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Mathematics · 2021 · 26 Aug · Shift 1

20 questions from this JEE Main paper

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2021 · 26 Aug · Shift 1
Mathematics

Mathematics · 2021 · 26 Aug · Shift 1

20 questions from this JEE Main paper

Statistics1 questions Differential Equations1 questions Probability1 questions Matrices and Determinants2 questions Differentiation2 questions Sets and Relations1 questions Complex Numbers2 questions Circle2 questions Definite Integration1 questions Sequences and Series1 questions Quadratic Equation and Inequalities1 questions Permutations and Combinations2 questions Application of Derivatives1 questions Area Under the Curves1 questions Limits Continuity and Differentiability1 questions

Q23.The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. if $α$ and $β$ are the mean and standard deviation…
Mathematics · Statistics · MCQ
Q24.Let y = y(x) be a solution curve of the differential equation $(y + 1) tan^{2} x d x + tan x d y + y d x = 0$ , $x \in (0, \frac{π}{2})$ . If $x \to 0 + lim x y (x) = 1$ , then the value of $y (\frac{π}{4})$ …
Mathematics · Differential Equations · MCQ
Q25.Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = $\frac{5}{9}$ , is :
Mathematics · Probability · MCQ
Q26.Let $θ \in (0, \frac{π}{2})$ . If the system of linear equations $(1 + cos^{2} θ) x + sin^{2} θ y + 4 sin 3 θ z = 0 cos^{2} θ x + (1 + sin^{2} θ) y + 4 sin 3 θ z = 0 cos^{2} θ x + sin^{2} θ y + (1 + 4 sin 3 θ) z = 0$ …
Mathematics · Matrices and Determinants · MCQ
Q27.Let $f (x) = cos (2 tan^{- 1} sin (cot^{- 1} \frac{1 - x}{x}))$ , 0 < x < 1. Then :
Mathematics · Differentiation · MCQ
Q28.Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :
Mathematics · Sets and Relations · MCQ
Q29.The equation $ar g (\frac{z - 1}{z + 1}) = \frac{π}{4}$ represents a circle with :
Mathematics · Complex Numbers · MCQ
Q30.If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point ( $-$ 30, 0) and is tangent to the parabola y2 = 30x, then the length of this chord is :
Mathematics · Circle · MCQ
Q31.The value of $\frac{- 1}{2} \int \frac{1}{2} ((\frac{x + 1}{x - 1})^{2} + (\frac{x - 1}{x + 1})^{2} - 2)^{\frac{1}{2}} d x$ is :
Mathematics · Definite Integration · MCQ
Q32.If $A = (\frac{1}{5} \frac{- 2}{5} \frac{2}{5} \frac{1}{5})$ , $B = (1 i 01)$ …
Mathematics · Matrices and Determinants · MCQ
Q33.If the sum of an infinite GP a, ar, ar2, ar3, ....... is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, ....... is :
Mathematics · Sequences and Series · MCQ
Q34.Let $z = \frac{1 - i 3}{2}$ , $i = - 1$ . Then the value of $21 + (z + \frac{1}{z})^{3} + (z^{2} + \frac{1}{z ^{2}})^{3} + (z^{3} + \frac{1}{z ^{3}})^{3} + .... + (z^{21} + \frac{1}{z ^{21}})^{3}$ …
Mathematics · Complex Numbers · Numerical
Q35.The sum of all integral values of k (k $e$ 0) for which the equation $\frac{2}{x - 1} - \frac{1}{x - 2} = \frac{2}{k}$ in x has no real roots, is .
Mathematics · Quadratic Equation and Inequalities · Numerical
Q36.If $^{1} P_{1} + 2.^{2} P_{2} + 3.^{3} P_{3} + .... + 15.^{15} P_{15} =^{q} P_{r} - s, 0 \leq s \leq 1$ , then $^{q + s} C_{r - s}$ is equal to .
Mathematics · Permutations and Combinations · Numerical
Q37.A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then $(\frac{4}{π} + 1) k$ …
Mathematics · Application of Derivatives · Numerical
Q38.The area of the region $S = {(x, y) : 3 x^{2} \leq 4 y \leq 6 x + 24}$ is .
Mathematics · Area Under the Curves · Numerical
Q39.The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter d. Then d2 is equal to .
Mathematics · Circle · Numerical
Q40.If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then $\frac{d ^{2} y}{d x ^{2}}$ at x = 0 is equal to .
Mathematics · Differentiation · Numerical
Q41.The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is .
Mathematics · Permutations and Combinations · Numerical
Q42.Let a, b $\in$ R, b $\in$ 0, Define a function $f (x) = {a sin \frac{π}{2} (x - 1), \frac{t a n 2 x - s i n 2 x}{b x ^{3}}, f or x \leq 0 f or x > 0$ . If f is…
Mathematics · Limits Continuity and Differentiability · Numerical