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Mathematics · 2020 · 8 Jan · Shift 1

19 questions from this JEE Main paper

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2020 · 8 Jan · Shift 1
Mathematics

Mathematics · 2020 · 8 Jan · Shift 1

19 questions from this JEE Main paper

Permutations and Combinations2 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants2 questions 3D Geometry1 questions Application of Derivatives1 questions Functions1 questions Indefinite Integrals1 questions Probability1 questions Parabola1 questions Differential Equations1 questions Area Under the Curves1 questions Statistics1 questions Straight Lines and Pair of Straight Lines1 questions Complex Numbers1 questions Differentiation1 questions Limits Continuity and Differentiability1 questions Sequences and Series1 questions

Q21.An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is .
Mathematics · Permutations and Combinations · Numerical
Q22.The least positive value of 'a' for which the equation 2x2 + (a – 10)x + $\frac{33}{2}$ = 2a has real roots is
Mathematics · Quadratic Equation and Inequalities · Numerical
Q23.The number of all 3 × 3 matrices A, with enteries from the set {–1, 0, 1} such that the sum of the diagonal elements of AAT is 3, is
Mathematics · Matrices and Determinants · Numerical
Q24.The shortest distance between the lines $\frac{x - 3}{3} = \frac{y - 8}{- 1} = \frac{z - 3}{1}$ and $\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - 6}{4}$ is :
Mathematics · 3D Geometry · MCQ
Q25.Let ƒ(x) = xcos–1(–sin|x|), $x \in [- \frac{π}{2}, \frac{π}{2}]$ , then which of the following is true?
Mathematics · Application of Derivatives · MCQ
Q26.The inverse function of f(x) = $\frac{8 ^{2 x} - 8 ^{- 2 x}}{8 ^{2 x} + 8 ^{- 2 x}}$ , x $\in$ (-1, 1), is :
Mathematics · Functions · MCQ
Q27.If $\int \frac{c o s x d x}{s i n ^{3} x ( 1 + s i n ^{6} x ) ^{2/3}} = f (x) (1 + sin^{6} x)^{1/ λ} + c$ where c is a constant of integration, then $λ f (\frac{π}{3})$ …
Mathematics · Indefinite Integrals · MCQ
Q28.Let A and B be two independent events such that P(A) = $\frac{1}{3}$ and P(B) = $\frac{1}{6}$ . Then, which of the following is TRUE?
Mathematics · Probability · MCQ
Q29.The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x2 = 4y, internally in the ratio 1 : 2, is :
Mathematics · Parabola · MCQ
Q30.For which of the following ordered pairs ( $μ$ , $δ$ ), the system of linear equations x + 2y + 3z = 1 3x + 4y + 5z = $μ$ 4x + 4y + 4z = $δ$ is inconsistent ?
Mathematics · Matrices and Determinants · MCQ
Q31.Let y = y(x) be a solution of the differential equation, $1 - x^{2} \frac{d y}{d x} + 1 - y^{2} = 0$ , |x| < 1. If $y (\frac{1}{2}) = \frac{3}{2}$ , then $y (- \frac{1}{2})$ …
Mathematics · Differential Equations · MCQ
Q32.For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area…
Mathematics · Area Under the Curves · MCQ
Q33.The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by p and then reduced by q, where p $e$ 0 and q $e$ 0. If the new mean and new s.d. become half of their…
Mathematics · Statistics · MCQ
Q34.Let two points be A(1, –1) and B(0, 2). If a point P(x', y') be such that the area of $Δ$ PAB = 5 sq. units and it lies on the line, 3x + y – 4 $λ$ = 0, then a value of $λ$ is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.If the equation, x2 + bx + 45 = 0 (b $\in$ R) has conjugate complex roots and they satisfy |z +1| = 2 $10$ , then :
Mathematics · Complex Numbers · MCQ
Q36.Let ƒ(x) = (sin(tan–1x) + sin(cot–1x))2 – 1, |x| > 1. If $\frac{d y}{d x} = \frac{1}{2} \frac{d}{d x} (sin^{- 1} (f (x)))$ and $y (3) = \frac{π}{6}$ , then y( $- 3$ …
Mathematics · Differentiation · MCQ
Q37. $x \to 0 lim (\frac{3 x ^{2} + 2}{7 x ^{2} + 2})^{\frac{1}{x ^{2}}}$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q38.Let ƒ : R $\to$ R be such that for all x $\in$ R (21+x + 21–x), ƒ(x) and (3x + 3–x) are in A.P., then the minimum value of ƒ(x) is
Mathematics · Sequences and Series · MCQ
Q39.If a, b and c are the greatest value of 19Cp, 20Cq and 21Cr respectively, then :
Mathematics · Permutations and Combinations · MCQ