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Mathematics · 2020 · 2 Sep · Shift 1

18 questions from this JEE Main paper

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2020 · 2 Sep · Shift 1
Mathematics

Mathematics · 2020 · 2 Sep · Shift 1

18 questions from this JEE Main paper

Matrices and Determinants2 questions Area Under the Curves1 questions Probability1 questions Limits Continuity and Differentiability2 questions Binomial Theorem1 questions Sequences and Series1 questions Permutations and Combinations1 questions Vector Algebra1 questions Definite Integration1 questions Application of Derivatives1 questions Complex Numbers1 questions Inverse Trigonometric Functions1 questions Quadratic Equation and Inequalities1 questions Sets and Relations1 questions Statistics1 questions Differential Equations1 questions

Q20.Let S be the set of all $λ \in$ R for which the system of linear equations 2x – y + 2z = 2 x – 2y + $λ$ z = –4 x + $λ$ y + z = 4 has no solution. Then the set S :
Mathematics · Matrices and Determinants · MCQ
Q21.Area (in sq. units) of the region outside $\frac{∣ x ∣}{2} + \frac{∣ y ∣}{3} = 1$ and inside the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1$ is :
Mathematics · Area Under the Curves · MCQ
Q22.Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was…
Mathematics · Probability · MCQ
Q23.If a function f(x) defined by $f (x) = ⎩ ⎨ ⎧ a e^{x} + b e^{- x}, c x^{2}, a x^{2} + 2 c x, - 1 \leq x < 1 1 \leq x \leq 3 3 < x \leq 4$ be…
Mathematics · Limits Continuity and Differentiability · MCQ
Q24.Let $α$ > 0, $β$ > 0 be such that $α$ 3 + $β$ 2 = 4. If the maximum value of the term independent of x in the binomial expansion of $(α x^{\frac{1}{9}} + β x^{- \frac{1}{6}})^{10}$ is…
Mathematics · Binomial Theorem · MCQ
Q25.Let A be a 2 $\times$ 2 real matrix with entries from {0, 1} and |A| $e$ 0. Consider the following two statements : (P) If A $e$ I2 , then |A| = –1 (Q) If |A| = 1, then tr(A) = 2, where I2 denotes 2 $\times$ 2 identity matrix and tr(A)…
Mathematics · Matrices and Determinants · MCQ
Q26.The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :
Mathematics · Sequences and Series · MCQ
Q27.If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is .
Mathematics · Permutations and Combinations · Numerical
Q28.If $x \to 1 lim \frac{x + x ^{2} + x ^{3} + ... + x ^{n} - n}{x - 1}$ = 820, (n $\in$ N) then the value of n is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q29.Let $a$ , $b$ and $c$ be three unit vectors such that $a - b^{2}$ + $a - c^{2}$ = 8. Then $a + 2 b^{2}$ …
Mathematics · Vector Algebra · Numerical
Q30.The integral $0 \int 2 ∣ ∣ x - 1 ∣ - x ∣ d x$ is equal to .
Mathematics · Definite Integration · Numerical
Q31.If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to :
Mathematics · Application of Derivatives · MCQ
Q32.The value of $(\frac{1 + s i n \frac{2 π}{9} + i c o s \frac{2 π}{9}}{1 + s i n \frac{2 π}{9} - i c o s \frac{2 π}{9}})^{3}$ is :
Mathematics · Complex Numbers · MCQ
Q33.The domain of the function f(x) = $sin^{- 1} (\frac{∣ x ∣ + 5}{x ^{2} + 1})$ is (– $\infty$ , -a] $\cup$ [a, $\infty$ ). Then a is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q34.Let $α$ and $β$ be the roots of the equation 5x2 + 6x – 2 = 0. If Sn = $α$ n + $β$ n, n = 1, 2, 3...., then :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q35.If R = {(x, y) : x, y $\in$ Z, x2 + 3y2 $\leq$ 8} is a relation on the set of integers Z, then the domain of R–1 is :
Mathematics · Sets and Relations · MCQ
Q36.Let X = {x $\in$ N : 1 $\leq$ x $\leq$ 17} and Y = {ax + b: x $\in$ X and a, b $\in$ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to :
Mathematics · Statistics · MCQ
Q37.Let y = y(x) be the solution of the differential equation, $\frac{2 + s i n x}{y + 1} . \frac{d y}{d x} = - cos x$ , y > 0,y(0) = 1. If y( $π$ ) = a and $\frac{d y}{d x}$ at x = $π$ is b, then the ordered pair (a, b) is equal to…
Mathematics · Differential Equations · MCQ