If $f(x)=\begin{cases}\frac{1}{x^{3}}[x(1+a cos x)-b sinx] & if\ x \neq 0\\ & if\ x = 0\end{cases}$ is a continuous function, then the values of a and b, respectively, are:
1). $\frac{-5}{2},\frac{3}{2}$
2). $\frac{1}{3},\frac{1}{5}$
3). $\frac{-5}{2},\frac{-3}{2}$
4). $\frac{5}{2},\frac{-3}{2}$
Let $f(x)=\int_{0}^{sin^{2}x} sin^{-1}\sqrt{\mu\ }du$ and $g(x)=\int_{0}^{cos^{2}x} cos^{-1}\sqrt{\mu\ }du$. Then the value of $f(x)+g(x)$ is equal to :
1). $\frac{2\pi}{3}$
2). $\frac{\pi}{3}$
3). $\frac{\pi}{4}$
4). $\frac{\pi}{2}$
If $f$ is a function satisfying $2f(x)-3f(\frac{1}{x})=x^{2}$ for any non-zero value of $x$ . then the value of $f(2)$ is equal to :
1). $\frac{-7}{4}$
2). 4
3). -2
4). $\frac{-7}{8}$
If c and d are integers and c = dq + r, then :
1). (c, d) = (d, r)
2). (c, q) = (d, r)
3). (c, r) = (d, r)
4). (C, d) = (d, q)
The equation of the straight line that is equidistant from the lines x = —3.5 and x = 7.5 is :
1). x = 2
2). x = -2
3). x = 1
4). x = -1