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Mathematics · 2022 · 25 Jun · Shift 2

23 questions from this JEE Main paper

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2022 · 25 Jun · Shift 2
Mathematics

Mathematics · 2022 · 25 Jun · Shift 2

23 questions from this JEE Main paper

Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability2 questions Area Under the Curves1 questions Binomial Theorem2 questions Application of Derivatives2 questions Definite Integration2 questions Differential Equations1 questions Trigonometric Ratio and Identites1 questions Probability1 questions Inverse Trigonometric Functions1 questions Ellipse1 questions Statistics1 questions Vector Algebra1 questions Permutations and Combinations1 questions 3D Geometry1 questions

Q23.Let $A = {x \in R : ∣ x + 1∣ < 2}$ and $B = {x \in R : ∣ x - 1∣ \geq 2}$ . Then which one of the following statements is NOT true?
Mathematics · Quadratic Equation and Inequalities · MCQ
Q24.Let a, b $\in$ R be such that the equation $a x^{2} - 2 b x + 15 = 0$ has a repeated root $α$ . If $α$ and $β$ are the roots of the equation $x^{2} - 2 b x + 21 = 0$ , then $α^{2} + β^{2}$ is equal to :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q25.Let z1 and z2 be two complex numbers such that $\overline{z}_{1} = i \overline{z}_{2}$ and $ar g (\frac{z _{1}}{z _{2}}) = π$ . Then :
Mathematics · Complex Numbers · MCQ
Q26.The system of equations $- k x + 3 y - 14 z = 25 - 15 x + 4 y - k z = 3 - 4 x + y + 3 z = 4$ is consistent for all k in the set
Mathematics · Matrices and Determinants · MCQ
Q27. $x \to \frac{π}{2} lim (tan^{2} x ((2 sin^{2} x + 3 sin x + 4)^{\frac{1}{2}} - (sin^{2} x + 6 sin x + 2)^{\frac{1}{2}}))$ is equal to
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.The area of the region enclosed between the parabolas y2 = 2x $-$ 1 and y2 = 4x $-$ 3 is
Mathematics · Area Under the Curves · MCQ
Q29.The coefficient of x101 in the expression $(5 + x)^{500} + x (5 + x)^{499} + x^{2} (5 + x)^{498} + ..... + x^{500}$ , x > 0, is
Mathematics · Binomial Theorem · MCQ
Q30.Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2 / sec) at which the wet conical…
Mathematics · Application of Derivatives · MCQ
Q31.If $b_{n} = \int_{0}^{\frac{π}{2}} \frac{c o s ^{2} n x}{s i n x} d x, n \in N$ , then
Mathematics · Definite Integration · MCQ
Q32.If $y = y (x)$ is the solution of the differential equation $2 x^{2} \frac{d y}{d x} - 2 x y + 3 y^{2} = 0$ such that $y (e) = \frac{e}{3}$ , then y(1) is equal to :
Mathematics · Differential Equations · MCQ
Q33.The value of 2sin (12 $^{\circ}$ ) $-$ sin (72 $^{\circ}$ ) is :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q34.A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $\frac{1}{n}$ . If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :
Mathematics · Probability · MCQ
Q35.The value of $tan^{- 1} (\frac{c o s ( \frac{15 π}{4} ) - 1}{s i n ( \frac{π}{4} )})$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q36.The line y = x + 1 meets the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{2} = 1$ at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to :
Mathematics · Ellipse · MCQ
Q37.Let $A = (21 - 2 - 1)$ and $B = (- 1 - 1 22)$ . Then the number of elements in the set {(n, m) :…
Mathematics · Matrices and Determinants · Numerical
Q38.Let $f (x) = [2 x^{2} + 1]$ and $g (x) = {2 x - 3, 2 x + 3, x < 0 x \geq 0$ , where [t] is the greatest integer $\leq$ t. Then, in the open interval ( $-$ …
Mathematics · Limits Continuity and Differentiability · Numerical
Q39.The value of b > 3 for which $12 3 \int b \frac{1}{( x ^{2} - 1 ) ( x ^{2} - 4 )} d x = lo g_{e} (\frac{49}{40})$ , is equal to .
Mathematics · Definite Integration · Numerical
Q40.If the sum of the co-efficient of all the positive even powers of x in the binomial expansion of $(2 x^{3} + \frac{3}{x})^{10}$ is $5^{10} - β . 3^{9}$ , then $β$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q41.If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is $\frac{5 ( n + 1 )}{n}$ , then n is equal to .
Mathematics · Statistics · Numerical
Q42.Let $b = i + j + λ k$ , $λ \in$ R. If $a$ is a vector such that $a \times b = 13 i - j - 4 k$ and $a . b + 21 = 0$ …
Mathematics · Vector Algebra · Numerical
Q43.The total number of three-digit numbers, with one digit repeated exactly two times, is .
Mathematics · Permutations and Combinations · Numerical
Q44.Let $f (x) = ∣ (x - 1) (x^{2} - 2 x - 3) ∣ + x - 3, x \in R$ . If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal to .
Mathematics · Application of Derivatives · Numerical
Q45.Let l1 be the line in xy-plane with x and y intercepts $\frac{1}{8}$ and $\frac{1}{4 2}$ respectively, and l2 be the line in zx-plane with x and z intercepts $- \frac{1}{8}$ and $- \frac{1}{6 3}$ respectively. If d is the…
Mathematics · 3D Geometry · Numerical