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Mathematics · 2020 · 3 Sep · Shift 2

19 questions from this JEE Main paper

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2020 · 3 Sep · Shift 2
Mathematics

Mathematics · 2020 · 3 Sep · Shift 2

19 questions from this JEE Main paper

Definite Integration2 questions Vector Algebra1 questions Parabola1 questions Sets and Relations1 questions Hyperbola1 questions Matrices and Determinants1 questions Sequences and Series1 questions Permutations and Combinations1 questions Probability1 questions Differential Equations1 questions Limits Continuity and Differentiability1 questions Application of Derivatives1 questions Straight Lines and Pair of Straight Lines1 questions Statistics1 questions Complex Numbers1 questions Indefinite Integrals1 questions Binomial Theorem1 questions Quadratic Equation and Inequalities1 questions

Q22.Suppose f(x) is a polynomial of degree four, having critical points at –1, 0, 1. If T = {x $\in$ R | f(x) = f(0)}, then the sum of squares of all the elements of T is :
Mathematics · Definite Integration · MCQ
Q23.Let a, b c $\in$ R be such that a2 + b2 + c2 = 1. If $a cos θ = b cos (θ + \frac{2 π}{3}) = c cos (θ + \frac{4 π}{3})$ , where $θ = \frac{π}{9}$ , then the angle between the…
Mathematics · Vector Algebra · MCQ
Q24.Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 2 $5$ . Then, the distance between the centres of the circles C1 and C2 is :
Mathematics · Parabola · MCQ
Q25.Let R1 and R2 be two relation defined as follows : R1 = {(a, b) $\in$ R2 : a2 + b2 $\in$ Q} and R2 = {(a, b) $\in$ R2 : a2 + b2 $o t in$ Q}, where Q is the set of all rational numbers. Then :
Mathematics · Sets and Relations · MCQ
Q26.If the value of the integral $0 \int \frac{1}{2} \frac{x ^{2}}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x$ is $\frac{k}{6}$ , then k is equal to :
Mathematics · Definite Integration · MCQ
Q27.Let e1 and e2 be the eccentricities of the ellipse, $\frac{x ^{2}}{25} + \frac{y ^{2}}{b ^{2}} = 1$ (b < 5) and the hyperbola, $\frac{x ^{2}}{16} - \frac{y ^{2}}{b ^{2}} = 1$ respectively satisfying e1e2 = 1. If $α$ and $β$ …
Mathematics · Hyperbola · MCQ
Q28.Let S be the set of all integer solutions, (x, y, z), of the system of equations x – 2y + 5z = 0 –2x + 4y + z = 0 –7x + 14y + 9z = 0 such that 15 $\leq$ x2 + y2 + z2 $\leq$ 150. Then, the number of elements in the set S is equal to …
Mathematics · Matrices and Determinants · Numerical
Q29.If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to .
Mathematics · Sequences and Series · Numerical
Q30.The total number of 3-digit numbers, whose sum of digits is 10, is .
Mathematics · Permutations and Combinations · Numerical
Q31.The probability that a randomly chosen 5-digit number is made from exactly two digits is :
Mathematics · Probability · MCQ
Q32.If x3dy + xy dx = x2dy + 2y dx; y(2) = e and x > 1, then y(4) is equal to :
Mathematics · Differential Equations · MCQ
Q33. $x \to a lim \frac{( a + 2 x ) ^{\frac{1}{3}} - ( 3 x ) ^{\frac{1}{3}}}{( 3 a + x ) ^{\frac{1}{3}} - ( 4 x ) ^{\frac{1}{3}}}$ ( $a e$ 0) is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q34.If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10 cm, is :
Mathematics · Application of Derivatives · MCQ
Q35.If a $Δ$ ABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q36.Let xi (1 $\leq$ i $\leq$ 10) be ten observations of a random variable X. If $i = 1 \sum 10 (x_{i} - p) = 3$ and $i = 1 \sum 10 (x_{i} - p)^{2} = 9$ where 0 $e$ p $\in$ R, then…
Mathematics · Statistics · MCQ
Q37.If z1 , z2 are complex numbers such that Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and arg(z1 - z2) = $\frac{π}{6}$ , then Im(z1 + z2 ) is equal to :
Mathematics · Complex Numbers · MCQ
Q38.If $\int sin^{- 1} (\frac{x}{1 + x}) d x$ = A(x) $tan^{- 1} (x)$ + B(x) + C, where C is a constant of integration, then the ordered pair (A(x), B(x)) can be :
Mathematics · Indefinite Integrals · MCQ
Q39.If the term independent of x in the expansion of $(\frac{3}{2} x^{2} - \frac{1}{3 x})^{9}$ is k, then 18 k is equal to :
Mathematics · Binomial Theorem · MCQ
Q40.The set of all real values of $λ$ for which the quadratic equations, ( $λ$ 2 + 1)x2 – 4 $λ$ x + 2 = 0 always have exactly one root in the interval (0, 1) is :
Mathematics · Quadratic Equation and Inequalities · MCQ