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Mathematics · 2020 · 2 Sep · Shift 2

20 questions from this JEE Main paper

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2020 · 2 Sep · Shift 2
Mathematics

Mathematics · 2020 · 2 Sep · Shift 2

20 questions from this JEE Main paper

Matrices and Determinants2 questions Functions1 questions Trigonometric Ratio and Identites1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Parabola1 questions Sequences and Series1 questions Differential Equations1 questions Vector Algebra1 questions Definite Integration1 questions Differentiation1 questions Straight Lines and Pair of Straight Lines1 questions Statistics1 questions Area Under the Curves1 questions Probability1 questions Hyperbola1 questions Limits Continuity and Differentiability1 questions Complex Numbers1 questions Application of Derivatives1 questions

Q23.Let a, b, c $\in$ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = $a b c b c a c a b$ satisfies ATA = I, then a value of abc can…
Mathematics · Matrices and Determinants · MCQ
Q24.Let f : R $\to$ R be a function which satisfies f(x + y) = f(x) + f(y) $\forall$ x, y $\in$ R. If f(1) = 2 and g(n) = $k = 1 \sum (n - 1) f (k)$ , n $\in$ N then the value of n, for which g(n) = 20,…
Mathematics · Functions · MCQ
Q25.If the equation cos4 $θ$ + sin4 $θ$ + $λ$ = 0 has real solutions for $θ$ , then $λ$ lies in the interval :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q26.Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q27.Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line,…
Mathematics · Permutations and Combinations · MCQ
Q28.The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola, is :
Mathematics · Parabola · MCQ
Q29.If the sum of first 11 terms of an A.P., a1, a2, a3, .... is 0 (a $e$ 0), then the sum of the A.P., a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :
Mathematics · Sequences and Series · MCQ
Q30.If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x2dy= (2xy + y2)dx, then $f (\frac{1}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q31.Let the position vectors of points 'A' and 'B' be $i + j + k$ and $2 i + j + 3 k$ , respectively. A point 'P' divides the line segment AB internally in the ratio $λ$ : 1…
Mathematics · Vector Algebra · Numerical
Q32.Let [t] denote the greatest integer less than or equal to t. Then the value of $1 \int 2 ∣ 2 x - [3 x] ∣ d x$ is .
Mathematics · Definite Integration · Numerical
Q33.If y = $k = 1 \sum 6 k cos^{- 1} {\frac{3}{5} cos k x - \frac{4}{5} sin k x}$ , then $\frac{d y}{d x}$ at x = 0 is .
Mathematics · Differentiation · Numerical
Q34.The set of all possible values of $θ$ in the interval (0, $π$ ) for which the points (1, 2) and (sin $θ$ , cos $θ$ ) lie on the same side of the line x + y = 1 is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q35.If the variance of the terms in an increasing A.P., b1 , b2 , b3 ,....,b11 is 90, then the common difference of this A.P. is .
Mathematics · Statistics · Numerical
Q36.Let A = {X = (x, y, z)T: PX = 0 and x2 + y2 + z2 = 1} where $P = 1 - 2 1 239 1 - 4 - 1$ , then the set A :
Mathematics · Matrices and Determinants · MCQ
Q37.Consider a region R = {(x, y) $\in$ R : x2 $\leq$ y $\leq$ 2x}. if a line y = $α$ divides the area of region R into two equal parts, then which of the following is true?
Mathematics · Area Under the Curves · MCQ
Q38.Let EC denote the complement of an event E. Let E1 , E2 and E3 be any pairwise independent events with P(E1) > 0 and P(E1 $\cap$ E2 $\cap$ E3) = 0. Then P( $E_{2}^{C} \cap E_{3}^{C} / E_{1}$ ) is equal to :
Mathematics · Probability · MCQ
Q39.For some $θ \in (0, \frac{π}{2})$ , if the eccentricity of the hyperbola, x2–y2sec2 $θ$ = 10 is $5$ times the eccentricity of the ellipse, x2sec2 $θ$ + y2 = 5, then the length of the latus rectum of the…
Mathematics · Hyperbola · MCQ
Q40. $x \to 0 lim (tan (\frac{π}{4} + x))^{\frac{1}{x}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q41.The imaginary part of $(3 + 2 - 54)^{\frac{1}{2}} - (3 - 2 - 54)^{\frac{1}{2}}$ can be :
Mathematics · Complex Numbers · MCQ
Q42.Let f : (–1, $\infty$ ) $\to$ R be defined by f(0) = 1 and f(x) = $\frac{1}{x} lo g_{e} (1 + x)$ , x $e$ 0. Then the function f :
Mathematics · Application of Derivatives · MCQ