Podcast
Questions and Answers
Which of the following points lies on the curve E1?
Which of the following points lies on the curve E1?
- (0, 2)
- (2, 5)
- (4, -6)
- (3, 1) (correct)
What is the value of the definite integral $\int_{0}^{4\pi} (11 + 4 \cos^2 x + \cos^4 x) dx$?
What is the value of the definite integral $\int_{0}^{4\pi} (11 + 4 \cos^2 x + \cos^4 x) dx$?
- 12 - 2 (correct)
- -6
- 6
- 6 - π
In the arithmetic progression of natural numbers a1, a2, ..., an, what is the value of a6 if the volume of the parallelepiped formed by vectors a and c is 54?
In the arithmetic progression of natural numbers a1, a2, ..., an, what is the value of a6 if the volume of the parallelepiped formed by vectors a and c is 54?
- 7
- 2
- 10
- 5 (correct)
If P = [1 0 0; 4 1 0] and Q is such that q12 + q32 = P50 - Q, what is the sum of digits in q21?
If P = [1 0 0; 4 1 0] and Q is such that q12 + q32 = P50 - Q, what is the sum of digits in q21?
If b = ai + aj + ak and c = ai + aj + ak, what is the value of a such that volume of the parallelepiped formed by a, b, and c is 54?
If b = ai + aj + ak and c = ai + aj + ak, what is the value of a such that volume of the parallelepiped formed by a, b, and c is 54?
What is the point that does not lie on E2?
What is the point that does not lie on E2?
What is the value of $\lambda + \mu$ if the equation $y^2 + \lambda xy - \mu x^2 = 0$ represents lines through the origin parallel to lines dividing triangle ABC into three equal areas?
What is the value of $\lambda + \mu$ if the equation $y^2 + \lambda xy - \mu x^2 = 0$ represents lines through the origin parallel to lines dividing triangle ABC into three equal areas?
What is the value of $p - q$ if the area enclosed by the curves $y = x$ and $x + y - 2 = 0$ is expressed as $\frac{p}{q}$?
What is the value of $p - q$ if the area enclosed by the curves $y = x$ and $x + y - 2 = 0$ is expressed as $\frac{p}{q}$?
The curve satisfying the differential equation and passing through (2, 1) with eccentricity e is most likely a:
The curve satisfying the differential equation and passing through (2, 1) with eccentricity e is most likely a:
If $\lim_{n \to \infty} 2m[(n+1)(n+2)...(n+n)]^n = \frac{1}{8}$, then the value of 'a' in the expression is:
If $\lim_{n \to \infty} 2m[(n+1)(n+2)...(n+n)]^n = \frac{1}{8}$, then the value of 'a' in the expression is:
If the distance of a plane from the origin that passes through (1,1,1) and is perpendicular to the line $\frac{x-1}{3} = \frac{y-1}{0} = \frac{z-1}{4}$ is $rac{p}{q}$, what is the value of $p-q$?
If the distance of a plane from the origin that passes through (1,1,1) and is perpendicular to the line $\frac{x-1}{3} = \frac{y-1}{0} = \frac{z-1}{4}$ is $rac{p}{q}$, what is the value of $p-q$?
If the interval [0, 4] is divided into n equal sub-intervals by points $x_0, x_1, x_2, ..., x_{n-1} = 4$, what is the sum of all these sub-intervals?
If the interval [0, 4] is divided into n equal sub-intervals by points $x_0, x_1, x_2, ..., x_{n-1} = 4$, what is the sum of all these sub-intervals?
What is the value of the limit lim Δx → ∞ ∑(x_i Δx) for i from 1 to n?
What is the value of the limit lim Δx → ∞ ∑(x_i Δx) for i from 1 to n?
For the function f(x) = xf(x) + (1 - x)f(-x) = x^2 + x + 1, what is the greatest real number M such that f(x) ≥ M for all real numbers x?
For the function f(x) = xf(x) + (1 - x)f(-x) = x^2 + x + 1, what is the greatest real number M such that f(x) ≥ M for all real numbers x?
In a trapezium ABCD with AB parallel to CD, AD perpendicular to AB, and AB = 3CD, what is the area of the circle tangent to all sides if its radius is r?
In a trapezium ABCD with AB parallel to CD, AD perpendicular to AB, and AB = 3CD, what is the area of the circle tangent to all sides if its radius is r?
How many values of x in the form 1/n, where n is a natural number, lie in the interval [1/15, 10] and satisfy the equation {x} + {2x} + ... + {12x} = 78x?
How many values of x in the form 1/n, where n is a natural number, lie in the interval [1/15, 10] and satisfy the equation {x} + {2x} + ... + {12x} = 78x?
In the expansion of (2x^2 + 3x + 4)^10 = ∑a_xr, what is the value of a_9?
In the expansion of (2x^2 + 3x + 4)^10 = ∑a_xr, what is the value of a_9?
If a derivable function f: R+ → R satisfies f(xy) = f(x) + f(y) for all positive real numbers x, y, what is true about f?
If a derivable function f: R+ → R satisfies f(xy) = f(x) + f(y) for all positive real numbers x, y, what is true about f?
