List of top Higher Mathematics Questions

Show that the function given by \( f(x) = 12x - 3 \) is increasing on \( R \).
\( f : x \to y \) is an onto function then range of \( f = y \).
If \( A = [a_{ij}]_{m \times n} \) and \( B = [b_{ij}]_{j \times p} \), then order of \( AB \) will be \( m \times p \).
Integrating factor of differential equation \( \frac{dy}{dx} - y = \cos x \) is \( e^{-x} \).
Angle between vectors \( \vec{a} = \hat{i} + \hat{j} - \hat{k} \) and \( \vec{b} = \hat{i} - \hat{j} + \hat{k} \) is 60°.
\( \tan^{-1} 1/2 + \tan^{-1} 1/3 = \tan^{-1} 1/5 \).
What is trivial relation?
Find the principal value of \( \sin^{-1} \left( \frac{1}{\sqrt{2}} \right)\)
\( \int e^x [f(x) + f'(x)] dx \)= \(\underline{\hspace{2cm}}\)
Find magnitude of the vector \( \hat{i} + \hat{j} + \hat{k} \)
If \( A \) and \( B \) are two independent events with \( P(A) = 0.3 \) and \( P(B) = 0.4 \), then find \( P(B|A) \)
The number of arbitrary constants in the particular solution of a differential equation of third order are \(\underline{\hspace{2cm}}\)
The direction cosines of \( x \), \( y \), and \( z \)-axis are \(\underline{\hspace{2cm}}\) respectively.
\( \int \left( \sin^{-1} x + \cos^{-1} x \right) dx\) = \(\underline{\hspace{2cm}}\)
The vector sum of the three sides of a triangle taken in order is \(\underline{\hspace{2cm}}\)
Rate of change of area of circle per second with respect to its radius \( r \) when \( r = 5 \, \text{cm} \) will be \(\underline{\hspace{2cm}}\)
\( \tan^{-1} \sqrt{3} - \sec^{-1}(-2) \) is equal to:
In the function \( f : \mathbb{R} \rightarrow \mathbb{R} \), given by \( f(x) = 5x \):