse · MCQ
Q47.Let $3, a, b, c$ be in A.P. and $3, a - 1, b + 1, c + 9$ be in G.P. Then, the arithmetic mean of $c$ and $c$ is :
Mathematics · Sequences and Series · MCQ
Q48.Let $C : x^{2} + y^{2} = 4$ and $C^{'} : x^{2} + y^{2} - 4 λ x + 9 = 0$ be two circles. If the set of all values of $λ$ so that the circles $C$ and $C$ intersect at two distinct points, is $\mathrm{R}-[\mathrm{a},…
Mathematics · Circle · MCQ
Q49.If $5 f (x) + 4 f (\frac{1}{x}) = x^{2} - 2, \forall x e q 0$ and $y = 9 x^{2} f (x)$ , then $y$ is strictly increasing in :
Mathematics · Application of Derivatives · MCQ
Q50.If the shortest distance between the lines $\frac{x - λ}{- 2} = \frac{y - 2}{1} = \frac{z - 1}{1}$ and $\frac{x - 3}{1} = \frac{y - 1}{- 2} = \frac{z - 2}{1}$ is 1 , then the sum of all possible values of $λ$ is :
Mathematics · 3D Geometry · MCQ
Q51.If $x = x (t)$ is the solution of the differential equation $(t + 1) d x = (2 x + (t + 1)^{4}) dt, x (0) = 2$ , then, $x (1)$ equals .
Mathematics · Differential Equations · Numerical
Q52.The number of elements in the set $S = {(x, y, z) : x, y, z \in Z, x + 2 y + 3 z = 42, x, y, z ⩾ 0}$ equals .
Mathematics · Permutations and Combinations · Numerical
Q53.If the Coefficient of $x^{30}$ in the expansion of $(1 + \frac{1}{x})^{6} (1 + x^{2})^{7} (1 - x^{3})^{8}; x e q 0$ is $α$ , then $∣ α ∣$ equals .
Mathematics · Binomial Theorem · Numerical
Q54.Let $3, 7, 11, 15, \dots, 403$ and $2, 5, 8, 11, \dots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to .
Mathematics · Sequences and Series · Numerical
Q55.Let ${x}$ denote the fractional part of $x$ and $f (x) = \frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, x e q 0$ . If $L$ and $R$ respectively denotes the left hand limit and the right hand limit…
Mathematics · Limits Continuity and Differentiability · Numerical
Q56.Let the line $L : 2 x + y = α$ pass through the point of the intersection $P$ (in the first quadrant) of the circle $x^{2} + y^{2} = 3$ and the parabola $x^{2} = 2 y$ . Let the line $L$ touch two circles $C_{1}$ …
Mathematics · Parabola · Numerical
Q57.Let $P = {z \in C : ∣ z + 2 - 3 i ∣ \leq 1}$ and $Q = {z \in C : z (1 + i) + \overset{z}{ˉ} (1 - i) \leq - 8}$ . Let in $P \cap Q$ , $∣ z - 3 + 2 i ∣$ be maximum and minimum at $z_{1}$ and $z_{2}$ …
Mathematics · Complex Numbers · Numerical
Q58.If $- π /2 \int π /2 \frac{8 2 c o s x d x}{( 1 + e ^{s i n x} ) ( 1 + s i n ^{4} x )} = α π + β lo g_{e} (3 + 22)$ , where $α^{2} + β^{2}$ are integers, then $α^{2} + β^{2}$ …
Mathematics · Definite Integration · Numerical
Q59.Let the line of the shortest distance between the lines $L_{1} : r = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (\hat{i} - \hat{j} + \hat{k}) and L_{2} : r = (4 \hat{i} + 5 \hat{j} + 6 \hat{k}) + μ (\hat{i} + \hat{j} - \hat{k})$ …
Mathematics · 3D Geometry · Numerical
Q60.Let $A = {1, 2, 3, \dots, 20}$ . Let $R_{1}$ and $R_{2}$ two relation on $A$ such that $R_{1} = {(a, b) : b$ is divisible by $a} R_{2} = {(a, b) : a$ is an integral multiple of $b}$ . Then, number of elements in $R_{1} - R_{2}$ is equal to …
Mathematics · Sets and Relations · Numerical