List of practice Questions

Suppose $\triangle ABC$ is an isosceles triangle with $\angle C = 90^\circ$, $A = (2, 3)$ and $B = (4, 5)$. Then the centroid of the triangle is
If the mean of the data $p,6,6,7,8,11,15,16$ is 3 times $p$, then the mean deviation of the data from its mean is
In a box, there are 8 red, 7 blue, and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is
Five-digit numbers are formed using digits 1,2,3,4,5 without repetition. Then the probability that the randomly chosen number is divisible by 4 is
If $4 + 6(e^{2x} + 1)\tanh x = 11\cosh x + 11\sinh x$, then $x =$
If $a = 2$, $b = 3$, $c = 4$ in a triangle $ABC$, then $\cos C =$
In a triangle $ABC$, $(b + c)\cos A + (c + a)\cos B + (a + b)\cos C =$
In how many ways can the letters of the word “MULTIPLE” be arranged keeping the position of the vowels fixed?
If $\dfrac{13x + 43}{2x^2 + 17x + 30} = \dfrac{A}{2x + 5} + \dfrac{B}{x + 6}$, then $A^2 + B^2 = $
In a triangle $ABC$, $\left(\tan \dfrac{A}{2} \tan \dfrac{B}{2} \tan \dfrac{C}{2} \right)^2 \le$
The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is
$1 + \sec^2 x \cdot \sin^2 x = $
If $e^{i\theta = \cos\theta + i\sin\theta$ then}
$\sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{2^n} \div \sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{5^n} =$
The sum of the real roots of the equation $|x - 2|^2 + |x - 2| - 2 = 0$ is
If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is
If $A = \begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix}$, then $(A^T)^2 + (12A)^T = $
If $A = \begin{bmatrix} 1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1 \end{bmatrix}$ is such that $A^2 = I$, then
Let $A = \begin{bmatrix} -2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1 \end{bmatrix}$. If the roots of the equation $\det A = 0$ are $l, m$ then $l^3 - m^3 =$
Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is
$\left\{ x \in \mathbb{R} \,\middle|\, \frac{\sqrt{|x^2 - 2|x| - 8}}{\log(2 - x - x^2)} \text{ is a real number} \right\} =$
The domain of the real valued function $f(x) = \sin\left(\log\left(\frac{\sqrt{4 - x^2}}{1 - x}\right)\right)$ is
The correct statements with respect to dialysis of colloidal solution are:
I. Colloidal particles can pass through the membrane
II. Animal bladder can be used as membrane
III. Cellophane is not used as membrane
IV. Ions and small molecules can diffuse through membrane into water
The outer electronic configuration of \(\text{Pd}^{2+}\) is
The IUPAC name of the following complex is \([Co(NH_2CH_2CH_2NH_2)_2Br_2]Br\)
The molality and molarity of a solution of glucose in water which is labeled as 10% (w/w) are respectively (density of solution = 1.2 g/mL)