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Mathematics · 2021 · 25 Feb · Shift 2

25 questions from this JEE Main paper

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2021 · 25 Feb · Shift 2
Mathematics

Mathematics · 2021 · 25 Feb · Shift 2

25 questions from this JEE Main paper

Parabola1 questions Functions2 questions Indefinite Integrals1 questions Probability2 questions Quadratic Equation and Inequalities1 questions Trigonometric Ratio and Identites1 questions Inverse Trigonometric Functions1 questions Matrices and Determinants3 questions Complex Numbers1 questions Sequences and Series1 questions Definite Integration2 questions Ellipse1 questions Hyperbola1 questions Binomial Theorem2 questions 3D Geometry1 questions Limits Continuity and Differentiability2 questions Vector Algebra1 questions Differential Equations1 questions

Q24.The shortest distance between the line x $-$ y = 1 and the curve x2 = 2y is :
Mathematics · Parabola · MCQ
Q25.A function f(x) is given by $f (x) = \frac{5 ^{x}}{5 ^{x} + 5}$ , then the sum of the series $f (\frac{1}{20}) + f (\frac{2}{20}) + f (\frac{3}{20}) + ....... + f (\frac{39}{20})$ …
Mathematics · Functions · MCQ
Q26.Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set A $\times$ B. Then :
Mathematics · Functions · MCQ
Q27.The integral $\int \frac{e ^{3 l o g_{e} 2 x} + 5 e ^{2 l o g_{e} 2 x}}{e ^{4 l o g_{e} x} + 5 e ^{3 l o g_{e} x} - 7 e ^{2 l o g_{e} x}} d x$ , x > 0, is equal to : (where c is a constant of integration)
Mathematics · Indefinite Integrals · MCQ
Q28.Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is :
Mathematics · Probability · MCQ
Q29.Let $α$ and $β$ be the roots of x2 $-$ 6x $-$ 2 = 0. If an = $α$ n $- β$ n for n $\geq$ 1, then the value of $\frac{a _{10} - 2 a _{8}}{3 a _{9}}$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q30.If 0 < x, y < $π$ and cosx + cosy $-$ cos(x + y) = $\frac{3}{2}$ , then sinx + cosy is equal to :
Mathematics · Trigonometric Ratio and Identites · MCQ
Q31.cosec $[2 cot^{- 1} (5) + cos^{- 1} (\frac{4}{5})]$ is equal to :
Mathematics · Inverse Trigonometric Functions · MCQ
Q32.Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2 $\to$ 2R2 + 5R3 on 2A, then det(B) is equal to :
Mathematics · Matrices and Determinants · MCQ
Q33.If $α$ , $β \in$ R are such that 1 $-$ 2i (here i2 = $-$ 1) is a root of z2 + $α$ z + $β$ = 0, then ( $α - β$ ) is equal to :
Mathematics · Complex Numbers · MCQ
Q34.The minimum value of $f (x) = a^{a^{x}} + a^{1 - a^{x}}$ , where a, $x \in R$ and a > 0, is equal to :
Mathematics · Sequences and Series · MCQ
Q35.If $I_{n} = \frac{π}{4} \int \frac{π}{2} cot^{n} x d x$ , then :
Mathematics · Definite Integration · MCQ
Q36.In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A…
Mathematics · Probability · MCQ
Q37.If for the matrix, $A = [1 α - α β]$ , $A A^{T} = I_{2}$ , then the value of $α^{4} + β^{4}$ is :
Mathematics · Matrices and Determinants · MCQ
Q38.If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :
Mathematics · Ellipse · MCQ
Q39.The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x $-$ y + 4z = 8
Mathematics · Matrices and Determinants · MCQ
Q40.A hyperbola passes through the foci of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their…
Mathematics · Hyperbola · MCQ
Q41.If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)2022 is divided by 8 is .
Mathematics · Binomial Theorem · Numerical
Q42.The total number of two digit numbers 'n', such that 3n + 7n is a multiple of 10, is .
Mathematics · Binomial Theorem · Numerical
Q43.The value of $- 2 \int 2 ∣3 x^{2} - 3 x - 6∣ d x$ is .
Mathematics · Definite Integration · Numerical
Q44.A line 'l' passing through origin is perpendicular to the lines $l_{1} : r = (3 + t) i + (- 1 + 2 t) j + (4 + 2 t) k l_{2} : r = (3 + 2 s) i + (3 + 2 s) j + (2 + s) k$ …
Mathematics · 3D Geometry · Numerical
Q45.A function f is defined on [ $-$ 3, 3] as $f (x) = {min {∣ x ∣, 2 - x^{2}}, [∣ x ∣], - 2 \leq x \leq 2 2 < ∣ x ∣ \leq 3$ where [x] denotes the greatest integer $\leq$ x.…
Mathematics · Limits Continuity and Differentiability · Numerical
Q46.Let $a = i + α j + 3 k$ and $b = 3 i - α j + k$ . If the area of the parallelogram whose adjacent sides are represented by the vectors $a$ …
Mathematics · Vector Algebra · Numerical
Q47.If $x \to 0 lim \frac{a x - ( e ^{4 x} - 1 )}{a x ( e ^{4 x} - 1 )}$ exists and is equal to b, then the value of a $-$ 2b is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q48.If the curve, y = y(x) represented by the solution of the differential equation (2xy2 $-$ y)dx + xdy = 0, passes through the intersection of the lines, 2x $-$ 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to .
Mathematics · Differential Equations · Numerical