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Mathematics · 2020 · 5 Sep · Shift 1

21 questions from this JEE Main paper

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2020 · 5 Sep · Shift 1
Mathematics

Mathematics · 2020 · 5 Sep · Shift 1

21 questions from this JEE Main paper

Permutations and Combinations2 questions Straight Lines and Pair of Straight Lines1 questions Binomial Theorem1 questions Limits Continuity and Differentiability3 questions Indefinite Integrals1 questions Ellipse1 questions Matrices and Determinants2 questions Sequences and Series1 questions Sets and Relations1 questions Statistics1 questions Application of Derivatives1 questions Complex Numbers1 questions 3D Geometry1 questions Definite Integration1 questions Inverse Trigonometric Functions1 questions Differential Equations1 questions Quadratic Equation and Inequalities1 questions

Q20.The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is :
Mathematics · Permutations and Combinations · Numerical
Q21.If the line, 2x - y + 3 = 0 is at a distance $\frac{1}{5}$ and $\frac{2}{5}$ from the lines 4x - 2y + $α$ = 0 and 6x - 3y + $β$ = 0, respectively, then the sum of all possible values of $α$ and $β$ is :
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q22.The natural number m, for which the coefficient of x in the binomial expansion of $(x^{m} + \frac{1}{x ^{2}})^{22}$ is 1540, is .............
Mathematics · Binomial Theorem · Numerical
Q23.If $α$ is positive root of the equation, p(x) = x2 - x - 2 = 0, then $x \to α^{+} lim \frac{1 - c o s ( p ( x ) )}{x + α - 4}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.If $\int (e^{2 x} + 2 e^{x} - e^{- x} - 1) e^{(e^{x} + e^{- x})} d x$ = $g (x) e^{(e^{x} + e^{- x})} + c$ where c is a constant of integration, then g(0) is equal to :
Mathematics · Indefinite Integrals · MCQ
Q25.Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is .
Mathematics · Permutations and Combinations · Numerical
Q26.If the co-ordinates of two points A and B are $(7, 0)$ and $(- 7, 0)$ respectively and P is any point on the conic, 9x2 + 16y2 = 144, then PA + PB is equal to :
Mathematics · Ellipse · MCQ
Q27.Let $f (x) = x . [\frac{x}{2}]$ , for -10< x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q28.Let $λ \in$ R . The system of linear equations 2x1 - 4x2 + $λ$ x3 = 1 x1 - 6x2 + x3 = 2 $λ$ x1 - 10x2 + 4x3 = 3 is inconsistent for:
Mathematics · Matrices and Determinants · MCQ
Q29.If $3^{2 s i n 2 α - 1}$ , 14 and $3^{4 - 2 s i n 2 α}$ are the first three terms of an A.P. for some $α$ , then the sixth terms of this A.P. is:
Mathematics · Sequences and Series · MCQ
Q30.If the minimum and the maximum values of the function $f : [\frac{π}{4}, \frac{π}{2}] \to R$ , defined by $f (θ) = - sin^{2} θ - cos^{2} θ 12 - 1 - sin^{2} θ - 1 - cos^{2} θ 10 11 - 2$ …
Mathematics · Matrices and Determinants · MCQ
Q31.A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :
Mathematics · Sets and Relations · MCQ
Q32.The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :
Mathematics · Statistics · MCQ
Q33.If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, -4), then PQ2 is equal to:
Mathematics · Application of Derivatives · MCQ
Q34.If the four complex numbers $z, \overline{z}, \overline{z} - 2 Re o l imi t s (\overline{z})$ and $z - 2 R e (z)$ represent the vertices of a square of side 4 units in the Argand plane, then $∣ z ∣$ is equal to :
Mathematics · Complex Numbers · MCQ
Q35.If the function $f (x) = {k_{1} (x - π)^{2} - 1, k_{2} cos x, x \leq π x > π$ is twice differentiable, then the ordered pair…
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.If (a, b, c) is the image of the point (1, 2, -3) in the line $\frac{x + 1}{2} = \frac{y - 3}{- 2} = \frac{z}{- 1}$ , then a + b + c is :
Mathematics · 3D Geometry · MCQ
Q37.The value of $\frac{- π}{2} \int \frac{π}{2} \frac{1}{1 + e ^{s i n x}} d x$ is:
Mathematics · Definite Integration · MCQ
Q38.If S is the sum of the first 10 terms of the series $tan^{- 1} (\frac{1}{3}) + tan^{- 1} (\frac{1}{7}) + tan^{- 1} (\frac{1}{13}) + tan^{- 1} (\frac{1}{21}) + ....$ …
Mathematics · Inverse Trigonometric Functions · MCQ
Q39.If y = y(x) is the solution of the differential equation $\frac{5 + e ^{x}}{2 + y} . \frac{d y}{d x} + e^{x} = 0$ satisfying y(0) = 1, then a value of y(loge13) is :
Mathematics · Differential Equations · MCQ
Q40.The product of the roots of the equation 9x2 - 18|x| + 5 = 0 is :
Mathematics · Quadratic Equation and Inequalities · MCQ