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Mathematics · 2022 · 27 Jun · Shift 2

22 questions from this JEE Main paper

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2022 · 27 Jun · Shift 2
Mathematics

Mathematics · 2022 · 27 Jun · Shift 2

22 questions from this JEE Main paper

Complex Numbers1 questions Sequences and Series1 questions Definite Integration3 questions Differential Equations2 questions Parabola1 questions Circle1 questions 3D Geometry1 questions Vector Algebra1 questions Statistics1 questions Probability2 questions Inverse Trigonometric Functions1 questions Trigonometric Ratio and Identites1 questions Functions1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations1 questions Limits Continuity and Differentiability1 questions Differentiation1 questions Area Under the Curves1 questions

Q23.The number of points of intersection of $∣ z - (4 + 3 i) ∣ = 2$ and $∣ z ∣ + ∣ z - 4∣ = 6$ , z $\in$ C, is :
Mathematics · Complex Numbers · MCQ
Q24.If a1, a2, a3 ...... and b1, b2, b3 ....... are A.P., and a1 = 2, a10 = 3, a1b1 = 1 = a10b10, then a4 b4 is equal to -
Mathematics · Sequences and Series · MCQ
Q25.If m and n respectively are the number of local maximum and local minimum points of the function $f (x) = 0 \int x^{2} \frac{t ^{2} - 5 t + 4}{2 + e ^{t}} d t$ , then the ordered pair (m, n) is equal to
Mathematics · Definite Integration · MCQ
Q26.Let f be a differentiable function in $(0, \frac{π}{2})$ . If $c o s x \int 1 t^{2} f (t) d t = sin^{3} x + cos x$ , then $\frac{1}{3} f^{'} (\frac{1}{3})$ is equal to
Mathematics · Definite Integration · MCQ
Q27.The integral $0 \int 1 \frac{1}{7 ^{[\frac{1}{x}]}} d x$ , where [ . ] denotes the greatest integer function, is equal to
Mathematics · Definite Integration · MCQ
Q28.If the solution curve of the differential equation $((tan^{- 1} y) - x) d y = (1 + y^{2}) d x$ passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is
Mathematics · Differential Equations · MCQ
Q29.If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $3 x + y - 29 = 0$ , is $x^{2} + a y^{2} + b x y + c x + d y + k = 0$ , then $a + b + c + d + k$ is equal to :
Mathematics · Parabola · MCQ
Q30.The set of values of k, for which the circle $C : 4 x^{2} + 4 y^{2} - 12 x + 8 y + k = 0$ lies inside the fourth quadrant and the point $(1, - \frac{1}{3})$ lies on or inside the circle C, is :
Mathematics · Circle · MCQ
Q31.The shortest distance between the lines $\frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{- 1}$ and $\frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3}$ , is :
Mathematics · 3D Geometry · MCQ
Q32.Let $a$ and $b$ be the vectors along the diagonals of a parallelogram having area $22$ . Let the angle between $a$ and $b$ be acute, $∣ a ∣ = 1$ , and $∣ a . b ∣ = ∣ a \times b ∣$ …
Mathematics · Vector Algebra · MCQ
Q33.The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and $\frac{9}{4}$ respectively. Then $x^{4} + y^{2}$ is equal to :
Mathematics · Statistics · MCQ
Q34.If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x $-$ 6y = 30, then the probability that y < 1 is :
Mathematics · Probability · MCQ
Q35.The value of $cot (n = 1 \sum 50 tan^{- 1} (\frac{1}{1 + n + n ^{2}}))$ is :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36. $α = sin 3 6^{\circ}$ is a root of which of the following equation?
Mathematics · Trigonometric Ratio and Identites · MCQ
Q37.Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S $\to$ S as $f (n) = {2 n 2 n - 11,, i f n = 1, 2, 3, 4, 5 i f n = 6, 7, 8, 9, 10$ . Let g : S $\to$ S be a…
Mathematics · Functions · Numerical
Q38.Let $α$ , $β$ be the roots of the equation $x^{2} - 4 λ x + 5 = 0$ and $α$ , $γ$ be the roots of the equation $x^{2} - (32 + 23) x + 7 + 3 λ 3 = 0$ , $λ$ > 0. If $β + γ = 32$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q39.Let A be a matrix of order 2 $\times$ 2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is .
Mathematics · Permutations and Combinations · Numerical
Q40.Let [t] denote the greatest integer $\leq$ t and {t} denote the fractional part of t. The integral value of $α$ for which the left hand limit of the function $f (x) = [1 + x] + \frac{α ^{2 [x] + {x}} + [ x ] - 1}{2 [ x ] + { x }}$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q41.If $y (x) = (x^{x})^{x}, x > 0$ , then $\frac{d ^{2} x}{d y ^{2}} + 20$ at x = 1 is equal to .
Mathematics · Differentiation · Numerical
Q42.If the area of the region ${(x, y) : x^{\frac{2}{3}} + y^{\frac{2}{3}} \leq 1, x + y \geq 0, y \geq 0}$ is A, then $\frac{256 A}{π}$ is equal to .
Mathematics · Area Under the Curves · Numerical
Q43.Let $y = y (x)$ be the solution of the differential equation $(1 - x^{2}) d y = (x y + (x^{3} + 2) 1 - x^{2}) d x, - 1$ -$$1 is equal to $\underline{\hspace{2cm}}$.
Mathematics · Differential Equations · Numerical
Q44.Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that $P (E_{n}) = \frac{n}{36}$ for every n = 1, 2, ........, 8. Then the number of elements in the set $$\left\{ {A \subseteq S:P(A) \ge {4 \over 5}}…
Mathematics · Probability · Numerical