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Question 6

Derive the formula for the curved surface area and total surface area of the frustum of cone.

ABC is an isosceles triangle with AB = AC = 4cm . A circle through B touches side AC at its middle point D and intersects side AB in point P. Find the value of AP

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the volume of the toy.

The vertices of a ΔABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that. Calculate the area of the ΔADE and compare it with the area of ΔABC. (Recall Converse of basic proportionality theorem and Theorem 6.6 related to

ratio of areas of two similar triangles)

In the given figure, a circle touches the side BC of $\Delta$ABC at P and AB and AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of $\Delta$ABC.

The centroid of a triangle whose vertices are (3,0), (7,0) and (8,6) is

$\frac{\text{sec}{17}^{\circ }}{\text{cosec}{73}^{\circ }}+\frac{\text{tan}{68}^{\circ }}{\text{cot}{22}^{\circ }}-[{\text{cos}}^2{44}^{\circ }+{\text{cos}}^2{46}^{\circ }]=$___.

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish. the work.

If A = $\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right],B=\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$, and $C=\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]$, find AB - 5C.

Find the zero of the polynomial $3x+2$.

The value of x which satisfies following pair of linear equations is:

(i) x + 2y = -2

(ii) x - 2y = 12

AD is the median of △ ABC and DE is the median of △ ABD. If area of △ BED = 2.5 sq cm, then the area of △ ABC = ____ sq cm.

Sum of two numbers is 135 and their H.C.F is 27. If their L.C.M is 162. Find the number.

Find the value of ${\theta }_1+{\theta }_2+{\theta }_3$ in each of the following

(1) 2 sin 2${\theta }_1$ = $\sqrt{3}$

(2) 2 cos 3${\theta }_2$ = 1

(3) $\sqrt{3}$tan 2${\theta }_3$ - 3 = 0

The ratio of the area enclosed by the curve $a{x}^2+b{y}^2=ab;a,b>0$ divided by the straight line $y=mx,m\ne 0,$ is

If ∆ABC is right angle at C, find the value of cot(A+B)

Construct a tangent to a circle of radius 5.5 cm from a point 3.5 cm away from it

The innder diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.

From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be $\alpha$ and $\beta$. If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is $\frac{h(tan\alpha +tan\beta )}{tan\alpha tan\beta }$ metres. [3 MARKS]

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, howmany terms are there and what is their sum?

The points (3,-4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.

Q1. if p(x)=x³-13x²+48x-55 has quotient x-5 and remainder 5-4x find diviso

Which of the following pair of rational numbers are smaller than -5?

State the SSS-criterion for similarity of triangles.

The equation (m being real), $m{x}^2+2x+m=0$ has two distinct roots if -

Which of the following sequence are in G.P?

(a) 5, 10, 20, ……..

(b) 1, −1, 1, −1, …….

(c) 2, 4, 6, 8, ………

(d) 1, 4, 9, 16, ……….