List of practice Questions

In triangle ABC. if a = 3 ,b = 4,c = 6, then $\frac{\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}}{\cot A +\cot B + cot C} = $
The length of the transverse common tangent of the circles $x^2 + y^2 - 2x + 4y + 4 = 0$ and $x^2 + y^2 + 4x - 2y + 1 = 0 $ is
The number of rational terms in the binomial expansion of $\left(\sqrt[4]{5} + \sqrt[5]{4}\right)^{100} $ is
The number of three digit numbers in which $9$ appears only in one place is
The numerically greatest term in the binomial expansion of $(2a - 3b)^{19}$ and $a = \frac{1}{4}$ and $b = \frac{2}{3}$ is
If A and B are the two real values of k for which the system of equations $x + 2y + z = 1,x + 3y + 4r = k.x + 5v + 10z = k^2 $ is consistent, then $A + B = $
Let $z = x + iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z - 1}{z + i}$ is 1. then a point that lies on the locus of $P$ is
If $z_{1} = 1 -2i ; z_{2} = 1 + i$ and $z_{3 } = 3 + 4i,$ then $ \left( \frac{1}{z_{1}} + \frac{3}{z_{2}}\right) \frac{z_{3}}{z_{2}} = $
If $1 , \omega , \omega^2$ are the cube roots of unity, then $\frac{1}{1+2\omega} + \frac{1}{2+\omega } - \frac{1}{1+\omega } = $
If $\tan \, \theta = \frac{\cos 25^{\circ} + \sin 25^{\circ} }{\cos 25^{\circ} - \sin 25^{\circ} }$ and $\theta$ is in the third quadrant, then $\theta = $
$\lim_{n \to\infty} n^{-nk} \left\{\left(n+1\right) \left(n+ \frac{1}{2}\right) \left(n + \frac{1}{2^{2}}\right) ...\left(n + \frac{1}{2^{k-1}}\right)\right\}^{n} = $
$\lim_{x \to \frac{\pi}{2}} \frac{1+ \cos2x }{\cot3x \left(3^{\sin2x} - 1\right)} = $
Natality refers to�
Select the correct match :
At a particular temperature, the ratio of molar conductance to specific conductance of 0.01 M NaCl solution is
The value of rate constant of a pseudo first order reaction
Acidity of $BF_3$ can be explained on which of the following concepts ?
Which of the following, represents the variation of inductive reactance $(X_L)$ with the frequency of voltage source (v) ?
Which of the following aqueous solutions should have the highest boiling point ?
Very pure $N_2$ can be obtained by
The energy equivalent to a substance of mass 1 g is
In Karnataka, the normal domestic power supply AC is 220 V, 50 Hz. Here 220 V and 50 Hz refer to
Which of the following is true for nucleolus
Select the incorrect match :
A person may be a haemophilic, only if his mother is a carrier or colourblind. The male parent cannot pass on a sex-linked gene to his son.