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284 questions found
Find the two regression equations related to the above data.
Evaluate:
cos (sin⁻¹(3/5) + sin⁻¹(5/13))
Force of gravity on 10 kg (g = 9.8 m/s²):
9.8 Joule
9.8 Newton
98 Joule
98 Newton
If 1, ω, ω² are the cube roots of unity, then:
ω = ω²
ω² = ω³
1 + ω + ω² = 0
1 + ω = ω²
Write the single term for C(n,r) + C(n,r−1).
Using the principle of mathematical induction, show that:
What is the domain of ?
$x \geq 1$ or $x \leq -1$
$(-\infty, \infty)$
$-1 < x < 1$
If a conic section has eccentricity , what is the equation of that conic section?
$\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$
$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$
is a parallelogram. Which one of the following represents area of the parallelogram?
Magnitude of vector product of two vectors along $\overrightarrow{AB}$ and $\overrightarrow{BD}$
Magnitude of vector product of two vectors along $\overrightarrow{AB}$ and $\overrightarrow{DC}$
Magnitude of vector product of two vectors along $\overrightarrow{AC}$ and $\overrightarrow{BC}$
Magnitude of vector product of two vectors along and
Let and be two dependent events. If , and , what is the value of ?
Equal to $P(B/A)$
Equal to $P(A)$
Less than $P(A \cap B)$
Less than
What is the integrating factor of the differential equation
?
$\tan x$
$e^{\tan x}$
$\sec^2 x$
What is the integral of
The concept of anti-derivative is necessary for solving a differential equation. Justify this statement with example.
Define L’Hospital’s rule.
The edge of a cube increases from to . What would be the approximate increment in volume?
$10^3 \text{ cm}^3$
$10.025^3 \text{ cm}^3$
$7.5187 \text{ cm}^3$
Write the slope of the tangent and normal to the curve at .
Solve:
Verify Rolle’s theorem for in .
If the limiting value of
at is $2f(x)$.
Write any one homogeneous differential equation in and solve it.