Area of the ellipse x^2 a^2 + y^2 b^2 =1 is:

If f(x) = |x - 3| and g(x) = fof(x), then for x > 10, g'(x) is equal to:

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The existence of the unique solution of the system of equations:
$x + y + z = \lambda$
$5x − y + µz = 10$
$2x + 3y − z = 6$
depends on

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If ${a^2} + {b^2} + {c^2} = - 2$ and $f(x) = \left| {\begin{array}{*{20}{c}}{1 + {a^2}x}&{(1 + {b^2})x}&{(1 + {c^2})x}\\{(1 + {a^2})x}&{1 + {b^2}x}&{(1 + {c^2})x}\\{(1 + {a^2})x}&{(1 + {b^2})x}&{1 + {c^2}x}\end{array}} \right|$ then $f(x)$ is a polynomial of degree

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At $x=\frac{5 \pi}{6}, f(x)=2 \sin 3 x+3 \cos 3 x$ is

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Choose the correct answer from the given four options:
The maximum value of $\sin\text{x}\cdot\cos\text{x}$ is:

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The function $f(x)=x+\sin x$ is

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$\int_{}^{} {\frac{{3\sin x + 2\cos x}}{{3\cos x + 2\sin x}}\;dx = } $

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Evaluate$:\ \int\sqrt{1+\text{y}}^2.\text{2ydy:}$

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If $3i + 4j$ and $ - 5i + 7j$ are the vector sides of any triangle, then its area is given by

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On the real line $R$, we define two functions $f$ and $g$ as follows:

$f(x)=\min \{x-[x], 1-x+[x]\}$

$g(x)=\max \{x-[x], 1-x+[x]\}$

where $[x]$ denotes the largest integer not exceeding $x$ :

The positive integer $n$ for which

$\int_0^n(g(x)-f(x)) d x=100$ is

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