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Mathematics · 2023 · 12 Apr · Shift 1

21 questions from this JEE Main paper

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2023 · 12 Apr · Shift 1
Mathematics

Mathematics · 2023 · 12 Apr · Shift 1

21 questions from this JEE Main paper

Probability2 questions Matrices and Determinants2 questions Differential Equations1 questions 3D Geometry1 questions Permutations and Combinations2 questions Complex Numbers1 questions Straight Lines and Pair of Straight Lines1 questions Quadratic Equation and Inequalities1 questions Ellipse1 questions Application of Derivatives1 questions Area Under the Curves1 questions Functions1 questions Circle1 questions Definite Integration1 questions Sets and Relations1 questions Limits Continuity and Differentiability1 questions Statistics1 questions Indefinite Integrals1 questions

Q23.Two dice A and B are rolled. Let the numbers obtained on A and B be $α$ and $β$ respectively. If the variance of $α - β$ is $\frac{p}{q}$ , where $p$ and $q$ are co-prime, then the sum of the positive divisors of $p$ is…
Mathematics · Probability · MCQ
Q24.Let $A = [10 \frac{1}{51} 1]$ . If $B = [1 - 1 2 - 1] A [- 1 1 - 2 1]$ ,…
Mathematics · Matrices and Determinants · MCQ
Q25.Let $y = y (x), y > 0$ , be a solution curve of the differential equation $(1 + x^{2}) d y = y (x - y) d x$ . If $y (0) = 1$ and $y (22) = β$ , then
Mathematics · Differential Equations · MCQ
Q26.Let the lines $l_{1} : \frac{x + 5}{3} = \frac{y + 4}{1} = \frac{z - α}{- 2}$ and $l_{2} : 3 x + 2 y + z - 2 = 0 = x - 3 y + 2 z - 13$ be coplanar. If the point $P (a, b, c)$ on $l_{1}$ is nearest to the point $Q (- 4, - 3, 2)$ , then $∣ a ∣ + ∣ b ∣ + ∣ c ∣$ …
Mathematics · 3D Geometry · MCQ
Q27.The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $0, 1, 3, 5, 7$ and 9 without repetition, is equal to :
Mathematics · Permutations and Combinations · MCQ
Q28.Let $C$ be the circle in the complex plane with centre $z_{0} = \frac{1}{2} (1 + 3 i)$ and radius $r = 1$ . Let $z_{1} = 1 + i$ and the complex number $z_{2}$ be outside the circle $C$ such that $∣ z_{1} - z_{0} ∣ ∣ z_{2} - z_{0} ∣ = 1$ …
Mathematics · Complex Numbers · MCQ
Q29.If the point $(α, \frac{7 3}{3})$ lies on the curve traced by the mid-points of the line segments of the lines $x cos θ + y sin θ = 7, θ \in (0, \frac{π}{2})$ between the co-ordinates…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.Let $x^{2} + 6 x + 3 = 0$ be the roots of the quadratic equation $x^{2} + 6 x + 3 = 0$ . Then $\frac{α ^{23} + β ^{23} + α ^{14} + β ^{14}}{α ^{15} + β ^{15} + α ^{10} + β ^{10}}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.Let $P (\frac{2 3}{7}, \frac{6}{7}), Q, R$ and $S$ be four points on the ellipse $9 x^{2} + 4 y^{2} = 36$ . Let $PQ$ and $RS$ be mutually perpendicular and…
Mathematics · Ellipse · MCQ
Q32.If the local maximum value of the function $f (x) = (\frac{3 e}{2 s i n x})^{s i n^{2} x}, x \in (0, \frac{π}{2})$ , is $\frac{k}{e}$ , then $(\frac{k}{e})^{8} + \frac{k ^{8}}{e ^{5}} + k^{8}$ is equal to
Mathematics · Application of Derivatives · MCQ
Q33.The area of the region enclosed by the curve $y = x^{3}$ and its tangent at the point $(- 1, - 1)$ is :
Mathematics · Area Under the Curves · MCQ
Q34.Let $D$ be the domain of the function $f (x) = sin^{- 1} (lo g_{3 x} (\frac{6 + 2 l o g _{3} x}{- 5 x}))$ . If the range of the function $g : D \to R$ defined by $g (x) = x - [x], ([x]$ …
Mathematics · Functions · MCQ
Q35.Let $D_{k} = 1 n n 2 k n^{2} + n + 2 n^{2} + n 2 k - 1 n^{2} n^{2} + n + 2$ . If $\sum_{k = 1}^{n} D_{k} = 96$ , then $n$ is equal to …
Mathematics · Matrices and Determinants · Numerical
Q36.Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?
Mathematics · Permutations and Combinations · Numerical
Q37.Two circles in the first quadrant of radii $r_{1}$ and $r_{2}$ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line $x + y = 2$ . Then $r_{1}^{2} + r_{2}^{2} - r_{1} r_{2}$ is equal to .
Mathematics · Circle · Numerical
Q38.A fair $n (n > 1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$ , then $n$ is equal to .
Mathematics · Probability · Numerical
Q39.If $\int_{- 0.15}^{0.15} 100 x^{2} - 1 d x = \frac{k}{3000}$ , then $k$ is equal to .
Mathematics · Definite Integration · Numerical
Q40.The number of relations, on the set ${1, 2, 3}$ containing $(1, 2)$ and $(2, 3)$ , which are reflexive and transitive but not symmetric, is .
Mathematics · Sets and Relations · Numerical
Q41.Let $[x]$ be the greatest integer $(- 2, 1)$ . Then the number of points in the interval $(- 2, 1)$ , where the function $f (x) = ∣ [x] ∣ + x - [x]$ is discontinuous, is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q42.Let the positive numbers $a_{1}, a_{2}, a_{3}, a_{4}$ and $a_{5}$ be in a G.P. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$ respectively, where $m$ and $n$ are co-prime. If the mean of their reciprocals is $\frac{31}{40}$ …
Mathematics · Statistics · Numerical
Q43.Let $I (x) = \int \frac{x + 7}{x} d x$ and $I (9) = 12 + 7 lo g_{e} 7$ . If $I (1) = α + 7 lo g_{e} (1 + 22)$ , then $α^{4}$ is equal to .
Mathematics · Indefinite Integrals · Numerical