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Mathematics · 2021 · 31 Aug · Shift 1

24 questions from this JEE Main paper

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2021 · 31 Aug · Shift 1
Mathematics

Mathematics · 2021 · 31 Aug · Shift 1

24 questions from this JEE Main paper

Application of Derivatives2 questions Definite Integration3 questions Vector Algebra1 questions Limits Continuity and Differentiability3 questions Sequences and Series1 questions Sets and Relations1 questions Indefinite Integrals1 questions Straight Lines and Pair of Straight Lines1 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants2 questions Parabola1 questions Differential Equations1 questions Complex Numbers1 questions Statistics1 questions Circle1 questions Permutations and Combinations1 questions Binomial Theorem1 questions Probability1 questions

Q22.The number of real roots of the equation $e^{4 x} + 2 e^{3 x} - e^{x} - 6 = 0$ is :
Mathematics · Application of Derivatives · MCQ
Q23.Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If $\int_{0}^{x} 1 - (f^{'} (t))^{2} d t = \int_{0}^{x} f (t) d t$ , $0 \leq x \leq 1$ and f(0) = 0, then $x \to 0 lim \frac{1}{x ^{2}} \int_{0}^{x} f (t) d t$ …
Mathematics · Definite Integration · MCQ
Q24.Let $a$ and $b$ be two vectors such that $2 a + 3 b = 3 a + b$ and the angle between $a$ and…
Mathematics · Vector Algebra · MCQ
Q25.The function $f (x) = x^{2} - 2 x - 3 . e^{∣ 9 x^{2} - 12 x + 4 ∣}$ is not differentiable at exactly :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference d. If the fourth term of GP is 3 r2, then r2 $-$ d…
Mathematics · Sequences and Series · MCQ
Q27.Which of the following is not correct for relation R on the set of real numbers ?
Mathematics · Sets and Relations · MCQ
Q28.The integral $\int \frac{1}{4 ( x - 1 ) ^{3} ( x + 2 ) ^{5}} d x$ is equal to : (where C is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q29.If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec $α -$ y sec $α$ = k cot 2 $α$ and x sin $α$ + y cos $α$ = k sin2 $α$ respectively, then k2 is equal to :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q30.cosec18 $^{\circ}$ is a root of the equation :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.If the following system of linear equations 2x + y + z = 5 x $-$ y + z = 3 x + y + az = b has no solution, then :
Mathematics · Matrices and Determinants · MCQ
Q32.The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :
Mathematics · Parabola · MCQ
Q33.If the function $f (x) = ⎩ ⎨ ⎧ \frac{1}{x} lo g_{e} (\frac{1 + \frac{x}{a}}{1 - \frac{x}{b}}) k \frac{c o s ^{2} x - s i n ^{2} x - 1}{x ^{2} + 1 - 1},,, x < 0 x = 0 x > 0$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q34.If $\frac{d y}{d x} = \frac{2 ^{x + y} - 2 ^{x}}{2 ^{y}}$ , y(0) = 1, then y(1) is equal to :
Mathematics · Differential Equations · MCQ
Q35. $x \to 0 lim \frac{s i n ^{2} ( π c o s ^{4} x )}{x ^{4}}$ is equal to :
Mathematics · Limits Continuity and Differentiability · MCQ
Q36.If $a_{r} = cos \frac{2 r π}{9} + i sin \frac{2 r π}{9}$ , r = 1, 2, 3, ....., i = $- 1$ , then the determinant $a_{1} a_{4} a_{7} a_{2} a_{5} a_{8} a_{3} a_{6} a_{9}$ …
Mathematics · Matrices and Determinants · MCQ
Q37.Let [t] denote the greatest integer $\leq$ t. Then the value of $8. - \frac{1}{2} \int 1 ([2 x] + ∣ x ∣) d x$ is .
Mathematics · Definite Integration · Numerical
Q38.A point z moves in the complex plane such that $ar g (\frac{z - 2}{z + 2}) = \frac{π}{4}$ , then the minimum value of $z - 92 - 2 i^{2}$ is equal to .
Mathematics · Complex Numbers · Numerical
Q39.If 'R' is the least value of 'a' such that the function f(x) = x2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then the value of |R $-$ S| is …
Mathematics · Application of Derivatives · Numerical
Q40.The mean of 10 numbers 7 $\times$ 8, 10 $\times$ 10, 13 $\times$ 12, 16 $\times$ 14, ....... is .
Mathematics · Statistics · Numerical
Q41.If the variable line 3x + 4y = $α$ lies between the two circles (x $-$ 1)2 + (y $-$ 1)2 = 1 and (x $-$ 9)2 + (y $-$ 1)2 = 4, without intercepting a chord on either circle, then the sum of all the integral values of $α$ is …
Mathematics · Circle · Numerical
Q42.The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is .
Mathematics · Permutations and Combinations · Numerical
Q43.If $x ϕ (x) = 5 \int x (3 t^{2} - 2 ϕ^{'} (t)) d t$ , x > $-$ 2, and $ϕ$ (0) = 4, then $ϕ$ (2) is .
Mathematics · Definite Integration · Numerical
Q44.If $(\frac{3 ^{6}}{4 ^{4}}) k$ is the term, independent of x, in the binomial expansion of $(\frac{x}{4} - \frac{12}{x ^{2}})^{12}$ , then k is equal to .
Mathematics · Binomial Theorem · Numerical
Q45.An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and…
Mathematics · Probability · Numerical