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Mathematics · 2019 · 9 Jan · Shift 1

22 questions from this JEE Main paper

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2019 · 9 Jan · Shift 1
Mathematics

Mathematics · 2019 · 9 Jan · Shift 1

22 questions from this JEE Main paper

Sequences and Series2 questions Matrices and Determinants2 questions Trigonometric Ratio and Identites1 questions Application of Derivatives1 questions Inverse Trigonometric Functions1 questions Hyperbola1 questions Differential Equations1 questions Complex Numbers2 questions Functions1 questions Parabola2 questions Limits Continuity and Differentiability2 questions Statistics1 questions Binomial Theorem1 questions Indefinite Integrals1 questions Permutations and Combinations1 questions Definite Integration1 questions Area Under the Curves1 questions

Q23.Let $a_{1}, a_{2}, ......., a_{30}$ be an A.P., $S = i = 1 \sum 30 a_{i}$ and $T = i = 1 \sum 15 a_{(2 i - 1)}$ . If $a_{5}$ = 27 and S - 2T = 75, then $a_{10}$ is equal to :
Mathematics · Sequences and Series · MCQ
Q24.If $A = [cos θ sin θ - sin θ cos θ]$ , then the matrix A–50 when $θ$ = $\frac{π}{12}$ , is equal to :
Mathematics · Matrices and Determinants · MCQ
Q25.For any $θ \in (\frac{π}{4}, \frac{π}{2})$ , the expression $3 (cos θ - sin θ)^{4}$ $+ 6 (sin θ + cos θ)^{2} + 4 sin^{6} θ$ equals :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q26.The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + (a2 – 1) z = a + 1 then
Mathematics · Matrices and Determinants · MCQ
Q27.The maximum volume (in cu.m) of the right circular cone having slant height 3 m is :
Mathematics · Application of Derivatives · MCQ
Q28.If $cos^{- 1} (\frac{2}{3 x}) + cos^{- 1} (\frac{3}{4 x}) = \frac{π}{2}$ (x > $\frac{3}{4}$ ), then x is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q29.Let $0 < θ < \frac{π}{2}$ . If the eccentricity of the hyperbola $\frac{x ^{2}}{c o s ^{2} θ} - \frac{y ^{2}}{s i n ^{2} θ}$ = 1 is greater than 2, then the length of its latus rectum lies in the interval :
Mathematics · Hyperbola · MCQ
Q30.If y = y(x) is the solution of the differential equation, x $\frac{d y}{d x}$ + 2y = x2, satisfying y(1) = 1, then y( $\frac{1}{2}$ ) is equal to :
Mathematics · Differential Equations · MCQ
Q31.Let A = ${θ \in (- \frac{π}{2}, π) : \frac{3 + 2 i s i n θ}{1 - 2 i s i n θ} i s p u r e l y ima g ina r y}$ . Then the sum of the elements in A is :
Mathematics · Complex Numbers · MCQ
Q32.For $x \in R - {0, 1}$ , Let f1(x) = $\frac{1}{x}$ , f2 (x) = 1 – x and f3 (x) = $\frac{1}{1 - x}$ be three given functions. If a function, J(x) satisfies (f2 o J o f1) (x) = f3 (x) then J(x) is equal to :
Mathematics · Functions · MCQ
Q33.Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?
Mathematics · Parabola · MCQ
Q34. $y \to 0 lim \frac{1 + 1 + y ^{4} - 2}{y ^{4}}$
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be
Mathematics · Sequences and Series · MCQ
Q36.5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is :
Mathematics · Statistics · MCQ
Q37.If the fractional part of the number ${\frac{2 ^{403}}{15}} i s \frac{k}{15}$ , then k is equal to :
Mathematics · Binomial Theorem · MCQ
Q38.Let f : R $\to$ R be a function defined as $f (x) = ⎩ ⎨ ⎧ 5 a + b x b + 5 x 30;;;; x \leq 1 1 < x < 3 3 \leq x < 5 x \geq 5$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q39.For x2 $e$ n $π$ + 1, n $\in$ N (the set of natural numbers), the integral $\int x \frac{2 s i n ( x ^{2} - 1 ) - s i n 2 ( x ^{2} - 1 )}{2 s i n ( x ^{2} - 1 ) + s i n 2 ( x ^{2} - 1 )} d x$ is equal to : (where c is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q40.Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is :
Mathematics · Permutations and Combinations · MCQ
Q41.Let $α$ and $β$ be two roots of the equation x2 + 2x + 2 = 0 , then $α^{15}$ + $β^{15}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q42.The value of $0 \int π ∣ cos x ∣^{3} d x$ is :
Mathematics · Definite Integration · MCQ
Q43.The area (in sq. units) bounded by the parabolae y = x2 – 1, the tangent at the point (2, 3) to it and the y-axis is :
Mathematics · Area Under the Curves · MCQ
Q44.If $θ$ denotes the acute angle between the curves, y = 10 – x2 and y = 2 + x2 at a point of their intersection, the |tan $θ$ | is equal to :
Mathematics · Parabola · MCQ