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Mathematics · 2021 · 31 Aug · Shift 2

21 questions from this JEE Main paper

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2021 · 31 Aug · Shift 2
Mathematics

Mathematics · 2021 · 31 Aug · Shift 2

21 questions from this JEE Main paper

Matrices and Determinants2 questions Inverse Trigonometric Functions1 questions Probability1 questions Functions1 questions Limits Continuity and Differentiability2 questions Ellipse1 questions Differential Equations2 questions Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Sequences and Series2 questions Straight Lines and Pair of Straight Lines1 questions Definite Integration1 questions Statistics1 questions Binomial Theorem1 questions Indefinite Integrals1 questions Area Under the Curves1 questions Application of Derivatives1 questions

Q22.If $α$ + $β$ + $γ$ = 2 $π$ , then the system of equations x + (cos $γ$ )y + (cos $β$ )z = 0 (cos $γ$ )x + y + (cos $α$ )z = 0 (cos $β$ )x + (cos $α$ )y + z = 0 has :
Mathematics · Matrices and Determinants · MCQ
Q23.The domain of the function $f (x) = sin^{- 1} (\frac{3 x ^{2} + x - 1}{( x - 1 ) ^{2}}) + cos^{- 1} (\frac{x - 1}{x + 1})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q24.Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :
Mathematics · Probability · MCQ
Q25.Let f : N $\to$ N be a function such that f(m + n) = f(m) + f(n) for every m, n $\in$ N. If f(6) = 18, then f(2) . f(3) is equal to :
Mathematics · Functions · MCQ
Q26.If $α = x \to \frac{π}{4} lim \frac{t a n ^{3} x - t a n x}{c o s ( x + \frac{π}{4} )}$ and $β = x \to 0 lim (cos x)^{c o t x}$ are the roots of the equation, ax2…
Mathematics · Limits Continuity and Differentiability · MCQ
Q27.The locus of mid-points of the line segments joining ( $-$ 3, $-$ 5) and the points on the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1$ is :
Mathematics · Ellipse · MCQ
Q28.If $\frac{d y}{d x} = \frac{2 ^{x} y + 2 ^{y} .2 ^{x}}{2 ^{x} + 2 ^{x + y} l o g _{e} 2}$ , y(0) = 0, then for y = 1, the value of x lies in the interval :
Mathematics · Differential Equations · MCQ
Q29.If $y \frac{d y}{d x} = x \frac{y ^{2}}{x ^{2}} + \frac{ϕ ( \frac{y ^{2}}{x ^{2}} )}{ϕ ^{'} ( \frac{y ^{2}}{x ^{2}} )}$ , x > 0, $ϕ$ > 0, and y(1) = $-$ 1, then $ϕ (\frac{y ^{2}}{4})$ …
Mathematics · Differential Equations · MCQ
Q30.The sum of the roots of the equation $x + 1 - 2 lo g_{2} (3 + 2^{x}) + 2 lo g_{4} (10 - 2^{- x}) = 0$ , is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.If z is a complex number such that $\frac{z - i}{z - 1}$ is purely imaginary, then the minimum value of | z $-$ (3 + 3i) | is :
Mathematics · Complex Numbers · MCQ
Q32.Let a1, a2, a3, ..... be an A.P. If $\frac{a _{1} + a _{2} + .... + a _{10}}{a _{1} + a _{2} + .... + a _{p}} = \frac{100}{p ^{2}}$ , p $e$ 10, then $\frac{a _{11}}{a _{10}}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q33.Let A be the set of all points ( $α$ , $β$ ) such that the area of triangle formed by the points (5, 6), (3, 2) and ( $α$ , $β$ ) is 12 square units. Then the least possible length of a line segment joining the origin to a…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q34.Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.If [x] is the greatest integer $\leq$ x, then $π^{2} 0 \int 2 (sin \frac{π x}{2}) (x - [x])^{[x]} d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q36.The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :
Mathematics · Statistics · MCQ
Q37.If the coefficient of a7b8 in the expansion of (a + 2b + 4ab)10 is K.216, then K is equal to .
Mathematics · Binomial Theorem · Numerical
Q38.The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is .
Mathematics · Sequences and Series · Numerical
Q39.If $\int \frac{s i n x}{s i n ^{3} x + c o s ^{3} x} d x = α lo g_{e} ∣1 + tan x ∣ + β lo g_{e} ∣1 - tan x + tan^{2} x ∣ + γ tan^{- 1} (\frac{2 t a n x - 1}{3}) + C$ , when C is constant of…
Mathematics · Indefinite Integrals · Numerical
Q40.The number of elements in the set ${A = (a 0 b d) : a, b, d \in {- 1, 0, 1} an d (I - A)^{3} = I - A^{3}}$ , where I is 2 $\times$ 2 identity matrix, is :
Mathematics · Matrices and Determinants · Numerical
Q41.If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = $\frac{3}{2}$ and the curve y = 1 + 4x $-$ x2, then 12 m is equal to .
Mathematics · Area Under the Curves · Numerical
Q42.Let f(x) be a cubic polynomial with f(1) = $-$ 10, f( $-$ 1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = $-$ 1. Then f(3) is equal to .
Mathematics · Application of Derivatives · Numerical