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The value of
$4[1–si{n}^2\theta ][1+ta{n}^2\theta ]$

If $x+y+z=0$
then $x^3+y^3+z^3$=___?

Find the area of the shaded region (in $c{m}^2$) as shown in figure of the two concentric circles with centre O and radius 7 $cm$ and 14 $cm$ respectively. Given $\angle$AOC = ${40}^{\circ }$.

(use $\pi$ = $\frac{22}{7}$)

Question 92 (xxviii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$x^4-y^4+x^2-y^2$

Question 5

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.

Question 57

Selling price of 9 articles is equal to the cost price of 15 articles. In this transaction, there is profit of $66\frac{2}{3}\%$

Question 1

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Question 60



State whether the following statement is True or False.



The model of a ship shown is of height 3.5 cm. The actual height of the ship is 210 cm if the scale chosen is 1 : 60.

Evaluate each of the following

$cose{c}^3{30}^{o}cos{60}^{o}ta{n}^3{45}^{o}si{n}^2{90}^{o}se{c}^2{45}^{o}cot{30}^o$

In the construction of mean proportional with 2 line segments, initially, we construct a ray which is greater than the ___________ of the given line segments.

If cos B = $\frac{3}{5}$ and (A + B) = ${90}^o$, find the value of sin A.

In $△ABC$ , $\angle B={90}^{\circ }$.

If $cotA=\frac{1}{\sqrt{3}}$ then,

find $\frac{cosA}{sinA}+\frac{sinC}{cosC}$

In the given figure AB = 8 cm. M is the midpoint of AB.

Semi circles are drawn on AB, AM and MB as diameter. A circle with centre ‘O’ touches all three semi circles as shown. Prove that the radius of this circle is .

Find x and y given

Fill
in the blanks:

(i) A
tangent to a circle intersects it in _______ point (s).

(ii) A
line intersecting a circle in two points is called a __________.

(iii) A
circle can have __________ parallel tangents at the most.

(iv) The
common point of a tangent to a circle and the circle is called ____.

The inner radius of a pipe is 2.1 cm.How much water can 12 m of this pipe hold?

Question 103

Solve the following:

There are 40 passengers in a bus, some with Rs. 3 tickets and remaining with Rs. 10 tickets. The total collection from these passengers is Rs. 295. Find how many passengers have tickets worth Rs. 3?

Sam is looking at the roof of the adjacent building from top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of the tip of other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building?

ABCD is a cyclic quadilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ }$ and $\angle BAC={30}^{\circ }$, find $\angle BCD$. Further if $AB=BC,$ find $\angle ECD$.

Find the roots of the following quadratic equation by factorisation method.

$9x^2-10x-8=0$

Find the least count of a vernier caliper whose 50 vernier scale divisions match with 49 main scale divisions?

Given: least count of main scale is 1 mm.

If $\overrightarrow{a}=2\hat{i}+3\hat{j}+4\hat{k}$ and $\overrightarrow{b}=4\hat{i}+3\hat{j}+2\hat{k}$, find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$.

The equation $x^2+px-q=0$ has one root as a square root of the other.
If $p^3+q^2=q(1+kp)$, find the value of k.

If the sum to n terms of an AP is given by $S_n$ = (11 - a + b)n + (a - b) $n^2$ , then the first term is _______ .

Find

(a)

(b)

(c)

Solve each of the following systems of equations by using the method of cross multiplication:

$3x+2y+25=0$,

$2x+y+10=0.$