List of practice Questions

If the system of equations $2x + 3y+5 = 0$, $x + ky + 5 = 0$, $kx - 12y - 14 = 0$ has non-trivial solution, then the value of $k$ is
If the trivial solution is the only solution of the system of equations $x - ky + z = 0$ $kx + 3y - kz = 0$ $3x +y - z = 0$ then the set of all values of k is :
If the value of a third order determinant is 11, then the value of the square of the determinant formed by the co-factors will be
If $\begin{vmatrix}y+z&x-z&x-y\\ y-z &z+x&y-x\\ z-y &z-x&x+y\end{vmatrix}= kxyz $ then the value of k is :
If (x + 9) = 0 is a factor of $\begin{vmatrix}x&3&7\\ 2&x&2\\ 7&6&x\end{vmatrix} = 0 $ , then the other factor is:
If x is a positive integer, then $\begin{vmatrix} x! & (x+1)! & (x+2)! \\[0.3em] (x+1)! & (x+2)! & (x+3)! \\[0.3em] (x+2)! & (x+3)! &(x+4)! \end{vmatrix}$ is equal to
Let A be a $3 \times 3$ matrix such that $A\begin{bmatrix}1&2&3\\ 0&2&3\\ 0&1&1\end{bmatrix} = \begin{bmatrix}0&0&1\\ 1&0&0\\ 0&1&0\end{bmatrix} $ Then $A^{-1}$ is :
The solution set of the equation $\begin{vmatrix}1&4&20\\ 1&-2&5\\ 1&2x&5x^{2}\end{vmatrix} = 0$ is
The solution set of the inequality $37 - (3x + 5) \ge 9x - 8 (x - 3)$ is
The solution set of the inequality $ { 5^{x + 2} } > \left( \frac{1}{25} \right)^{ {1 /x}}$ is
The solution set of the inequality $\left|9^{x}-3^{x+1}-15\right|< 2.9^{x}-3^{x}$ is
The value of the determinant $ \left| \begin{matrix} 15! & 16! & 17! \\ 16! & 17! & 18! \\ 17! & 18! & 19! \\ \end{matrix} \right| $ is equal to
$\begin{vmatrix}1&1&1\\ ^{n}C_{1}&^{n+1}C_{1}&^{n+2}C_{1}\\ ^{n}C_{2}&^{n+1}C_{2}&^{n+2}C_{2}\end{vmatrix} = $
Write the cofactors of each element of the first column of the following matrices. $A=\left[\begin{matrix}4&-1&2\\ 1&-3&2\\ 3&5&2\end{matrix}\right]$
$1$ volt is equivalent to
A $16 \,pF$ capacitor is connected to $70\, V$ supply. The amount of electric energy stored in the capacitor is
A ball of mass 1 g and charge $10^{-8}$ C moves from a point A, where potential is 600 V to the point B where potential is zero. Velocity of the ball at the point B is 20 $cms^{ -1}$. The velocity of the ball at the point A will be
A bullet of mass $2g$ is having a charge of $ 2\mu C $ . Through what potential difference must it be accelerated, starting from rest, to acquire a speed of $10 \,m/s$?
A capacitor having capacity of $2.0 \,\mu$ F is charged to $200 \,V$ and then the plates of the capacitor are connected to a resistance wire. The heat produced in joule will be
A capacitor is connected to .a cell of emf E having someJntemal resistance r. The potential difference across the:
A capacitor of $4\, \mu F$ is connected as shown in the circuit. The internal resistance of the battery is $0.5\,\Omega$ The amount of charge on the capacitor plates will be
A capacitor of capacitance $700\, pF$ is charged by $100\, V$ battery. The electrostatic energy stored by the capacitor is
A capacitor of capacity $C_1$ is charged by connecting it across a battery of e.m.f. $V_0$. The battery is then removed and the capacitor is connected in parallel with an uncharged capacitor of capacity $C_2$.The potential difference across this combination is
A certain charge $Q$ is divided at first into two parts, $q$ and $Q - q$. Later on the charges are placed at a certain distance. If the force of interaction between two charges is maximum, then $Q/q$ =
A charge of $10^{-9} C$ is placed on each of the $64$ identical drops of radius $2\, cm$. They are then combined to form a bigger drop. Its potential will be