List of practice Questions

Solubility of which among the following solids in water changes slightly with temperature ?
The equation of the plane through $(-1, 1 , 2 ) $ whose normal makes equal acute angles with co-ordinate axes is
If $\int \sqrt{\frac{x - 5}{x -7}} dx = A \sqrt{x^2 - 12 x + 35 } + \log \, | x - 6 + \sqrt{x^2 - 12x + 35} | + C $ then $A = $
If $c$ denotes the contradiction then dual of the compound statement $\sim p \wedge ( q \vee c)$ is
The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
If vector $\vec{r}$ with d.c.s. $l, m, n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is
$\int^1_0 x \, \tan^{-1} x\,dx = $
The value of $\cos^{-1} \left(\cot\left(\frac{\pi}{2}\right)\right) + \cos^{-1} \left(\sin\left(\frac{2\pi}{3}\right)\right) $ is
The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point
The maximum value of $f(x) = \frac{\log \, x }{x} (x \neq 0 , x \neq 1)$ is
The number of principal solutions of $\tan 2 \theta = 1$ is
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
A water sample has ppm level concentration of following anions $F^{-} = 10 ;\, SO^{2-}_4 = 100 ;\, NO^{-}_3 = 50$ The anion/anions that make/makes the water sample unsuitable for drinking is / are :
Hydra is biologically believed to be
Choose the word which best expresses the meaning of the underlined word in the sentence.
Decay is an \(\underline{\text{immutable}}\) factor of human life.
This is a barbarous
Plausible though it sounds, the weakness of the hypothesis is that it does not incorporate all relevant facts.

You need not tutor him anymore; he knows the ropes now. 

Find the correct spelling :

If he is expecting his colleague's cooperation in these sensitive matters, he is raking up the wrong tree. 

Life has its share of problems; one should take them on the face rather than shying away from them. 

Tick the antonym of the underlined word :
The famous poet turned out to be a fraud.
Choose the word which best expresses the meaning of the underlined word in the sentence.
His \(\underline{\text{conjecture }}\) was better than mine.
In a park, nine friends are sitting in a row facing north. M is at the extreme right. Q is left to R but right to P. O is standing right to N and left to P. Similarly, S is right to R and left to T. A is at the extreme left. Who is sitting in between P and M, if O is not there?
If South-East becomes North, North-East becomes West and so on. What will West become?