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Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1m and base radius 3.5cm? (Take π=22/7)

A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

The area (in $\text{sq.units}$) enclosed between the curve $4x^2+9y^2=36$ and $2x+3y\ge 6$ is

An aeroplane at an altitude of 250m observes the angle of depression of two boats on opposite banks of a river to be ${45}^o$ and ${60}^o$ respectively. Find width of the river.
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C divides AB in the ratio 5 : 4. If A is (2, 7 ) and B(-3,-8) find the coordinators of C. Find the equation of the line perpendicular to AB passing through C.

If the quadratic equation $12x^2–2bx+9=0$ has no real root, then which of the following is always true?

Find 'X' in the image if the volume of the cylinder and the sphere are equal.

Find the condition that the point $P(x,y)$ may lie on the line joining (3, 4) and (-5, -6).

If P(a,b) divides B(h,k) and C(l,m) such that $a$ = $\frac{pl+qh}{p+q}$. Find the ratio in which P divides BC.

P, Q, R are consecutive integers. Which of the following is true?

The angle of elevation of the top of a vertical tower from a point on the ground is ${60}^{\circ }$. From another point 10 m vertically above the first, its angle of elevation is ${30}^{\circ }$ . Find the height of the tower.

Point out the mistakes in the following table.

$\begin{array}{ccccc}\text{Literate}& \text{Less than 20}& 20-30& 30-40& \text{40 and above}\\ \text{Male}& & & & \\ \text{Female}& & & & \end{array}$

Find the L.C.M. of the following expressions by division method.

a³ − 3a² − 10a + 24 and a³ − 2a² − 9a + 18

1. 5

The area of a triangle is 5 square units. Two of its vertices are (2, 1) and (3, -2) and the third vertex lies on y = x + 3, the third vertex is

A hollow cylindrical pipe is $210cm$ long. Its outer and inner diameters are $10cm$ and $6cm$ respectively. Find the volume of the copper used in making the pipe ___

In Fig.4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

OR
In Fig.5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

Question 92 (xiii)

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

$\frac{x^2}{8}-\frac{y^2}{18}$

In a cyclic quadrilateral ABCD,A=(x+1)° , B=(y+8)°,C=(3y+23)°,,D=(4x+12)° find all the angles

If S is the focus of a parabola and PQ is any focal chord, then the semi-latus rectum of the parabola is

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is ${30}^{\circ }$. Find the height of the tower. [2 MARKS]

When 19779 and 17997 are divided by a certain number they leave the same reminder. Find the largest such divisor and reminder. How many such divisor are there?