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Question 8(a)
A cement company earns a profit of Rs 8 per bag of white cements old and a loss of Rs 5 per bag of grey cements old.
The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

The ⏊ to a chord from the centre of a circle divides the chord in the ratio:

$1\le |x-2|\le 3$

Number of tangents from a point lying inside the circle is

ABC is the right-angled triangle with $\angle$ABC=${90}^{\circ }$. The centre of the circle passing through ABC lies on _______.

Solve, using cross-multiplication

$4x-y=55y-4x=7$

If in a group of goats and hens the number of legs is 24 more than the twice the number of heads, then the number of goats in the group is

The variance of first n natural numbers is $\frac{n^2-1}{12}$.

A boy of height 150 cm is walking away from the base of a lamp-post at a speed of 1.5 m/s. If the lamp is 4.5 m above the ground, find the length of his shadow after 6 seconds.

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Then, select the statements that are true.

In Fig., a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:

If cos A= 2 sin A, then the value of cosec A is

The line 4 – 3 + 12 = 0 meets the -axis at A. Write down the co-ordinates of A. Determine the equation of the line passing through A and perpendicular to 4 – 3 + 12 = 0.

The sum of the $4^{th}$ and the $8^{th}$ terms of an A. P . is 24 and the sum of the $6^{th}$ and the ${10}^{th}$ terms of the same A. P. is 34. Find the first three terms of the A. P.

P(3, 3), Q(7, 6) and R(3, 6) are the coordinates of a triangle. A, B and C are the reflection points of P, Q and R respectively about Y = 0. The area of the triangle formed by the points B, C and D(3, -9) is ___.

At the foot of a mountain the elevation of its summit is ${45}^{\circ };$ after ascending 1000 m towards the mountain up a slope of ${30}^{\circ }$ inclination, the elevation is found to be ${60}^{\circ }$. Find the height of the mountain.

For accurate prediction of events and presenting statistics, select the most important information required.

If the points (a,1), (1,-1) and (11,4) are collinear then the value of a is

The figure shown below depicts the distance travelled by a body as a function of time.

The average speed and maximum speed between 0 and 20 s are:

From which point shown below can we draw two tangents to the following circle?

P is a point outside the circle, R inside the circle and Q lies on the circle.

In the given figure, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.

Find the value of $\frac{4}{3}ta{n}^2{60}^{\circ }+3co{s}^2{30}^{\circ }-2se{c}^2{30}^{\circ }-\frac{3}{4}co{t}^2{60}^{\circ }$

Angle ABC = 50${}^{\circ }$ and BA = BC = 5 cm. The mid points of BA and BC are M and N respectively. Draw the locus of a point which is equidistant from BA and BC, 2.5 cm from M and 2.5 cm from N. Mark the point P, which is 4 cm from both M and N, and equidistant from BA and BC. Then the length of PC is

(a) Use the information given in the adjoining histogram to construct a frequency table.

(b) Use this table to construct an ogive

As CIRCLE is to RICELC, so also SQUARE is to:

The ratio of volume to the total surface area of a solid sphere is 8. Find its radius.

The difference of square of two no. Is 180. The square of the smaller no. Is 8 times the larger no. Find the two no.

Construct a $\Delta ABC$ in which AB = 6 cm, $\angle A={30}^{\circ }and\angle B={60}^{\circ }.$ Construct another $\Delta A{B}^{\prime }{C}^{\prime }\text{similar to}\Delta ABC$ with base AB' = 8 cm.

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$4x^2-4x-3$

There are 20 tickets numbered as 1, 2, 3, ..., 20 respectively. oNe ticket is drawn at random. What is the probability that the number on the ticket drawn is a multiple of 5 ?
(a) $\frac{1}{4}$ (b) $\frac{1}{5}$ (c) $\frac{2}{5}$ $\frac{3}{10}$

A right angled triangle whose sides are $3cm,4cm$ and $5cm$ is revolved about the sides containing the right angle in two days. Find the difference in volumes of the two cones so formed. Also,find their curved surfaces.

The volume of a hemi-sphere is 2425$\frac{1}{2}c{m}^3$. Find its curved surface area.

A tree 10(2+$\sqrt{3}$) metres high is broken by the wind at a height 10$\sqrt{3}$ metres from its root in such a way that top struck the ground at certain angle and horizontal distance from the root of the tree to the point where the top meets the ground is 10 m. Find the angle of elevation made by the top of the tree with the ground.

In a quadratic equation ax² + bx +c , if D = 0, then find the roots,

Vikram travels 4 m east, take a right turn and again travels for 3 m. How far is he from the starting point?

The algebraic expression for sequence 1 + (1 + 5), 2 + (2 + 5), 3 + (3 + 5), ... is

Find the equation of the perpendicular bisector of the line segment joining the points $(3,4)$ and $(-1,2)$.

In a single throw of a die, find the probability of getting (a) a number greater than 2 (b) a prime number (c) a composite number.

The number of bottles of distilled water filled by ( – 5) machines in (2 + 3) hours and the number of similar bottles filled by ( – 2) machines in ( – 5) hours are in the ratio 7 : 3 find .

On dividing $x^3-3x^2+x+2$ by a polynomial g(x), the quotient and remainder were $x-2$ and $-2x+4$, respectively. Find g(x).

A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [Approximately]

Sum of digits of two digits number is 8. The digit in tens place is thrice the digit in unit place. Find the digit.

There is a circular path around a sport field. Sonia takes 18min to drive one around of the field, while Ravi takes 12min for the same. Suppose they both start at the same point at the same time, and go in the same direction, after how minutes will they meet again at the starting point?

In the equation 6${sin}^2$$\theta$ - 11sin$\theta$ + 4 = 0, show that one value of $\theta$ is absurd and find the other value.