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Mathematics · 2019 · 12 Jan · Shift 2

21 questions from this JEE Main paper

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2019 · 12 Jan · Shift 2
Mathematics

Mathematics · 2019 · 12 Jan · Shift 2

21 questions from this JEE Main paper

Definite Integration1 questions Probability2 questions Differential Equations1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability2 questions Circle1 questions Sequences and Series2 questions Binomial Theorem1 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants2 questions Statistics1 questions Straight Lines and Pair of Straight Lines1 questions Complex Numbers1 questions Sets and Relations1 questions Application of Derivatives1 questions Indefinite Integrals1 questions Ellipse1 questions

Q24.The integral $1 \int e {(\frac{x}{e})^{2 x} - (\frac{e}{x})^{x}}$ loge x dx is equal to :
Mathematics · Definite Integration · MCQ
Q25.In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his…
Mathematics · Probability · MCQ
Q26.If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as $\frac{x ^{2} - 2 y}{x}$ , then the curve also passes through the point :
Mathematics · Differential Equations · MCQ
Q27.There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the…
Mathematics · Permutations and Combinations · MCQ
Q28. $x \to 1^{-} lim \frac{π - 2 s i n ^{- 1} x}{1 - x}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q29.If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the locus of the foot of perpendicular from O on AB is :
Mathematics · Circle · MCQ
Q30.If nC4, nC5 and nC6 are in A.P., then n can be :
Mathematics · Sequences and Series · MCQ
Q31.The total number of irrational terms in the binomial expansion of (71/5 – 31/10)60 is :
Mathematics · Binomial Theorem · MCQ
Q32.The number of integral values of m for which the quadratic expression, (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x $\in$ R, is always positive, is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q33.The set of all values of $λ$ for which the system of linear equations x – 2y – 2z = $λ$ x x + 2y + z = $λ$ y – x – y = $λ$ z has a non-trivial solutions :
Mathematics · Matrices and Determinants · MCQ
Q34.The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :
Mathematics · Statistics · MCQ
Q35.If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q36.Let f be a differentiable function such that f(1) = 2 and f '(x) = f(x) for all x $\in$ R R. If h(x) = f(f(x)), then h'(1) is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q37.Let z1 and z2 be two complex numbers satisfying | z1 | = 9 and | z2 – 3 – 4i | = 4. Then the minimum value of | z1 – z2 | is :
Mathematics · Complex Numbers · MCQ
Q38.If A = $1 - sin θ - 1 sin θ 1 - sin θ 1 sin θ 1$ ; then for all $θ \in$ $(\frac{3 π}{4}, \frac{5 π}{4})$ …
Mathematics · Matrices and Determinants · MCQ
Q39.In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC nor for NSS is :
Mathematics · Probability · MCQ
Q40.Let Z be the set of integers. If A = {x $\in$ Z : 2(x + 2) (x2 $-$ 5x + 6) = 1} and B = {x $\in$ Z : $-$ 3 < 2x $-$ 1 < 9}, then the number of subsets of the set A $\times$ B, is
Mathematics · Sets and Relations · MCQ
Q41.If the function f given by f(x) = x3 – 3(a – 2)x2 + 3ax + 7, for some a $\in$ R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $\frac{f ( x ) - 14}{( x - 1 ) ^{2}} = 0 (x e 1)$ …
Mathematics · Application of Derivatives · MCQ
Q42.The integral $\int \frac{3 x ^{13} + 2 x ^{11}}{( 2 x ^{4} + 3 x ^{2} + 1 ) ^{4}} d x$ is equal to : (where C is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q43.Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If $Δ$ S'BS is a right angled triangle with right angle at B and area ( $Δ$ S'BS) = 8 sq. units, then the length of a latus rectum of…
Mathematics · Ellipse · MCQ
Q44.If sin4 $α$ + 4 cos4 $β$ + 2 = 4 $2$ sin $α$ cos $β$ ; $α$ , $β \in$ [0, $π$ ], then cos( $α$ + $β$ ) $-$ cos( $α - β$ ) is equal to :
Mathematics · Sequences and Series · MCQ