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Mathematics · 2021 · 27 Aug · Shift 2

19 questions from this JEE Main paper

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2021 · 27 Aug · Shift 2
Mathematics

Mathematics · 2021 · 27 Aug · Shift 2

19 questions from this JEE Main paper

3D Geometry1 questions Matrices and Determinants2 questions Inverse Trigonometric Functions1 questions Parabola1 questions Differential Equations1 questions Quadratic Equation and Inequalities1 questions Application of Derivatives1 questions Circle1 questions Area Under the Curves1 questions Differentiation1 questions Definite Integration1 questions Limits Continuity and Differentiability1 questions Probability1 questions Complex Numbers1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Statistics1 questions Indefinite Integrals1 questions

Q23.The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $-$ n = 0 and mn + nl + lm = 0, is :
Mathematics · 3D Geometry · MCQ
Q24.Let $A = [x + 1] [x] [x] [x + 2] [x + 3] [x + 2] [x + 3] [x + 3] [x + 4]$ , where [t] denotes the greatest integer less than or…
Mathematics · Matrices and Determinants · MCQ
Q25.Let M and m respectively be the maximum and minimum values of the function f(x) = tan $-$ 1 (sin x + cos x) in $[0, \frac{π}{2}]$ , then the value of tan(M $-$ m) is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q26.If two tangents drawn from a point P to the parabola y2 = 16(x $-$ 3) are at right angles, then the locus of point P is :
Mathematics · Parabola · MCQ
Q27.If the solution curve of the differential equation (2x $-$ 10y3)dy + ydx = 0, passes through the points (0, 1) and (2, $β$ ), then $β$ is a root of the equation :
Mathematics · Differential Equations · MCQ
Q28.Let [ $λ$ ] be the greatest integer less than or equal to $λ$ . The set of all values of $λ$ for which the system of linear equations x + y + z = 4, 3x + 2y + 5z = 3, 9x + 4y + (28 + [ $λ$ ])z = [ $λ$ ] has a…
Mathematics · Matrices and Determinants · MCQ
Q29.The set of all values of K > $-$ 1, for which the equation $(3 x^{2} + 4 x + 3)^{2} - (k + 1) (3 x^{2} + 4 x + 3) (3 x^{2} + 4 x + 2) + k (3 x^{2} + 4 x + 2)^{2} = 0$ has real roots, is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q30.A box open from top is made from a rectangular sheet of dimension a $\times$ b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :
Mathematics · Application of Derivatives · MCQ
Q31.Let Z be the set of all integers, $A = {(x, y) \in Z \times Z : (x - 2)^{2} + y^{2} \leq 4}$ $B = {(x, y) \in Z \times Z : x^{2} + y^{2} \leq 4}$ $C = {(x, y) \in Z \times Z : (x - 2)^{2} + (y - 2)^{2} \leq 4}$ If the total number of…
Mathematics · Circle · MCQ
Q32.The area of the region bounded by the parabola (y $-$ 2)2 = (x $-$ 1), the tangent to it at the point whose ordinate is 3 and the x-axis is :
Mathematics · Area Under the Curves · MCQ
Q33.If $y (x) = cot^{- 1} (\frac{1 + s i n x + 1 - s i n x}{1 + s i n x - 1 - s i n x}), x \in (\frac{π}{2}, π)$ , then $\frac{d y}{d x}$ at $x = \frac{5 π}{6}$ is :
Mathematics · Differentiation · MCQ
Q34.The value of the integral $0 \int 1 \frac{x d x}{( 1 + x ) ( 1 + 3 x ) ( 3 + x )}$ is :
Mathematics · Definite Integration · MCQ
Q35.If $x \to \infty lim (x^{2} - x + 1 - a x) = b$ , then the ordered pair (a, b) is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.The probability distribution of random variable X is given by : Let p = P(1 < X < 4 | X < 3). If 5p = $λ$ K, then $λ$ equal to . Includes table
Mathematics · Probability · Numerical
Q37.Let z1 and z2 be two complex numbers such that $ar g (z_{1} - z_{2}) = \frac{π}{4}$ and z1, z2 satisfy the equation | z $-$ 3 | = Re(z). Then the imaginary part of z1 + z2 is equal to .
Mathematics · Complex Numbers · Numerical
Q38.Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A $\subseteq$ S : A $e ϕ$ and the sum of all the elements of A is not a multiple of 3} is .
Mathematics · Permutations and Combinations · Numerical
Q39.3 $\times$ 722 + 2 $\times$ 1022 $-$ 44 when divided by 18 leaves the remainder .
Mathematics · Binomial Theorem · Numerical
Q40.An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If $μ$ …
Mathematics · Statistics · Numerical
Q41.If $\int \frac{2 e ^{x} + 3 e ^{- x}}{4 e ^{x} + 7 e ^{- x}} d x = \frac{1}{14} (ux + v lo g_{e} (4 e^{x} + 7 e^{- x})) + C$ , where C is a constant of integration, then u + v is equal to .
Mathematics · Indefinite Integrals · Numerical