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Mathematics · 2020 · 6 Sep · Shift 1

19 questions from this JEE Main paper

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2020 · 6 Sep · Shift 1
Mathematics

Mathematics · 2020 · 6 Sep · Shift 1

19 questions from this JEE Main paper

Area Under the Curves1 questions Differential Equations1 questions Complex Numbers1 questions Sequences and Series1 questions Definite Integration2 questions Sets and Relations1 questions Limits Continuity and Differentiability1 questions Vector Algebra1 questions Application of Derivatives1 questions Quadratic Equation and Inequalities1 questions Statistics1 questions Binomial Theorem1 questions Functions1 questions Probability1 questions Straight Lines and Pair of Straight Lines1 questions Matrices and Determinants2 questions Permutations and Combinations1 questions

Q20.The area (in sq. units) of the region A = {(x, y) : |x| + |y| $\leq$ 1, 2y2 $\geq$ |x|}
Mathematics · Area Under the Curves · MCQ
Q21.The general solution of the differential equation $1 + x^{2} + y^{2} + x^{2} y^{2}$ + xy $\frac{d y}{d x}$ = 0 is : (where C is a constant of integration)
Mathematics · Differential Equations · MCQ
Q22.The region represented by {z = x + iy $\in$ C : |z| – Re(z) $\leq$ 1} is also given by the inequality : {z = x + iy $\in$ C : |z| – Re(z) $\leq$ 1}
Mathematics · Complex Numbers · MCQ
Q23.Let a , b, c , d and p be any non zero distinct real numbers such that (a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then :
Mathematics · Sequences and Series · MCQ
Q24. $x \to 1 lim \frac{0 \int ( x - 1 ) ^{2} t c o s ( t ^{2} ) d t}{( x - 1 ) s i n ( x - 1 )}$
Mathematics · Definite Integration · MCQ
Q25.Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is .
Mathematics · Sets and Relations · Numerical
Q26.Let f : R $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ x^{5} sin (\frac{1}{x}) + 5 x^{2}, 0, x^{5} cos (\frac{1}{x}) + λ x^{2}, x < 0 x = 0 x > 0$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q27.If $a$ and $b$ are unit vectors, then the greatest value of $3 a + b + a - b$ is …
Mathematics · Vector Algebra · Numerical
Q28.If I1 = $0 \int 1 (1 - x^{50})^{100} d x$ and I2 = $0 \int 1 (1 - x^{50})^{101} d x$ such that I2 = $α$ I1 then $α$ equals to :
Mathematics · Definite Integration · MCQ
Q29.The position of a moving car at time t is given by f(t) = at2 + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t1 , t2 ] is attained at the point :
Mathematics · Application of Derivatives · MCQ
Q30.If $α$ and $β$ be two roots of the equation x2 – 64x + 256 = 0. Then the value of $(\frac{α ^{3}}{β ^{5}})^{1/8} + (\frac{β ^{3}}{α ^{5}})^{1/8}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.If $i = 1 \sum n (x_{i} - a) = n$ and $i = 1 \sum n (x_{i} - a)^{2} = na$ (n, a > 1) then the standard deviation of n observations x1 , x2 , ..., xn is :
Mathematics · Statistics · MCQ
Q32.If {p} denotes the fractional part of the number p, then ${\frac{3 ^{200}}{8}}$ , is equal to :
Mathematics · Binomial Theorem · MCQ
Q33.If f(x + y) = f(x)f(y) and $x = 1 \sum \infty f (x) = 2$ , x, y $\in$ N, where N is the set of all natural number, then the value of $\frac{f ( 4 )}{f ( 2 )}$ is :
Mathematics · Functions · MCQ
Q34.Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :
Mathematics · Probability · MCQ
Q35.A ray of light coming from the point (2, $23$ ) is incident at an angle 30o on the line x = 1 at the point A. The ray gets reflected on the line x = 1 and meets x-axis at the point B. Then, the line AB passes through the point :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q36.The values of $λ$ and $μ$ for which the system of linear equations x + y + z = 2 x + 2y + 3z = 5 x + 3y + $λ$ z = $μ$ has infinitely many solutions are, respectively:
Mathematics · Matrices and Determinants · MCQ
Q37.Let m and M be respectively the minimum and maximum values of $cos^{2} x 1 + cos^{2} x cos^{2} x 1 + sin^{2} x sin^{2} x sin^{2} x sin 2 x sin 2 x 1 + sin 2 x$ …
Mathematics · Matrices and Determinants · MCQ
Q38.Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
Mathematics · Permutations and Combinations · MCQ