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Mathematics · 2022 · 27 Jul · Shift 1

23 questions from this JEE Main paper

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2022 · 27 Jul · Shift 1
Mathematics

Mathematics · 2022 · 27 Jul · Shift 1

23 questions from this JEE Main paper

Sets and Relations1 questions Functions2 questions Complex Numbers2 questions Matrices and Determinants2 questions Binomial Theorem1 questions Sequences and Series1 questions Definite Integration3 questions Area Under the Curves1 questions Differential Equations2 questions Vector Algebra1 questions Probability1 questions Straight Lines and Pair of Straight Lines1 questions Circle1 questions Inverse Trigonometric Functions1 questions Statistics1 questions Hyperbola1 questions Ellipse1 questions

Q24.Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R_{1} b \Leftrightarrow ab \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$ Then,
Mathematics · Sets and Relations · MCQ
Q25.Let $f, g : N - {1} \to N$ be functions defined by $f (a) = α$ , where $α$ is the maximum of the powers of those primes $p$ such that $p^{α}$ divides $a$ , and $g (a) = a + 1$ , for all $a \in N - {1}$ …
Mathematics · Functions · MCQ
Q26.Let the minimum value $v_{0}$ of $v = ∣ z ∣^{2} + ∣ z - 3 ∣^{2} + ∣ z - 6 i ∣^{2}, z \in C$ is attained at $z = z_{0}$ . Then $2 z_{0}^{2} - \overset{z}{ˉ}_{0}^{3} + 3^{2} + v_{0}^{2}$ is equal to :
Mathematics · Complex Numbers · MCQ
Q27.Let $A = (1 - 2 2 - 5)$ . Let $α, β \in R$ be such that $α A^{2} + β A = 2 I$ . Then $α + β$ is equal to
Mathematics · Matrices and Determinants · MCQ
Q28.The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by 7 is
Mathematics · Binomial Theorem · MCQ
Q29.Suppose $a_{1}, a_{2}, \dots, a_{n}$ , .. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is $5 : 17$ and , $110 < a_{15} < 120$ , then the…
Mathematics · Sequences and Series · MCQ
Q30.Let $f : R \to R$ be a function defined as $f (x) = a sin (\frac{π [ x ]}{2}) + [2 - x], a \in R$ where $[t]$ is the greatest integer less than or equal to $t$ . If $x \to - 1 lim f (x)$ …
Mathematics · Definite Integration · MCQ
Q31.Let $I = \int_{π /4}^{π /3} (\frac{8 s i n x - s i n 2 x}{x}) d x$ . Then
Mathematics · Definite Integration · MCQ
Q32.The area of the smaller region enclosed by the curves $y^{2} = 8 x + 4$ and $x^{2} + y^{2} + 43 x - 4 = 0$ is equal to
Mathematics · Area Under the Curves · MCQ
Q33.Let $y = y_{1} (x)$ and $y = y_{2} (x)$ be two distinct solutions of the differential equation $\frac{d y}{d x} = x + y$ , with $y_{1} (0) = 0$ and $y_{2} (0) = 1$ respectively. Then, the number of points of intersection of $y = y_{1} (x)$ and $y = y_{2} (x)$ is
Mathematics · Differential Equations · MCQ
Q34.Let $a = α \hat{i} + \hat{j} + β \hat{k}$ and $b = 3 \hat{i} - 5 \hat{j} + 4 \hat{k}$ be two vectors, such that $a \times b = - \hat{i} + 9 \hat{j} + 12 \hat{k}$ . Then the projection of $b - 2 a$ on $b + a$ …
Mathematics · Vector Algebra · MCQ
Q35.Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $S$ , is a multiple of 7 but not divisible by 5 , then $9 p$ is equal to :
Mathematics · Probability · MCQ
Q36.Let $A (1, 1), B (- 4, 3), C (- 2, - 5)$ be vertices of a triangle $A B C, P$ be a point on side $B C$ , and $Δ_{1}$ and $Δ_{2}$ be the areas of triangles $A P B$ and $A B C$ , respectively. If $Δ_{1} : Δ_{2} = 4 : 7$ , then the area…
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q37.If the circle $x^{2} + y^{2} - 2 g x + 6 y - 19 c = 0, g, c \in R$ passes through the point $(6, 1)$ and its centre lies on the line $x - 2 cy = 8$ , then the length of intercept made by the circle on $x$ -axis is :
Mathematics · Circle · MCQ
Q38.Let a function $f : R \to R$ be defined as : $f (x) = ⎩ ⎨ ⎧ 0 \int x (5 - ∣ t - 3∣) d t, x^{2} + b x x > 4, x \leq 4$ where $b \in R$ . If $f$ is continuous…
Mathematics · Definite Integration · MCQ
Q39.For $k \in R$ , let the solutions of the equation $cos (sin^{- 1} (x cot (tan^{- 1} (cos (sin^{- 1} x))))) = k, 0 < ∣ x ∣ < \frac{1}{2}$ be $α$ and $β$ ,…
Mathematics · Inverse Trigonometric Functions · Numerical
Q40.The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is .
Mathematics · Statistics · Numerical
Q41.An ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ passes through the vertices of the hyperbola $H : \frac{x ^{2}}{49} - \frac{y ^{2}}{64} = - 1$ . Let the major and minor axes of the ellipse $E$ coincide with the transverse and conjugate…
Mathematics · Hyperbola · Numerical
Q42.Let $y = y (x)$ be the solution curve of the differential equation $sin (2 x^{2}) lo g_{e} (tan x^{2}) d y + (4 x y - 42 x sin (x^{2} - \frac{π}{4})) d x = 0$ , $0 < x < \frac{π}{2}$ …
Mathematics · Differential Equations · Numerical
Q43.Let $f (x) = 2 x^{2} - x - 1$ and $S = {n \in Z : ∣ f (n) ∣ \leq 800}$ . Then, the value of $n \in S \sum f (n)$ is equal to .
Mathematics · Functions · Numerical
Q44.Let $S$ be the set containing all $3 \times 3$ matrices with entries from ${- 1, 0, 1}$ . The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{T} A$ is 6 is .
Mathematics · Matrices and Determinants · Numerical
Q45.If the length of the latus rectum of the ellipse $x^{2} + 4 y^{2} + 2 x + 8 y - λ = 0$ is 4 , and $l$ is the length of its major axis, then $λ + l$ is equal to .
Mathematics · Ellipse · Numerical
Q46.Let $S = {z \in C : z^{2} + \overset{z}{ˉ} = 0}$ . Then $z \in S \sum (Re (z) + Im (z))$ is equal to .
Mathematics · Complex Numbers · Numerical