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Mathematics · 2021 · 26 Feb · Shift 1

21 questions from this JEE Main paper

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2021 · 26 Feb · Shift 1
Mathematics

Mathematics · 2021 · 26 Feb · Shift 1

21 questions from this JEE Main paper

Binomial Theorem1 questions Limits Continuity and Differentiability1 questions Matrices and Determinants2 questions Definite Integration3 questions Permutations and Combinations1 questions Sets and Relations1 questions Straight Lines and Pair of Straight Lines1 questions Circle1 questions Inverse Trigonometric Functions1 questions Application of Derivatives1 questions Differential Equations3 questions Sequences and Series1 questions Logarithm1 questions Quadratic Equation and Inequalities1 questions Area Under the Curves1 questions Trigonometric Ratio and Identites1 questions

Q23.The maximum value of the term independent of 't' in the expansion of $(t x^{\frac{1}{5}} + \frac{( 1 - x ) ^{\frac{1}{10}}}{t})^{10}$ where x $\in$ (0, 1) is :
Mathematics · Binomial Theorem · MCQ
Q24.The value of $h \to 0 lim 2 {\frac{3 s i n ( \frac{π}{6} + h ) - c o s ( \frac{π}{6} + h )}{3 h ( 3 c o s h - s i n h )}}$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q25.Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2 is 1, then the possible number of such matrices is :
Mathematics · Matrices and Determinants · MCQ
Q26.The value of $- π /2 \int π /2 \frac{c o s ^{2} x}{1 + 3 ^{x}} d x$ is :
Mathematics · Definite Integration · MCQ
Q27.The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is :
Mathematics · Permutations and Combinations · MCQ
Q28.Let R = {(P, Q) | P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1, $-$ 1) is the set :
Mathematics · Sets and Relations · MCQ
Q29.The value of $n = 1 \sum 100 n - 1 \int n e^{x - [x]} d x$ , where [ x ] is the greatest integer $\leq$ x, is :
Mathematics · Definite Integration · MCQ
Q30.The intersection of three lines x $-$ y = 0, x + 2y = 3 and 2x + y = 6 is a :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q31.In the circle given below, let OA = 1 unit, OB = 13 unit and PQ $⊥$ OB. Then, the area of the triangle PQB (in square units) is : Includes diagram
Mathematics · Circle · MCQ
Q32.The value of $(a + 1) (a + 2) (a + 2) (a + 3) (a + 3) (a + 4) a + 2 a + 3 a + 4 111$ is :
Mathematics · Matrices and Determinants · MCQ
Q33.If $\frac{s i n ^{1} x}{a} = \frac{c o s ^{- 1} x}{b} = \frac{t a n ^{- 1} y}{c}$ ; $0 < x < 1$ , then the value of $cos (\frac{π c}{a + b})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q34.The maximum slope of the curve $y = \frac{1}{2} x^{4} - 5 x^{3} + 18 x^{2} - 19 x$ occurs at the point :
Mathematics · Application of Derivatives · MCQ
Q35.The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0. The number of bacteria is increased by 20% in 2 hours. If the population of bacteria is…
Mathematics · Differential Equations · MCQ
Q36.In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is 25. Then, the sum of 4th, 6th and 8th terms is equal to :
Mathematics · Sequences and Series · MCQ
Q37.The value of the integral $0 \int π ∣ sin 2 x ∣ d x$ is .
Mathematics · Definite Integration · Numerical
Q38.The number of solutions of the equation log4(x $-$ 1) = log2(x $-$ 3) is .
Mathematics · Logarithm · Numerical
Q39.The sum of 162th power of the roots of the equation x3 $-$ 2x2 + 2x $-$ 1 = 0 is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q40.The area bounded by the lines y = || x $-$ 1 | $-$ 2 | is .
Mathematics · Area Under the Curves · Numerical
Q41.The difference between degree and order of a differential equation that represents the family of curves given by $y^{2} = a (x + \frac{a}{2})$ , a > 0 is .
Mathematics · Differential Equations · Numerical
Q42.If y = y(x) is the solution of the equation $e^{s i n y} cos y \frac{d y}{d x} + e^{s i n y} cos x = cos x$ , y(0) = 0; then $1 + y (\frac{π}{6}) + \frac{3}{2} y (\frac{π}{3}) + \frac{1}{2} y (\frac{π}{4})$ …
Mathematics · Differential Equations · Numerical
Q43.The number of integral values of 'k' for which the equation $3 sin x + 4 cos x = k + 1$ has a solution, k $\in$ R is .
Mathematics · Trigonometric Ratio and Identites · Numerical