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Mathematics · 2018 · 15 Apr · Shift 1

22 questions from this JEE Main paper

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2018 · 15 Apr · Shift 1
Mathematics

Mathematics · 2018 · 15 Apr · Shift 1

22 questions from this JEE Main paper

Permutations and Combinations1 questions Sequences and Series2 questions Matrices and Determinants2 questions Complex Numbers1 questions Quadratic Equation and Inequalities2 questions Sets and Relations1 questions Hyperbola1 questions Probability1 questions Statistics1 questions Vector Algebra1 questions Differential Equations1 questions Straight Lines and Pair of Straight Lines1 questions Definite Integration1 questions Area Under the Curves1 questions Application of Derivatives1 questions Indefinite Integrals1 questions Limits Continuity and Differentiability1 questions Differentiation2 questions

Q26.n $-$ digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :
Mathematics · Permutations and Combinations · MCQ
Q27.If x1, x2, . . ., xn and $\frac{1}{h _{1}}$ , $\frac{1}{h _{2}}$ , . . . , $\frac{1}{h _{n}}$ are two A.P..s such that x3 = h2 = 8 and x8 = h7 = 20, then x5.h10 equals :
Mathematics · Sequences and Series · MCQ
Q28.Let S be the set of all real values of k for which the systemof linear equations x + y + z = 2 2x + y $-$ z = 3 3x + 2y + kz = 4 has a unique solution. Then S is :
Mathematics · Matrices and Determinants · MCQ
Q29.Let $A$ be a matrix such that $A . [1023]$ is a scalar matrix and |3A| = 108. Then A2 equals :
Mathematics · Matrices and Determinants · MCQ
Q30.The set of all $α \in$ R, for which w = $\frac{1 + ( 1 - 8 α ) z}{1 - z}$ is purely imaginary number, for all z $\in$ C satisfying |z| = 1 and Re z $e$ 1, is :
Mathematics · Complex Numbers · MCQ
Q31.If $λ \in$ R is such that the sum of the cubes of the roots of the equation, x2 + (2 $- λ$ ) x + (10 $- λ$ ) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q32.Consider the following two binary relations on the set A = {a, b, c} : R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}. Then :
Mathematics · Sets and Relations · MCQ
Q33.If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :
Mathematics · Sequences and Series · MCQ
Q34.If the tangents drawn to the hyperbola 4y2 = x2 + 1 intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB is :
Mathematics · Hyperbola · MCQ
Q35.If tanA and tanB are the roots of the quadratic equation, 3x2 $-$ 10x $-$ 25 = 0, then the value of 3 sin2(A + B) $-$ 10 sin(A + B).cos(A + B) $-$ 25 cos2(A + B) is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q36.A box 'A' contains $2$ white, $3$ red and $2$ black balls. Another box 'B' contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns out to be…
Mathematics · Probability · MCQ
Q37.The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $λ$ and then each of them is decreased by 25, their mean remains the same. Then $λ$ is equal to :
Mathematics · Statistics · MCQ
Q38.If $a, b,$ and $C$ are unit vectors such that $a + 2 b + 2 c = 0,$ then $a \times c$ …
Mathematics · Vector Algebra · MCQ
Q39.Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} + 2 y = f (x),$ where $f (x) = {1, 0, x \in [0, 1] o t h er w i se$ …
Mathematics · Differential Equations · MCQ
Q40.In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4. Then area of $Δ$ ABC (in sq. units) is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q41.The value of the integral $- \frac{π}{2} \int \frac{π}{2} sin^{4} x (1 + lo g (\frac{2 + s i n x}{2 - s i n x})) d x$ is :
Mathematics · Definite Integration · MCQ
Q42.The area (in sq. units) of the region {x $\in$ R : x $\geq$ 0, y $\geq$ 0, y $\geq$ x $-$ 2 and y $\leq x$ }, is :
Mathematics · Area Under the Curves · MCQ
Q43.If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :
Mathematics · Application of Derivatives · MCQ
Q44.If $f (\frac{x - 4}{x + 2}) = 2 x + 1,$ (x $\in$ R $-$ {1, } $-$ 2}), then $\int f (x) d x$ is equal to : (where C is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q45.Let S = {( $λ$ , $μ$ ) $\in$ R $\times$ R : f(t) = (| $λ$ | e|t| $- μ$ ). sin (2|t|), t $\in$ R, is a differentiable function}. Then S is a subset of :
Mathematics · Limits Continuity and Differentiability · MCQ
Q46.If x2 + y2 + sin y = 4, then the value of $\frac{d ^{2} y}{d x ^{2}}$ at the point ( $-$ 2,0) is :
Mathematics · Differentiation · MCQ
Q47.If $f (x) = cos x 2 sin x tan x x x^{2} x 1 2 x 1,$ then $x \to 0 lim \frac{f ^{'} ( x )}{x}$
Mathematics · Differentiation · MCQ