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Mathematics · 2020 · 7 Jan · Shift 2

18 questions from this JEE Main paper

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2020 · 7 Jan · Shift 2
Mathematics

Mathematics · 2020 · 7 Jan · Shift 2

18 questions from this JEE Main paper

Sequences and Series1 questions Binomial Theorem1 questions Permutations and Combinations1 questions Definite Integration2 questions Straight Lines and Pair of Straight Lines1 questions Limits Continuity and Differentiability1 questions Statistics1 questions Matrices and Determinants1 questions 3D Geometry1 questions Application of Derivatives1 questions Sets and Relations1 questions Complex Numbers1 questions Differentiation1 questions Vector Algebra1 questions Area Under the Curves1 questions Differential Equations1 questions Quadratic Equation and Inequalities1 questions

Q21.Let $a_{1}$ , $a_{2}$ , $a_{3}$ ,....... be a G.P. such that $a_{1}$ < 0, $a_{1}$ + $a_{2}$ = 4 and $a_{3}$ + $a_{4}$ = 16. If $i = 1 \sum 9 a_{i} = 4 λ$ , then $λ$ is equal to:
Mathematics · Sequences and Series · MCQ
Q22.The coefficient of x7 in the expression (1 + x)10 + x(1 + x)9 + x2(1 + x)8 + ......+ x10 is:
Mathematics · Binomial Theorem · MCQ
Q23.The number of ordered pairs (r, k) for which 6.35Cr = (k2 - 3). 36Cr + 1, where k is an integer, is :
Mathematics · Permutations and Combinations · MCQ
Q24.The value of $α$ for which $4 α - 1 \int 2 e^{- α ∣ x ∣} d x = 5$ , is:
Mathematics · Definite Integration · MCQ
Q25.The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line x = y is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q26.If the function ƒ defined on $(- \frac{1}{3}, \frac{1}{3})$ by f(x) = ${\frac{1}{x} lo g_{e} (\frac{1 + 3 x}{1 - 2 x}), k, w h e n x e 0 w h e n x = 0$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q27.If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to .
Mathematics · Statistics · Numerical
Q28.If the system of linear equations, x + y + z = 6 x + 2y + 3z = 10 3x + 2y + $λ$ z = $μ$ has more than two solutions, then $μ$ - $λ$ 2 is equal to .
Mathematics · Matrices and Determinants · Numerical
Q29.If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ( $α$ , 7, 1) is $(\frac{5}{3}, \frac{7}{3}, \frac{17}{3})$ , then $α$ is equal to .
Mathematics · 3D Geometry · Numerical
Q30.Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points. If $x \to 0 lim (2 + \frac{f ( x )}{x ^{3}}) = 4$ , then which one of the following is not true?
Mathematics · Application of Derivatives · MCQ
Q31.Let X = {n $\in$ N : 1 $\leq$ n $\leq$ 50}. If A = {n $\in$ X: n is a multiple of 2} and B = {n $\in$ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is .
Mathematics · Sets and Relations · Numerical
Q32.If $\frac{3 + i s i n θ}{4 - i c o s θ}$ , $θ \in$ [0, 2 $θ$ ], is a real number, then an argument of sin $θ$ + icos $θ$ is :
Mathematics · Complex Numbers · MCQ
Q33.If $θ$ 1 and $θ$ 2 be respectively the smallest and the largest values of $θ$ in (0, 2 $π$ ) - { $π$ } which satisfy the equation, 2cot2 $θ$ - $\frac{5}{s i n θ}$ + 4 = 0, then $θ_{1} \int θ_{2} cos^{2} 3 θ d θ$ …
Mathematics · Definite Integration · MCQ
Q34.Let y = y(x) be a function of x satisfying $y 1 - x^{2} = k - x 1 - y^{2}$ where k is a constant and $y (\frac{1}{2}) = - \frac{1}{4}$ . Then $\frac{d y}{d x}$ at x = $\frac{1}{2}$ , is equal to :
Mathematics · Differentiation · MCQ
Q35.Let $a$ , $b$ and $c$ be three unit vectors such that $a + b + c = 0$ . If $λ = a . b + b . c + c . a$ …
Mathematics · Vector Algebra · MCQ
Q36.The area (in sq. units) of the region {(x, y) $\in$ R2 | 4x2 $\leq$ y $\leq$ 8x + 12} is :
Mathematics · Area Under the Curves · MCQ
Q37.Let y = y(x) be the solution curve of the differential equation, $(y^{2} - x) \frac{d y}{d x} = 1$ , satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is :
Mathematics · Differential Equations · MCQ
Q38.Let $α$ and $β$ be the roots of the equation x2 - x - 1 = 0. If pk = $(α)^{k} + (β)^{k}$ , k $\geq$ 1, then which one of the following statements is not true?
Mathematics · Quadratic Equation and Inequalities · MCQ