Arts (English Medium) Class 12 - CBSE Question Bank Solutions

There are two values of a which makes the determinant  \[∆ = \begin{vmatrix}1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2a\end{vmatrix}\]  equal to 86. The sum of these two values is

If \[\begin{vmatrix}a & p & x \\ b & q & y \\ c & r & z\end{vmatrix} = 16\] , then the value of \[\begin{vmatrix}p + x & a + x & a + p \\ q + y & b + y & b + q \\ r + z & c + z & c + r\end{vmatrix}\] is

The value of \[\begin{vmatrix}1 & 1 & 1 \\ {}^n C_1 & {}^{n + 2} C_1 & {}^{n + 4} C_1 \\ {}^n C_2 & {}^{n + 2} C_2 & {}^{n + 4} C_2\end{vmatrix}\] is

Show that the derivative of the function f given by 

If for the function 

\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]

If  \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\] 

Examine the differentialibilty of the function f defined by

\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text {  if } 0 \leq x \leq 1\end{array}\end{cases}\] 

If  \[\lim_{x \to c} \frac{f\left( x \right) - f\left( c \right)}{x - c}\]  exists finitely, write the value of  \[\lim_{x \to c} f\left( x \right)\]

Let \[f\left( x \right)\begin{cases}a x^2 + 1, & x > 1 \\ x + 1/2, & x \leq 1\end{cases}\] . Then, f (x) is derivable at x = 1, if 

Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0

Solve the following system of equations by matrix method:
 5x + 2y = 3
 3x + 2y = 5

Solve the following system of equations by matrix method:
3x + 4y − 5 = 0
x − y + 3 = 0

Solve the following system of equations by matrix method:
3x + y = 19
3x − y = 23

Solve the following system of equations by matrix method:
3x + 7y = 4
x + 2y = −1

Solve the following system of equations by matrix method:
3x + y = 7
5x + 3y = 12