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Mathematics · 2021 · 20 Jul · Shift 2

21 questions from this JEE Main paper

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2021 · 20 Jul · Shift 2
Mathematics

Mathematics · 2021 · 20 Jul · Shift 2

21 questions from this JEE Main paper

Inverse Trigonometric Functions1 questions 3D Geometry1 questions Definite Integration3 questions Functions1 questions Limits Continuity and Differentiability3 questions Probability1 questions Application of Derivatives1 questions Differential Equations2 questions Statistics1 questions Parabola2 questions Matrices and Determinants1 questions Vector Algebra2 questions Logarithm1 questions Straight Lines and Pair of Straight Lines1 questions

Q25.The value of $tan (2 tan^{- 1} (\frac{3}{5}) + sin^{- 1} (\frac{5}{13}))$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q26.The lines x = ay $-$ 1 = z $-$ 2 and x = 3y $-$ 2 = bz $-$ 2, (ab $e$ 0) are coplanar, if :
Mathematics · 3D Geometry · MCQ
Q27.If [x] denotes the greatest integer less than or equal to x, then the value of the integral $\int_{- π /2}^{π /2} [[x] - sin x] d x$ is equal to :
Mathematics · Definite Integration · MCQ
Q28.If the real part of the complex number $(1 - cos θ + 2 i sin θ)^{- 1}$ is $\frac{1}{5}$ for $θ \in (0, π)$ , then the value of the integral $\int_{0}^{θ} sin x d x$ is equal to:
Mathematics · Definite Integration · MCQ
Q29.Let $f : R - {\frac{α}{6}} \to R$ be defined by $f (x) = \frac{5 x + 3}{6 x - α}$ . Then the value of $α$ for which (fof)(x) = x, for all $x \in R - {\frac{α}{6}}$ , is :
Mathematics · Functions · MCQ
Q30.If $f : R \to R$ is given by $f (x) = x + 1$ , then the value of $n \to \infty lim \frac{1}{n} [f (0) + f (\frac{5}{n}) + f (\frac{10}{n}) + ...... + f (\frac{5 ( n - 1 )}{n})]$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q31.Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $-$ k), the probability that exactly one of B and C occurs is (1 $-$ 2k), the probability that exactly one of C and A occurs is (1 $-$ k) and…
Mathematics · Probability · MCQ
Q32.The sum of all the local minimum values of the twice differentiable function f : R $\to$ R defined by $f (x) = x^{3} - 3 x^{2} - \frac{3 f ^{''} ( 2 )}{2} x + f^{''} (1)$ is :
Mathematics · Application of Derivatives · MCQ
Q33.Let y = y(x) satisfies the equation $\frac{d y}{d x} - ∣ A ∣ = 0$ , for all x > 0, where $A = y 02 sin x - 1 0 11 \frac{1}{x}$ . If $y (π) = π + 2$ …
Mathematics · Differential Equations · MCQ
Q34.If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $\frac{20}{3}$ , respectively, then the value of | a $-$ b | is equal to :
Mathematics · Statistics · MCQ
Q35.Let $g (t) = \int_{- π /2}^{π /2} cos (\frac{π}{4} t + f (x)) d x$ , where $f (x) = lo g_{e} (x + x^{2} + 1), x \in R$ . Then which one of the following is correct?
Mathematics · Definite Integration · MCQ
Q36.Let P be a variable point on the parabola $y = 4 x^{2} + 1$ . Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :
Mathematics · Parabola · MCQ
Q37.The value of k $\in$ R, for which the following system of linear equations 3x $-$ y + 4z = 3, x + 2y $-$ 3z = $-$ 2 6x + 5y + kz = $-$ 3, has infinitely many solutions, is :
Mathematics · Matrices and Determinants · MCQ
Q38.In a triangle ABC, if $B C = 3$ , $C A = 5$ and $B A = 7$ , then the projection of the vector $B A$ on $B C$ …
Mathematics · Vector Algebra · MCQ
Q39.The number of solutions of the equation $lo g_{(x + 1)} (2 x^{2} + 7 x + 5) + lo g_{(2 x + 5)} (x + 1)^{2} - 4 = 0$ , x > 0, is :
Mathematics · Logarithm · Numerical
Q40.Let a curve y = y(x) be given by the solution of the differential equation $cos (\frac{1}{2} cos^{- 1} (e^{- x})) d x = e^{2 x} - 1 d y$ . If it intersects y-axis at y = $-$ 1, and the intersection point of…
Mathematics · Differential Equations · Numerical
Q41.For p > 0, a vector $v_{2} = 2 i + (p + 1) j$ is obtained by rotating the vector $v_{1} = 3 p i + j$ by an angle $θ$ about origin in counter clockwise…
Mathematics · Vector Algebra · Numerical
Q42.Consider a triangle having vertices A( $-$ 2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point $(0, \frac{α}{2})$ , then the value of…
Mathematics · Straight Lines and Pair of Straight Lines · Numerical
Q43.If the point on the curve y2 = 6x, nearest to the point $(3, \frac{3}{2})$ is ( $α$ , $β$ ), then 2( $α$ + $β$ ) is equal to .
Mathematics · Parabola · Numerical
Q44.Let a function $g : [0, 4] \to R$ be defined as $g (x) = {0 \leq t \leq x max {t^{3} - 6 t^{2} + 9 t - 3} 4 - x 0 \leq x \leq 3 3 < x \leq 4$ then the number of…
Mathematics · Limits Continuity and Differentiability · Numerical
Q45.If $x \to 0 lim \frac{α x e ^{x} - β l o g _{e} ( 1 + x ) + γ x ^{2} e ^{- x}}{x s i n ^{2} x} = 10, α, β, γ \in R$ , then the value of $α$ + $β$ + $γ$ is .
Mathematics · Limits Continuity and Differentiability · Numerical