Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

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

Solve the following system of equations by matrix method:
 x + y − z = 3
2x + 3y + z = 10
3x − y − 7z = 1

Solve the following system of equations by matrix method:
x + y + z = 3
2x − y + z = − 1
2x + y − 3z = − 9

Solve the following system of equations by matrix method:
6x − 12y + 25z = 4
4x + 15y − 20z = 3
2x + 18y + 15z = 10