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Mathematics · 2022 · 26 Jul · Shift 2

20 questions from this JEE Main paper

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2022 · 26 Jul · Shift 2
Mathematics

Mathematics · 2022 · 26 Jul · Shift 2

20 questions from this JEE Main paper

Quadratic Equation and Inequalities1 questions Complex Numbers1 questions Matrices and Determinants2 questions Parabola1 questions Application of Derivatives1 questions Limits Continuity and Differentiability1 questions Differentiation1 questions Definite Integration1 questions Differential Equations2 questions Circle1 questions Hyperbola1 questions Inverse Trigonometric Functions1 questions Indefinite Integrals1 questions Area Under the Curves1 questions Sets and Relations1 questions Permutations and Combinations1 questions Statistics1 questions Sequences and Series1 questions

Q20.The minimum value of the sum of the squares of the roots of $x^{2} + (3 - a) x + 1 = 2 a$ is:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q21.If $z = x + i y$ satisfies $∣ z ∣ - 2 = 0$ and $∣ z - i ∣ - ∣ z + 5 i ∣ = 0$ , then :
Mathematics · Complex Numbers · MCQ
Q22. $Let A = 111 and B = 9^{2} 1 2^{2} - 1 5^{2} - 1 0^{2} 1 3^{2} 1 6^{2} 1 1^{2} - 1 4^{2} 1 7^{2}, then the value of A^{'} B A is:$ …
Mathematics · Matrices and Determinants · MCQ
Q23.Let $P$ and $Q$ be any points on the curves $(x - 1)^{2} + (y + 1)^{2} = 1$ and $y = x^{2}$ , respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval :
Mathematics · Parabola · MCQ
Q24.If the maximum value of $a$ , for which the function $f_{a} (x) = tan^{- 1} 2 x - 3 a x + 7$ is non-decreasing in $(- \frac{π}{6}, \frac{π}{6})$ , is $\overset{a}{ˉ}$ , then $f_{\overset{a}{ˉ}} (\frac{π}{8})$ is equal to :
Mathematics · Application of Derivatives · MCQ
Q25.Let $β = x \to 0 lim \frac{α x - ( e ^{3 x} - 1 )}{α x ( e ^{3 x} - 1 )}$ for some $α \in R$ . Then the value of $α + β$ is :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.The value of $lo g_{e} 2 \frac{d}{d x} (lo g_{c o s x} cosec x)$ at $x = \frac{π}{4}$ is
Mathematics · Differentiation · MCQ
Q27. $0 \int 20 π (∣ sin x ∣ + ∣ cos x ∣)^{2} d x is equal to$
Mathematics · Definite Integration · MCQ
Q28.Let the solution curve $y = f (x)$ of the differential equation $\frac{d y}{d x} + \frac{x y}{x ^{2} - 1} = \frac{x ^{4} + 2 x}{1 - x ^{2}}$ , $x \in (- 1, 1)$ pass through the origin. Then $- \frac{3}{2} \int \frac{3}{2} f (x) d x$ …
Mathematics · Differential Equations · MCQ
Q29.Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^{2} - 4 x - 6 = 0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2} + 2 y - 7 = 0$ . If $PQ$ is a diameter of the circle $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$ …
Mathematics · Circle · MCQ
Q30.If the line $x - 1 = 0$ is a directrix of the hyperbola $k x^{2} - y^{2} = 6$ , then the hyperbola passes through the point :
Mathematics · Hyperbola · MCQ
Q31.If $0 < x < \frac{1}{2}$ and $\frac{s i n ^{- 1} x}{α} = \frac{c o s ^{- 1} x}{β}$ , then the value of $sin (\frac{2 π α}{α + β})$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q32. $The integral \int \frac{( 1 - \frac{1}{3} ) ( c o s x - s i n x )}{( 1 + \frac{2}{3} s i n 2 x )} d x is equal to$
Mathematics · Indefinite Integrals · MCQ
Q33.The area bounded by the curves $y = x^{2} - 1$ and $y = 1$ is
Mathematics · Area Under the Curves · MCQ
Q34.Let $A = {1, 2, 3, 4, 5, 6, 7}$ and $B = {3, 6, 7, 9}$ . Then the number of elements in the set ${C \subseteq A : C \cap B e q ϕ}$ is .
Mathematics · Sets and Relations · Numerical
Q35.Numbers are to be formed between 1000 and 3000 , which are divisible by 4 , using the digits $1, 2, 3, 4, 5$ and 6 without repetition of digits. Then the total number of such numbers is .
Mathematics · Permutations and Combinations · Numerical
Q36.The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $σ$ is the standard deviation of the data after omitting the two wrong…
Mathematics · Statistics · Numerical
Q37.Suppose $y = y (x)$ be the solution curve to the differential equation $\frac{d y}{d x} - y = 2 - e^{- x}$ such that $x \to \infty lim y (x)$ is finite. If $a$ and $b$ are respectively the $x$ - and $y$ -intercepts of the tangent to…
Mathematics · Differential Equations · Numerical
Q38.Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.'s having at least 3 terms and at most 33 terms is .
Mathematics · Sequences and Series · Numerical
Q39.The number of matrices $A = (a c b d)$ , where $a, b, c, d \in {- 1, 0, 1, 2, 3, \dots\dots, 10}$ , such that $A = A^{- 1}$ , is .
Mathematics · Matrices and Determinants · Numerical