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Mathematics · 2019 · 9 Apr · Shift 2

21 questions from this JEE Main paper

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2019 · 9 Apr · Shift 2
Mathematics

Mathematics · 2019 · 9 Apr · Shift 2

21 questions from this JEE Main paper

Definite Integration2 questions Trigonometric Ratio and Identites1 questions Complex Numbers1 questions Differential Equations1 questions Sequences and Series1 questions Limits Continuity and Differentiability2 questions Area Under the Curves1 questions Statistics1 questions Circle1 questions Vector Algebra1 questions Functions1 questions Sets and Relations1 questions Quadratic Equation and Inequalities1 questions Indefinite Integrals1 questions Matrices and Determinants2 questions 3D Geometry1 questions Straight Lines and Pair of Straight Lines1 questions Application of Derivatives1 questions

Q22.The value of the integral $0 \int 1 x cot^{- 1} (1 - x^{2} + x^{4}) d x$ is :-
Mathematics · Definite Integration · MCQ
Q23.The value of sin 10º sin30º sin50º sin70º is :-
Mathematics · Trigonometric Ratio and Identites · MCQ
Q24.Let z $\in$ C be such that |z| < 1. If $ω = \frac{5 + 3 z}{5 ( 1 - z )}$ z, then :
Mathematics · Complex Numbers · MCQ
Q25.If $cos x \frac{d y}{d x} - y sin x = 6 x$ , (0 < x < $\frac{π}{2}$ ) and $y (\frac{π}{3})$ = 0 then $y (\frac{π}{6})$ is equal to :-
Mathematics · Differential Equations · MCQ
Q26.If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its 11th term is :-
Mathematics · Sequences and Series · MCQ
Q27.If the function $f (x) = {a ∣ π - x ∣ + 1, x \leq 5 b ∣ x - π ∣ + 3, x > 5$ is continuous at x = 5, then the value of a – b is :-
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.The area (in sq. units) of the region A = {(x, y) : $\frac{y ^{2}}{2} \leq$ x $\leq$ y + 4} is :-
Mathematics · Area Under the Curves · MCQ
Q29.The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then $\frac{y}{x}$ is equal to
Mathematics · Statistics · MCQ
Q30.A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (–8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :
Mathematics · Circle · MCQ
Q31.If a unit vector $a$ makes angles $π$ /3 with $i$ , $π$ / 4 with $j$ and $θ \in$ (0, $π$ ) with $k$ , then a value of $θ$ is :-
Mathematics · Vector Algebra · MCQ
Q32.The domain of the definition of the function $f (x) = \frac{1}{4 - x ^{2}} + lo g_{10} (x^{3} - x)$ is
Mathematics · Functions · MCQ
Q33.Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read…
Mathematics · Sets and Relations · MCQ
Q34.If m is chosen in the quadratic equation (m2 + 1) x2 – 3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :-
Mathematics · Quadratic Equation and Inequalities · MCQ
Q35. $\int e^{s e c x} (sec x tan x f (x) + sec x tan x + se x^{2} x) d x$ = esecxf(x) + C then a possible choice of f(x) is :-
Mathematics · Indefinite Integrals · MCQ
Q36.The total number of matrices $A = 0 2 x 2 x 2 y y - y 1 - 1 1$ (x, y $\in$ R,x $e$ y) for which ATA = 3I3 is :-
Mathematics · Matrices and Determinants · MCQ
Q37.If $f (x) = [x] - [\frac{x}{4}]$ ,x $\in$ 4 , where [x] denotes the greatest integer function, then
Mathematics · Limits Continuity and Differentiability · MCQ
Q38.The vertices B and C of a $Δ$ ABC lie on the line, $\frac{x + 2}{3} = \frac{y - 1}{0} = \frac{z}{4}$ such that BC = 5 units. Then the area (in sq. units) of this triangle, given that the point A(1, –1, 2), is :
Mathematics · 3D Geometry · MCQ
Q39.If the two lines x + (a – 1) y = 1 and 2x + a2y = 1 (a $\in$ R – {0, 1}) are perpendicular, then the distance of their point of intersection from the origin is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q40.A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $tan^{- 1} (\frac{1}{2})$ . Water is poured into it at a constant rate of 5 cubic meter per minute. The the rate (in m/min.),…
Mathematics · Application of Derivatives · MCQ
Q41.If f : R $\to$ R is a differentiable function and f(2) = 6, then $x \to 2 lim \frac{6 \int f ( x ) 2 t d t}{( x - 2 )}$ is :-
Mathematics · Definite Integration · MCQ
Q42.If the system of equations 2x + 3y – z = 0, x + ky – 2z = 0 and 2x – y + z = 0 has a non-trival solution (x, y, z), then $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ is equal to :-
Mathematics · Matrices and Determinants · MCQ