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Mathematics · 2020 · 4 Sep · Shift 1

18 questions from this JEE Main paper

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2020 · 4 Sep · Shift 1
Mathematics

Mathematics · 2020 · 4 Sep · Shift 1

18 questions from this JEE Main paper

Sets and Relations1 questions Probability1 questions Binomial Theorem1 questions Matrices and Determinants2 questions Limits Continuity and Differentiability1 questions Differentiation1 questions Straight Lines and Pair of Straight Lines1 questions Statistics1 questions Quadratic Equation and Inequalities2 questions Complex Numbers1 questions Application of Derivatives1 questions Indefinite Integrals2 questions Definite Integration1 questions Ellipse1 questions Differential Equations1 questions

Q22.A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:
Mathematics · Sets and Relations · MCQ
Q23.The probability of a man hitting a target is $\frac{1}{10}$ . The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$ , is .
Mathematics · Probability · Numerical
Q24.Let $(2 x^{2} + 3 x + 4)^{10} = r = 0 \sum 20 a_{r} x^{r}$ Then $\frac{a _{7}}{a _{13}}$ is equal to .
Mathematics · Binomial Theorem · Numerical
Q25.If the system of equations x - 2y + 3z = 9 2x + y + z = b x - 7y + az = 24, has infinitely many solutions, then a - b is equal to.........
Mathematics · Matrices and Determinants · Numerical
Q26.Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x) + f(y) + xy2 + x2y, for all real x and y. $x \to 0 lim \frac{f ( x )}{x} = 1$ , then f'(3) is equal to .
Mathematics · Limits Continuity and Differentiability · Numerical
Q27.If $(a + 2 b cos x) (a - 2 b cos y) = a^{2} - b^{2}$ where a > b > 0, then $\frac{d x}{d y} a t (\frac{π}{4}, \frac{π}{4})$ is :
Mathematics · Differentiation · MCQ
Q28.Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is :
Mathematics · Straight Lines and Pair of Straight Lines · MCQ
Q29.The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :
Mathematics · Statistics · MCQ
Q30.Let $α$ and $β$ be the roots of x2 - 3x + p=0 and $γ$ and $δ$ be the roots of x2 - 6x + q = 0. If $α, β, γ, δ$ form a geometric progression.Then ratio (2q + p) : (2q - p) is:
Mathematics · Quadratic Equation and Inequalities · MCQ
Q31.If $A = [cos θ i sin θ i sin θ cos θ]$ , $(θ = \frac{π}{24})$ and $A^{5} = [a c b d]$ …
Mathematics · Matrices and Determinants · MCQ
Q32.Let $u = \frac{2 z + i}{z - k i}$ , z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :
Mathematics · Complex Numbers · MCQ
Q33.Let f be a twice differentiable function on (1, 6). If f(2) = 8, f’(2) = 5, f’(x) $\geq$ 1 and f''(x) $\geq$ 4, for all x $\in$ (1, 6), then :
Mathematics · Application of Derivatives · MCQ
Q34.Let $f (x) = \int \frac{x}{( 1 + x ) ^{2}} d x (x \geq 0)$ . Then f(3) – f(1) is eqaul to :
Mathematics · Indefinite Integrals · MCQ
Q35.Let $f (x) = ∣ x - 2 ∣$ and g(x) = f(f(x)), $x \in [0, 4]$ . Then $0 \int 3 (g (x) - f (x)) d x$ is equal to:
Mathematics · Definite Integration · MCQ
Q36.The integral $\int (\frac{x}{x s i n x + c o s x})^{2} d x$ is equal to (where C is a constant of integration):
Mathematics · Indefinite Integrals · MCQ
Q37.Let $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, $$\phi \left( t \right) = {5 \over {12}} + t -…
Mathematics · Ellipse · MCQ
Q38.Let y = y(x) be the solution of the differential equation, xy'- y = x2(xcosx + sinx), x > 0. if y ( $π$ ) = $π$ then $y^{''} (\frac{π}{2}) + y (\frac{π}{2})$ is equal to :
Mathematics · Differential Equations · MCQ
Q39.Let [t] denote the greatest integer $\leq$ t. Then the equation in x, [x]2 + 2[x+2] - 7 = 0 has :
Mathematics · Quadratic Equation and Inequalities · MCQ