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Mathematics · 2021 · 27 Jul · Shift 2

22 questions from this JEE Main paper

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2021 · 27 Jul · Shift 2
Mathematics

Mathematics · 2021 · 27 Jul · Shift 2

22 questions from this JEE Main paper

Straight Lines and Pair of Straight Lines2 questions Binomial Theorem1 questions Functions1 questions Complex Numbers2 questions Trigonometric Ratio and Identites1 questions Statistics1 questions Area Under the Curves1 questions Differential Equations2 questions Limits Continuity and Differentiability2 questions Quadratic Equation and Inequalities2 questions Sets and Relations2 questions Circle1 questions Definite Integration2 questions Permutations and Combinations1 questions Matrices and Determinants1 questions

Q23.The point P (a, b) undergoes the following three transformations successively : (a) reflection about the line y = x. (b) translation through 2 units along the positive direction of x-axis. (c) rotation through angle $\frac{π}{4}$ about…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q24.A possible value of 'x', for which the ninth term in the expansion of ${3^{l o g_{3} 25^{x - 1} + 7} + 3^{(- \frac{1}{8}) l o g_{3} (5^{x - 1} + 1)}}^{10}$ in the increasing powers…
Mathematics · Binomial Theorem · MCQ
Q25.Let f : R $\to$ R be defined as $f (x + y) + f (x - y) = 2 f (x) f (y), f (\frac{1}{2}) = - 1$ . Then, the value of $k = 1 \sum 20 \frac{1}{s i n ( k ) s i n ( k + f ( k ))}$ is equal to :
Mathematics · Functions · MCQ
Q26.Let C be the set of all complex numbers. Let S1 = {z $\in$ C : |z $-$ 2| $\leq$ 1} and S2 = {z $\in$ C : z(1 + i) + $\overline{z}$ (1 $-$ i) $\geq$ 4}. Then, the maximum value of $z - \frac{5}{2}^{2}$ for z $\in$ S1 $\cap$ S2…
Mathematics · Complex Numbers · MCQ
Q27.If $tan (\frac{π}{9}), x, tan (\frac{7 π}{18})$ are in arithmetic progression and $tan (\frac{π}{9}), y, tan (\frac{5 π}{18})$ are also in arithmetic…
Mathematics · Trigonometric Ratio and Identites · MCQ
Q28.Let the mean and variance of the frequency distribution $x : f : x_{1} = 2 4 x_{2} = 6 4 x_{3} = 8 α x_{4} = 9 β$ be 6 and 6.8…
Mathematics · Statistics · MCQ
Q29.The area of the region bounded by y $-$ x = 2 and x2 = y is equal to :
Mathematics · Area Under the Curves · MCQ
Q30.Let y = y(x) be the solution of the differential equation (x $-$ x3)dy = (y + yx2 $-$ 3x4)dx, x > 2. If y(3) = 3, then y(4) is equal to :
Mathematics · Differential Equations · MCQ
Q31.The value of $x \to 0 lim (\frac{x}{8 1 - s i n x - 8 1 + s i n x})$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q32.Two sides of a parallelogram are along the lines 4x + 5y = 0 and 7x + 2y = 0. If the equation of one of the diagonals of the parallelogram is 11x + 7y = 9, then other diagonal passes through the point :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q33.Let $α = x \in R max {8^{2 s i n 3 x} . 4^{4 c o s 3 x}}$ and $β = x \in R min {8^{2 s i n 3 x} . 4^{4 c o s 3 x}}$ . If $8 x^{2} + b x + c = 0$ is a quadratic equation whose roots are $α$ …
Mathematics · Quadratic Equation and Inequalities · MCQ
Q34.Let $f : [0, \infty) \to [0, 3]$ be a function defined by $f (x) = {max {sin t : 0 \leq t \leq x}, 2 + cos x, 0 \leq x \leq π x > π$ Then which of the following…
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Let N be the set of natural numbers and a relation R on N be defined by $R = {(x, y) \in N \times N : x^{3} - 3 x^{2} y - x y^{2} + 3 y^{3} = 0}$ . Then the relation R is :
Mathematics · Sets and Relations · MCQ
Q36.Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $65$ on the x-axis. Then the radius of the circle C is equal to :
Mathematics · Circle · MCQ
Q37.Let f : (a, b) $\to$ R be twice differentiable function such that $f (x) = \int_{a}^{x} g (t) d t$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :
Mathematics · Definite Integration · MCQ
Q38.If the real part of the complex number $z = \frac{3 + 2 i c o s θ}{1 - 3 i c o s θ}, θ \in (0, \frac{π}{2})$ is zero, then the value of sin23 $θ$ + cos2 $θ$ is equal to .
Mathematics · Complex Numbers · Numerical
Q39.If $\int_{0}^{π} (sin^{3} x) e^{- s i n^{2} x} d x = α - \frac{β}{e} \int_{0}^{1} t e^{t} d t$ , then $α$ + $β$ is equal to .
Mathematics · Definite Integration · Numerical
Q40.The number of real roots of the equation e4x $-$ e3x $-$ 4e2x $-$ ex + 1 = 0 is equal to .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q41.Let y = y(x) be the solution of the differential equation dy = e $α$ x + y dx; $α \in$ N. If y(loge2) = loge2 and y(0) = loge $(\frac{1}{2})$ , then the value of $α$ is equal to .
Mathematics · Differential Equations · Numerical
Q42.Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)10 . (11)11 . (13)13 is equal to .
Mathematics · Permutations and Combinations · Numerical
Q43.Let A = {n $\in$ N | n2 $\leq$ n + 10,000}, B = {3k + 1 | k $\in$ N} an dC = {2k | k $\in$ N}, then the sum of all the elements of the set A $\cap$ (B $-$ C) is equal to .
Mathematics · Sets and Relations · Numerical
Q44.If $A = 100110111$ and M = A + A2 + A3 + ....... + A20, then the sum of all the elements of the matrix M is equal to …
Mathematics · Matrices and Determinants · Numerical