# Maths Questions

## Find the total surface area of hemisphere of radius 10cm ?

Solution : Here radius = 10 cm We know that the surface area of hemisphere = $$3 \pi r^2$$ = $$3 \times 3.14 \times 10 \times 10$$ = 942 $$cm^2$$

## What should be the height of the conical tent ?

Question : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath. …

## What is the Equation of Director Circle of Hyperbola ?

Solution : The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. The equation to the director circle is : $$x^2+y^2$$ = $$a^2-b^2$$ If $$b^2$$ < $$a^2$$, this circle is real ; If $$b^2$$ = $$a^2$$ the radius of the circle is zero & it …

## What is the parametric equation of ellipse ?

Solution : The equation x = acos$$\theta$$ & y = bsin$$\theta$$ together represent the parametric equation of ellipse $${x_1}^2\over a^2$$ + $${y_1}^2\over b^2$$ = 1, where $$\theta$$ is a parameter. Note that if P($$\theta$$) = (acos$$\theta$$, bsin$$\theta$$) is on the ellipse then ; Q($$\theta$$) = (acos$$\theta$$, bsin$$\theta$$) is on auxilliary circle. A circle described on …

Solution : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as y = $$\sqrt{sin x + y}$$ Squaring on both sides, $$\implies$$  $$y^2$$  = sin x + y By using differentiation of infinite series, Differentiating both sides with respect to x, 2y $$dy\over … ## Find \(dy\over dx$$ where x = a{cos t + $${1\over 2} log tan^2 {t\over 2}$$} and y = a sin t

Solution : We have, x = a{cos t + $${1\over 2} log tan^2 {t\over 2}$$} and y = a sin t $$\implies$$ x = a{cos t + $${1\over 2} \times 2 log tan{t\over 2}$$} and y = a sin t $$\implies$$ x = a{cos t + {$$log tan{t\over 2}$$} and y = a sin t …

## What is the integration of $$e^x$$ ?

Solution : The integration of $$e^x$$ with respect to x is $$e^x$$ + C. Since $$d\over dx$$ $$e^x$$ = $$e^x$$ dx On integrating both sides, we get $$\int$$ $$e^x$$ dx = $$e^x$$ Hence, the integration of $$e^x$$ is $$e^x$$ + C

## Find the determinant of A = $$\begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{bmatrix}$$.

Solution : | A | = $$\begin{vmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{vmatrix}$$ By using 3×3 determinant formula, $$\implies$$ | A | = $$3\begin{vmatrix} 2 & 1 \\ 1 & -1 \end{vmatrix}$$ – $$(-2)\begin{vmatrix} 1 & 1 \\ 0 & -1 \end{vmatrix}$$ + …

## Find the determinant of $$\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}$$.

Solution : Let | A | = $$\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}$$ By using 2×2 determinant formula, we obtain | A | = ( $$sin^2x$$) – ($$-cos^2x$$) = $$sin^2x$$ + $$cos^2x$$ = 1