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Mathematics · 2021 · 25 Jul · Shift 1

22 questions from this JEE Main paper

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2021 · 25 Jul · Shift 1
Mathematics

Mathematics · 2021 · 25 Jul · Shift 1

22 questions from this JEE Main paper

Application of Derivatives1 questions Sequences and Series1 questions Hyperbola1 questions Limits Continuity and Differentiability1 questions Definite Integration2 questions Binomial Theorem3 questions Differential Equations2 questions Area Under the Curves1 questions Functions1 questions Matrices and Determinants1 questions Probability1 questions Quadratic Equation and Inequalities2 questions Ellipse1 questions Statistics1 questions Vector Algebra1 questions Permutations and Combinations1 questions Complex Numbers1 questions

Q24.Let $f (x) = 3 sin^{4} x + 10 sin^{3} x + 6 sin^{2} x - 3$ , $x \in [- \frac{π}{6}, \frac{π}{2}]$ . Then, f is :
Mathematics · Application of Derivatives · MCQ
Q25.Let Sn be the sum of the first n terms of an arithmetic progression. If S3n = 3S2n, then the value of $\frac{S _{4 n}}{S _{2 n}}$ is :
Mathematics · Sequences and Series · MCQ
Q26.The locus of the centroid of the triangle formed by any point P on the hyperbola $16 x^{2} - 9 y^{2} + 32 x + 36 y - 164 = 0$ , and its foci is :
Mathematics · Hyperbola · MCQ
Q27.Let f : R $\to$ R be defined as $f (x) = ⎩ ⎨ ⎧ \frac{λ ∣ x ^{2} - 5 x + 6 ∣}{μ ( 5 x - x ^{2} - 6 )}, e^{\frac{t a n ( x - 2 )}{x - [ x ]}}, μ, x < 2 x > 2 x = 2$ …
Mathematics · Limits Continuity and Differentiability · MCQ
Q28.The value of the definite integral $π /24 \int 5 π /24 \frac{d x}{1 + 3 t a n 2 x}$ is :
Mathematics · Definite Integration · MCQ
Q29.If b is very small as compared to the value of a, so that the cube and other higher powers of $\frac{b}{a}$ can be neglected in the identity $\frac{1}{a - b} + \frac{1}{a - 2 b} + \frac{1}{a - 3 b} + ..... + \frac{1}{a - nb} = α n + β n^{2} + γ n^{3}$ …
Mathematics · Binomial Theorem · MCQ
Q30.Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} = 1 + x e^{y - x}, - 2 < x < 2, y (0) = 0$ then, the minimum value of $y (x), x \in (- 2, 2)$ is equal to :
Mathematics · Differential Equations · MCQ
Q31.The area (in sq. units) of the region, given by the set ${(x, y) \in R \times R ∣ x \geq 0, 2 x^{2} \leq y \leq 4 - 2 x}$ is :
Mathematics · Area Under the Curves · MCQ
Q32.Let g : N $\to$ N be defined as g(3n + 1) = 3n + 2, g(3n + 2) = 3n + 3, g(3n + 3) = 3n + 1, for all n $\geq$ 0. Then which of the following statements is true?
Mathematics · Functions · MCQ
Q33.Let $f : [0, \infty) \to [0, \infty)$ be defined as $f (x) = \int_{0}^{x} [y] d y$ where [x] is the greatest integer less than or equal to x. Which of the following is true?
Mathematics · Definite Integration · MCQ
Q34.The values of a and b, for which the system of equations 2x + 3y + 6z = 8 x + 2y + az = 5 3x + 5y + 9z = b has no solution, are :
Mathematics · Matrices and Determinants · MCQ
Q35.Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is $k (\frac{3}{4})^{9}$ then k lies in the set :
Mathematics · Probability · MCQ
Q36.The number of real roots of the equation $e^{6 x} - e^{4 x} - 2 e^{3 x} - 12 e^{2 x} + e^{x} + 1 = 0$ is :
Mathematics · Quadratic Equation and Inequalities · MCQ
Q37.Let an ellipse $E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ , $a^{2} > b^{2}$ , passes through $(\frac{3}{2}, 1)$ and has eccentricity $\frac{1}{3}$ . If a circle, centered at focus…
Mathematics · Ellipse · MCQ
Q38.Let y = y(x) be solution of the following differential equation $e^{y} \frac{d y}{d x} - 2 e^{y} sin x + sin x cos^{2} x = 0, y (\frac{π}{2}) = 0$ If $y (0) = lo g_{e} (α + β e^{- 2})$ , then $4(\alpha + \beta…
Mathematics · Differential Equations · Numerical
Q39.Consider the following frequency distribution : If the sum of all frequencies is 584 and median is 45, then | $α - β$ | is equal to . Includes table
Mathematics · Statistics · Numerical
Q40.Let $p = 2 i + 3 j + k$ and $q = i + 2 j + k$ be two vectors. If a vector $r = (α i + β j + γ k)$ …
Mathematics · Vector Algebra · Numerical
Q41.The ratio of the coefficient of the middle term in the expansion of (1 + x)20 and the sum of the coefficients of two middle terms in expansion of (1 + x)19 is .
Mathematics · Binomial Theorem · Numerical
Q42.There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the…
Mathematics · Permutations and Combinations · Numerical
Q43.If $α$ , $β$ are roots of the equation $x^{2} + 5 (2) x + 10 = 0$ , $α$ > $β$ and $P_{n} = α^{n} - β^{n}$ for each positive integer n, then the value of $(\frac{P _{17} P _{20} + 5 2 P _{17} P _{19}}{P _{18} P _{19} + 5 2 P _{18}^{2}})$ …
Mathematics · Quadratic Equation and Inequalities · Numerical
Q44.The term independent of 'x' in the expansion of $(\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}$ , where x $e$ 0, 1 is equal to .
Mathematics · Binomial Theorem · Numerical
Q45.Let $S = {n \in N (01 i 0)^{n} (a c b d) = (a c b d) \forall a, b, c, d \in R}$ …
Mathematics · Complex Numbers · Numerical