List of practice Questions

If $A$ is a square matrix of order $3$ and a is a real number, then determinant $ |\alpha \,\,\,A| $ is equal to

The ratio in which ZX-plane divides the line segment AB joining the points $ A(4,2,3) $ and $ B(-2,4,5) $ is equal to

The contrapositive statement of the proposition $ p\to \sim q $ is

The number of straight lines which can be drawn through the point $ (-2,\,\,\,2) $ so that its distance from $ (-3,\,\,1) $ will be equal $6$ units is

The value of the integral $ \int{\frac{1}{{{e}^{2x}}+{{e}^{-2x}}}}\,\,dx $ is equal to

A force $2$ units acts along the line $ x-4=y-5. $ The moment of the force about the point $ (1,\,\,1) $ along $Z-axis$ is equal to

The three distinct points $ A(at_{1}^{2},\,2a{{t}_{1}}),\,\,B(at_{2}^{2},\,\,2a{{t}_{2}}) $ and $ C(0,\,a) $ (where $a$ is a real number) are collinear, if

The value of $k$ for which the equation $ {{x}^{2}}-4xy-{{y}^{2}}+6x+2y+k=0 $ represents a pair of straight lines is

If $ f(x)\,=kx\,-\,\cos \,x $ is monotonically increasing for all $ x\in R, $ then

The Van't Hoff factor $I$ for a compound which undergoes dissociation in one solvent and association in other solvent is respectively :

Which of the following is not due to total internal reflection?

Two radioactive nuclei $P$ and $Q$, in a given sample decay into a stable nucleus $R$. At time $t = 0$, number of $P$ species are $4\, N_0$ and that of $Q$ are $N_0$. Half-life of $P$ (for conversion to $R$) is $1$ minute where as that of $Q$ is $2$ minutes. Initially there are no nuclei of $R$ present in the sample. When number of nuclei of $P$ and $Q$ are equal, the number of nuclei of $R$ present in the sample would be

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume ($? = 1.4$ and $2^{-1.4} = 0.38$). The ratio of the final to initial pressure is

The ultimate source of energy in biosphere is

The testes in humans are situated outside the abdominal cavity inside a pouch called scrotum. The purpose served is for

Standard electrode potential of three metals $X, Y $ and $Z$ are $-1.2\,V, + 0.5\,V$ and $-3.0\,V $respectively. The reducing power of these metals will be

A chemical reaction proceeds into the following steps Step I,$\hspace15mm 2A \rightleftharpoons X$ fast Step II,$\hspace10mm X + B \rightleftharpoons Y$ slow Step III,$\hspace10mm Y + B \rightleftharpoons $ Product fast The law for the overall reaction is

By what factor does the average velocity of a gaseous molecule increase when the temperature (in kelvin) is doubled?

Phagocytosis and pinocytosis are collectively termed as

The amount of heat evolved when $500 \, cm^3$ of $0.1 \, M \, HCl$ is mixed with $200\,cm^3$ of $0.2 \, M \, NaOH$ is

Effective filtration pressure in glomerulus is caused due to...................

Which of the following conditions correctly describes the manner of determining the sex in the given example ?

Bacillus thuringiensis forms protein crystals which contain insectidical protein. This protein

The potential energy of a system increases if work is done

The following is the diagram of T.S. of Anther. Identify the parts labelled A, B, C.