List of practice Questions

A zookeeper had $x$ baboons and $y$ monkeys in an enclosure. One day, the zookeeper was told that seven of the animals have escaped. From only this information, he was able to deduce that at least one baboon has escaped. Which of the following does not represent a possible $(x, y)$ pair?

Shown below is a number puzzle. Only one piece can be slid horizontally or vertically in one move. What is the least number of moves required to bring the piece with number 10 to the empty position x?

The foci of a hyperbola are (±2,0) and its eccentricity is $\frac{3}{2}$ . A tangent, perpendicular to the line 2x + 3y = 6, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the x- and y-axes are a and b respectively, then |6a| + |5b| is equal to_____.

Answer the following questions in about 40 words: Who was the pale-faced woman? What was she doing?

If y=y(x) is the solution of the differential equation $\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}},x>1$ such that $y(2)=\frac{2}{9}\log_e(2+\sqrt3)\ \text{and}\ y(\sqrt2)=\alpha\log_e(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}∈\N,$ then αβγ is equal to

Choose the one which is different from the rest three:

A consolidated drained (CD) triaxial test was carried out on a sand sample with the known effective shear strength parameters, $c' = 0$ and $\phi' = 30^\circ$. In the test, prior to the failure, when the sample was undergoing axial compression under constant cell pressure, the drainage valve was accidentally closed. At the failure, 360 kPa deviatoric stress was recorded along with 70 kPa pore water pressure. If the test is repeated without such error, and no back pressure is applied in either of the tests, what is the deviatoric stress (in kPa, in integer) at the failure?

Fabry disease in humans is a X-linked disease. The probability (in percentage) for a phenotypically normal father and a carrier mother to have a son with Fabry disease is ________________.

Distinguish between free vibrations and forced vibrations (Two points).

Justify with reasons:
[Fe(H$_2$O)$_6$]$^{3+}$ is stronger paramagnetic while [Fe(CN)$_6$]$^{3-}$ is weaker paramagnetic.

Let f(x) = $\displaystyle\sum_{k=1}^{10} kx^k$ , x ∈ R. If 2f(2) + f(2) = 190(2)ⁿ + 1 then n is equal to____.

A boy presented with a fever and chills. Rapid test was positive for specific antigen HRP-2. Which of the following species of Plasmodium is the most likely causative agent?

Arrange the following in increasing order of their boiling points:
1-chloropropane, 2-chloropropane, 1-chlorobutane
(A) 2-chloropropane $<$ 1-chloropropane $<$ 1-chlorobutane

The figure shows a square pyramid that will be cut into multiple solids by extending the purple and red shapes. Select the solids that will result from the cuts.