Amount of oxalic acid present in a solution can be determined by its titration with $$KMn{O}_4$$ solution in the presence of $$H_{2}S{O}_4.$$ The titration gives unsatisfactory result when carried out in the presence of $$HCl,$$ because $$HCl$$ :

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being :

The bond dissociation energy of B - F in BF3 is 646 kJ mol-1 whereas that of C - F in CF4 is 515 kj mol-1. The correct reason for higher B - F bond dissociation energy as compared to that of C - F is

Which of the following pair of species have the same bond order?

$$\alpha$$-D-(+)-glucose and $$\beta$$-D-(+)-glucose are

Let A = \left| {\matrix{ 5 & {5\alpha } & \alpha \cr 0 & \alpha & {5\alpha } \cr 0 & 0 & 5 \cr } } \right|. If $$\left|A^2\right|=25,$$ then $$\left|\alpha \right|$$ equals

If D = \left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + x} & 1 \cr 1 & 1 & {1 + y} \cr } } \right| for $$x\ne 0,y\ne 0,$$ then $$D$$ is :

Two aeroplanes $$\mathrm{I}$$ and $$\mathrm{I}$$$$\mathrm{I}$$ bomb a target in succession. The probabilities of $$\mathrm{I}$$ and $$\mathrm{I}$$$$\mathrm{I}$$ scoring a hit correctly are $$0.3$$ and $$0.2,$$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is :

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $$9$$ twice is :

The differential equation of all circles passing through the origin and having their centres on the $$x$$-axis is :

Let $$P=\left(-1,0\right),Q=\left(0,0\right)$$ and $$R=\left(3,3\sqrt{3}\right)$$ be three point. The equation of the bisector of the angle $$PQR$$ is :

If one of the lines of $$m{y}^2+\left(1-m^2\right)xy-m{x}^2=0$$ is a bisector of angle between the lines $$xy=0,$$ then $$m$$ is :

Let A $$\left(h,k\right)$$, B$$\left(1,1\right)$$ and C $$(2,1)$$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is $$1$$ square unit, then the set of values which $${}^{\prime }{k}^{\prime }$$ can take is given by :

A tower stands at the centre of a circular park. $$A$$ and $$B$$ are two points on the boundary of the park such that $$AB(=a)$$ subtends an angle of $$60^{\circ }$$ at the foot of the tower, and the angle of elevation of the top of the tower from $$A$$ or $$B$$ is $$30^{\circ }$$. The height of the tower is :

The sum of the series $${}^{20}{C}_0-{}^{20}{C}_1+{}^{20}{C}_2-{}^{20}{C}_3+.....-.....+{}^{20}{C}_{10}$$ is

In the binomial expansion of $${\left(a-b\right)}^n,n\ge 5,$$ the sum of $$5^{th}$$ and $$6^{th}$$ terms is zero, then $$a/b$$ equals

\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}} equals

The largest interval lying in \left( { - {\pi \over 2},{\pi \over 2}} \right) for which the function f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {{x \over 2} - 1} \right)$$+\log \left(\cos x\right)$$, is defined, is

The equation of a tangent to the parabola $$y^2=8x$$ is $$y=x+2$$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is :

Let F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right), where f\left( x \right) = \int\limits_l^x {{{\log t} \over {1 + t}}dt,} Then $$F(e)$$ equals