PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.

Let 
\[f : R \to R\]  be given by \[f\left( x \right) = x^2 - 3\] Then, \[f^{- 1}\] is given by 

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Let f : R → R be given by f(x) = tanx. Then, f^-1(1) is

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Let f : R→ R be defined as, f(x) =  \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\] 

Then, find f( \[-\]1) + f(2) + f(4)

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Let A = {1, 2, ... , n} and B = {a, b}. Then the number of subjections from A into B is

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If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

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If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is

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Let f : R  \[-\] \[\left\{ \frac{3}{5} \right\}\] \[\to\]  R be defined by f(x) = \[\frac{3x + 2}{5x - 3}\] Then,

If \[A = \begin{vmatrix}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{vmatrix}\]  and C_ij is cofactor of a_ij in A, then value of |A| is given 

Discuss the continuity and differentiability of the 

Write the adjoint of the matrix \[A = \begin{bmatrix}- 3 & 4 \\ 7 & - 2\end{bmatrix} .\]

If C_ij is the cofactor of the element a_ij of the matrix \[A = \begin{bmatrix}2 & - 3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & - 7\end{bmatrix}\], then write the value of a₃₂C₃₂.

Write \[A^{- 1}\text{ for }A = \begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]

The general solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x}\] is

The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is

The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by

The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is

The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is