List of top Mathematics Questions

By using properties of determinants,show that:I\(\begin{vmatrix} x & x^2 & yz\\ y & y^2 & zx\\z&z^2&xy \end{vmatrix}\)=(x-y)(y-z)(z-x)(xy+yz+zx)

Using the property of determinants and without expanding,prove that:\(\begin{vmatrix} b+c & q+r & y+z\\ c+a & r+p & z+x\\ a+b&p+q&x+y \end{vmatrix}\)=2\(\begin{vmatrix} a & p & x\\ b & q & y\\c&r&z \end{vmatrix}\)

If A= \(\begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}\) show that A²-5A+7I=0

Show that the matrix \(B'AB\) is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Find the inverse of each of the matrices, if it exists\(\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 2 & -3\\ -1 & 2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix}\)

Find the inverse of each of the matrices, if it exists.
\(\begin{bmatrix} 3 & 10\\ 2 & 7\end{bmatrix}\)

Prove \(tan^{-1}\sqrt{x}=\frac{1}{2}cos^{-1}(\frac{1-x}{1+x}),x∈[0,1]\)

Which of the following differential equations has y=x as one of its particular solution?

Area bounded by the curve y=x³, the x-axis and the ordinates x=2 and x=1 is

Find the area bounded by curves(x-1)²+y²=1 and x²+y²=1

Area of the region bounded by the curve y²=4x, y-axis and the line y=3 is

Area lying in the first quadrant and bounded by the circle x²+y²=4 and the lines x=0 and x=2 is

Find the area of the region bounded by the curve y²=4x and the line x=3

Find the area bounded by the curve x²=4y and the line x=4y-2

\(∫_0^\frac{2}{3} \frac{dx}{4+9x^2}\) equals

\(∫_1^{\sqrt{3}}\frac{dx}{1+x^2}\)  equals

Evaluate the definite integral: \(∫^{\frac{\pi}{4}}_0 sin2xdx\)

Find the maximum area of an isosceles triangle inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with its vertex at one end of the major axis.

 

Find the intervals in which the function f given by  \(f(x)=x^3+\frac{1}{x^3},x≠0\) is (i)increasing (ii)decreasing

Show that the normal at any point θ to the curve \(x=acosθ+aθsinθ,y=asinθ-aθcosθ\) is at a constant distance from the origin.

Find the equation of the normal to curve \(y^2=4x\) at the point (1,2)

Using differentials,find the approximate value of each of the following (a) \((\frac{17}{81})^\frac{1}{4}\) (b) \((33)^{-\frac{1}{5}}\)