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Mathematics · 2021 · 20 Jul · Shift 1

23 questions from this JEE Main paper

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2021 · 20 Jul · Shift 1
Mathematics

Mathematics · 2021 · 20 Jul · Shift 1

23 questions from this JEE Main paper

Definite Integration2 questions Statistics1 questions Quadratic Equation and Inequalities1 questions Matrices and Determinants3 questions Complex Numbers1 questions Functions1 questions Differential Equations2 questions Application of Derivatives2 questions Inverse Trigonometric Functions1 questions Limits Continuity and Differentiability2 questions Probability2 questions Vector Algebra2 questions Binomial Theorem1 questions Area Under the Curves1 questions Permutations and Combinations1 questions

Q22.Let a be a positive real number such that $\int_{0}^{a} e^{x - [x]} d x = 10 e - 9$ where [ x ] is the greatest integer less than or equal to x. Then a is equal to:
Mathematics · Definite Integration · MCQ
Q23.The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :
Mathematics · Statistics · MCQ
Q24.The value of the integral $- 1 \int 1 lo g_{e} (1 - x + 1 + x) d x$ is equal to:
Mathematics · Definite Integration · MCQ
Q25.If $α$ and $β$ are the distinct roots of the equation $x^{2} + (3)^{1/4} x + 3^{1/2} = 0$ , then the value of $α^{96} (α^{12} - 1) + β^{96} (β^{12} - 1)$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q26.Let $A = [2 a 30]$ , a $\in$ R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible…
Mathematics · Matrices and Determinants · MCQ
Q27.If z and $ω$ are two complex numbers such that $∣ z ω ∣ = 1$ and $ar g (z) - ar g (ω) = \frac{3 π}{2}$ , then $ar g (\frac{1 - 2 z ω}{1 + 3 z ω})$ is :…
Mathematics · Complex Numbers · MCQ
Q28.Let [ x ] denote the greatest integer $\leq$ x, where x $\in$ R. If the domain of the real valued function $f (x) = \frac{∣ [ x ] ∣ - 2}{∣ [ x ] ∣ - 3}$ is ( $- \infty$ , a) $] \cup$ [b, c) $\cup$ [4, $\infty$ ),…
Mathematics · Functions · MCQ
Q29.Let y = y(x) be the solution of the differential equation $x tan (\frac{y}{x}) d y = (y tan (\frac{y}{x}) - x) d x$ , $- 1 \leq x \leq 1$ , $y (\frac{1}{2}) = \frac{π}{6}$ . Then the…
Mathematics · Differential Equations · MCQ
Q30.Let $A = [a_{ij}]$ be a 3 $\times$ 3 matrix, where $a_{ij} = ⎩ ⎨ ⎧ 1 - x 2 x + 1,,, i f i = j i f ∣ i - j ∣ = 1 o t h er w i se .$ …
Mathematics · Application of Derivatives · MCQ
Q31.The number of real roots of the equation $tan^{- 1} x (x + 1) + sin^{- 1} x^{2} + x + 1 = \frac{π}{4}$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.Let y = y(x) be the solution of the differential equation $e^{x} 1 - y^{2} d x + (\frac{y}{x}) d y = 0$ , y(1) = $-$ 1. Then the value of (y(3))2 is equal to :
Mathematics · Differential Equations · MCQ
Q33.Let 'a' be a real number such that the function f(x) = ax2 + 6x $-$ 15, x $\in$ R is increasing in $(- \infty, \frac{3}{4})$ and decreasing in $(\frac{3}{4}, \infty)$ . Then the function g(x) = ax2 $-$ 6x…
Mathematics · Application of Derivatives · MCQ
Q34.Let a function f : R $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ sin x - e^{x} a + [- x] 2 x - b i f i f i f x \leq 0 0 < x < 1 x \geq 1$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q35.Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :
Mathematics · Probability · MCQ
Q36.The probability of selecting integers a $\in$ [ $-$ 5, 30] such that x2 + 2(a + 4)x $-$ 5a + 64 > 0, for all x $\in$ R, is :
Mathematics · Probability · MCQ
Q37.Let $a$ , $b$ , $c$ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle $θ$ , with the vector $a$ + $b$ + $c$ …
Mathematics · Vector Algebra · Numerical
Q38.Let $A = 100 - 1 10 0 - 1 1$ and B = 7A20 $-$ 20A7 + 2I, where I is an identity matrix of order 3 $\times$ 3. If B = [bij], then b13is…
Mathematics · Matrices and Determinants · Numerical
Q39.The number of rational terms in the binomial expansion of $(4^{\frac{1}{4}} + 5^{\frac{1}{6}})^{120}$ is .
Mathematics · Binomial Theorem · Numerical
Q40.If the shortest distance between the lines $r_{1} = α i + 2 j + 2 k + λ (i - 2 j + 2 k)$ , $λ \in$ R, $α$ > 0 and $r_{2} = - 4 i - k + μ (3 i - 2 j - 2 k)$ …
Mathematics · Vector Algebra · Numerical
Q41.Let T be the tangent to the ellipse E : x2 + 4y2 = 5 at the point P(1, 1). If the area of the region bounded by the tangent T, ellipse E, lines x = 1 and x = $5$ is $α 5$ + $β$ + $γ$ cos $-$ 1 $(\frac{1}{5})$ …
Mathematics · Area Under the Curves · Numerical
Q42.Let a, b, c, d in arithmetic progression with common difference $λ$ . If $x + a - c x - 1 x - b + d x + b x + c x + d x + a x + b x + c = 2$ …
Mathematics · Matrices and Determinants · Numerical
Q43.There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsman and 1 wicketkeeper, is…
Mathematics · Permutations and Combinations · Numerical
Q44.If the value of $x \to 0 lim (2 - cos x cos 2 x)^{(\frac{x + 2}{x ^{2}})}$ is equal to ea, then a is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical