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Mathematics · 2022 · 27 Jul · Shift 2

19 questions from this JEE Main paper

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2022 · 27 Jul · Shift 2
Mathematics

Mathematics · 2022 · 27 Jul · Shift 2

19 questions from this JEE Main paper

Inverse Trigonometric Functions1 questions Complex Numbers1 questions Quadratic Equation and Inequalities1 questions Limits Continuity and Differentiability1 questions Definite Integration4 questions Sequences and Series1 questions Area Under the Curves2 questions Straight Lines and Pair of Straight Lines1 questions 3D Geometry1 questions Probability1 questions Functions1 questions Binomial Theorem1 questions Application of Derivatives1 questions Differentiation1 questions Vector Algebra1 questions

Q22.The domain of the function $f (x) = sin^{- 1} [2 x^{2} - 3] + lo g_{2} (lo g_{\frac{1}{2}} (x^{2} - 5 x + 5))$ , where [t] is the greatest integer function, is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q23.Let S be the set of all $(α, β), π < α, β < 2 π$ , for which the complex number $\frac{1 - i s i n α}{1 + 2 i s i n α}$ is purely imaginary and $\frac{1 + i c o s β}{1 - 2 i c o s β}$ is purely real. Let $Z_{α β} = sin 2 α + i cos 2 β, (α, β) \in S$ …
Mathematics · Complex Numbers · MCQ
Q24.If $x^{2} - (5 + 3^{l o g_{3} 5} - 5^{l o g_{5} 3}) x + 3 (3^{(l o g_{3} 5)^{\frac{1}{3}}} - 5^{(l o g_{5} 3)^{\frac{2}{3}}} - 1) = 0$ are the roots of the equation $x^{2} - (5 + 3^{l o g_{3} 5} - 5^{l o g_{5} 3}) x + 3 (3^{(l o g_{3} 5)^{\frac{1}{3}}} - 5^{(l o g_{5} 3)^{\frac{2}{3}}} - 1) = 0$ , then the…
Mathematics · Quadratic Equation and Inequalities · MCQ
Q25.If for $p e q q e q 0$ , the function $f (x) = \frac{7 p ( 729 + x ) - 3}{3 729 + q x - 9}$ is continuous at $x = 0$ , then :
Mathematics · Limits Continuity and Differentiability · MCQ
Q26.Let $f (x) = 2 + ∣ x ∣ - ∣ x - 1∣ + ∣ x + 1∣, x \in R$ . Consider $(S 1) : f^{'} (- \frac{3}{2}) + f^{'} (- \frac{1}{2}) + f^{'} (\frac{1}{2}) + f^{'} (\frac{3}{2}) = 2 (S 2) : - 2 \int 2 f (x) d x = 12$ …
Mathematics · Definite Integration · MCQ
Q27.Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5 . Let the sum of its first five terms be $\frac{98}{25}$ . Then the sum of the first 21 terms of an AP, whose first term is $10 ar, n^{th}$ …
Mathematics · Sequences and Series · MCQ
Q28.The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$ , is equal to :
Mathematics · Area Under the Curves · MCQ
Q29. $0 \int 2 (2 x^{2} - 3 x + [x - \frac{1}{2}]) d x$ , where [t] is the greatest integer function, is equal to :
Mathematics · Definite Integration · MCQ
Q30.Consider a curve $y = y (x)$ in the first quadrant as shown in the figure. Let the area $A_{1}$ is twice the area $A_{2}$ . Then the normal to the curve perpendicular to the line $2 x - 12 y = 15$ does NOT pass through the point. Includes diagram
Mathematics · Area Under the Curves · MCQ
Q31.The equations of the sides $AB, BC$ and CA of a triangle ABC are $2 x + y = 0, x + p y = 39$ and $x - y = 3$ respectively and $P (2, 3)$ is its circumcentre. Then which of the following is NOT true?
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q32.If the length of the perpendicular drawn from the point $P (a, 4, 2)$ , a $\frac{x + 1}{2} = \frac{y - 3}{3} = \frac{z - 1}{- 1}$ on the line $\frac{x + 1}{2} = \frac{y - 3}{3} = \frac{z - 1}{- 1}$ is $26$ units and $Q (α_{1}, α_{2}, α_{3})$ is the image of the…
Mathematics · 3D Geometry · MCQ
Q33.A six faced die is biased such that $3 \times P ($ a prime number $) = 6 \times P ($ a composite number $) = 2 \times P (1)$ . Let X be a random variable that counts the number of times one gets a perfect square on…
Mathematics · Probability · MCQ
Q34.The number of functions $f$ , from the set $A = {x \in N : x^{2} - 10 x + 9 \leq 0}$ to the set $B = {n^{2} : n \in N}$ such that $f (x) \leq (x - 3)^{2} + 1$ , for every $x \in A$ …
Mathematics · Functions · Numerical
Q35.Let for the $9^{th}$ term in the binomial expansion of $(3 + 6 x)^{n}$ , in the increasing powers of $6 x$ , to be the greatest for $x = \frac{3}{2}$ , the least value of $n$ is $n_{0}$ . If $k$ is the…
Mathematics · Binomial Theorem · Numerical
Q36.A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $tan^{- 1} \frac{3}{4}$ . Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter…
Mathematics · Application of Derivatives · Numerical
Q37.For the curve $C : (x^{2} + y^{2} - 3) + (x^{2} - y^{2} - 1)^{5} = 0$ , the value of $3 y^{'} - y^{3} y^{''}$ , at the point $(α, α)$ , $α > 0$ , on C, is equal to .
Mathematics · Differentiation · Numerical
Q38.Let $f (x) = min {[x - 1], [x - 2], \dots, [x - 10]}$ where [t] denotes the greatest integer $0 \int 10 f (x) d x + 0 \int 10 (f (x))^{2} d x + 0 \int 10 ∣ f (x) ∣ d x$ . Then $0 \int 10 f (x) d x + 0 \int 10 (f (x))^{2} d x + 0 \int 10 ∣ f (x) ∣ d x$ …
Mathematics · Definite Integration · Numerical
Q39.Let f be a differentiable function satisfying $f (x) = \frac{2}{3} 0 \int 3 f (\frac{λ ^{2} x}{3}) d λ, x > 0$ and $f (1) = 3$ . If $y = f (x)$ passes through the point $(α, 6)$ ,…
Mathematics · Definite Integration · Numerical
Q40.Let $a$ , $b$ , $c$ be three non-coplanar vectors such that $a \times b$ = 4 $c$ , $b \times c$ = 9 $a$ …
Mathematics · Vector Algebra · Numerical