List of practice Questions

The ........ argument put forth for not disclosing the facts did not impress anybody.

Director, he said, would ....... the matter at once.

The approximate value of $\int₁⁵x²dx$ using trapezoidal rule with $n=4$ is

Choose the alternative which best expresses the meaning of the word given in capital letters.
PREPOSTEROUS

Choose the alternative which best expresses the meaning of the word given in capital letters.
SOLITUDE

Choose the alternative which best expresses the meaning of the word given in capital letters.
PROPITIOUS

The value of the integral $\int_π/2³π/2[sin~x]dx$, where $[·]$ denotes the greatest integer function, is

The area of the loop of the curve $ay²=x²(a-x)$ is

If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is

The point in the interval [0, 2π], where $f(x)=eˣsin~x$ has maximum slope, is

If $\int f(x)dx=F(x)$, then $\int x³f(x²)dx$ is equal to

If $y=sin(m~sin^-1x)$, then $(1-x²)y^\prime\prime-xy^\prime}$ is equal to

If $f(x)=(ax+b)sin~x+(cx+d)cos~x$, then the values of a, b, c and d such that $f^\prime(x)=x~cos~x$ for all x, are

The direction cosines of any normal to the xy-plane are

The locus of the equation $xy+yz=0$ is

The reflection of the point (2, 1, 3) in the plane $3x-2y-z=9$ is

If \( f(x) = \begin{cases} b, & 0 \leq x < 1 \\ x + 3, & 1 < x \leq 2 \\ 4, & x = 1 \end{cases} \) , then the value of \( (a, b) \) for which \( f(x) \) cannot be continuous at \( x = 1 \) is

If $f(x)=logₓ(log~x)$, then $f^\prime(x)$ at $x=e$ is

If $(mᵢ, 1/mᵢ)$ are four distinct points on a circle, then

If the normal to the parabola $y²=4ax$ at the point $(at², 2at)$ cuts the parabola again at $(aT², 2aT)$, then

The number of real tangents that can be drawn to the ellipse $3x²+5y²=32$ passing through (3, 5) is

If the equation $lx²+2mxy+ny²=0$ represents a pair of conjugate diameters of the hyperbola $x²/a² - y²/b² = 1$, then

If $e$ is the eccentricity of the hyperbola $x²/a² - y²/b² = 1$ and $θ$ is the angle between the asymptotes, then $\cos(θ/2)$ is equal to

The tangent and normal to a rectangular hyperbola $xy=c²$ at a point cut off intercepts $a₁, a₂$ on one axis and $b₁, b₂$ on the other, then $a₁a₂ + b₁b₂$ is equal to