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The cost of a machine is supposed to depreciate each year by 12% of its value at the beginning of the year. If the machine is valued at Rs. 44,000 at the beginning of 2008, find its value :

(i) at the end of 2009.

(ii) at the beginning of 2007.

Which of these cannot be the area of a right-angled triangle if the hypotenuse of the triangle is 13 m and one other side is 5 m?

Which of the following figures include triangles/parallelograms on the same base and between the same parallel lines?

Construct an angle of ${67.5}^{\circ }$ by using the ruler and compasses.

The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motor cyclilst for riding.

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 45 cm, find the area between two consecutive ribs of the umbrella.

At what rate per cent will a sum of Rs. 4,000 yield Rs. 1,324 as compound interest in 3 years?

Determine the point on the graph of the linear equation 2x+5y=19 whose ordinate is 1½ times of its abscissa

The price of a table and a chair together is 2500 rupees. The price of 3 tables and 4 chairs of this kind is 8000 rupees. What is the price of each?

In the given figure if AB || EF, $\angle ABC={70}^{\circ }$ and $\angle EFD={40}^{\circ }$, then find x.

Statement 1: In an equilateral triangle, the heights onto all the sides are equal.
Statement 2: The base lengths are also equal in an equilateral triangle.

There are 6 friends A,B,C,D,E and F. B does not want to sit next to D,E or F and E does not want to sit next to A,B or C. In how many ways can you arrange these 6 people around a circular table?

Question 119

Find the value of n.

$\frac{2^n\times 2^6}{2^{-3}}=2^{18}$

The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of the shorter side.

ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.

Express each of the following decimals in the form $\frac{p}{q}$ :

$\left(i\right)0.39$

$\left(ii\right)0.750$

$\left(iii\right)2.15$

$\left(iv\right)7.010$

$\left(v\right)9.90$

$\left(vi\right)1.0001$

Find the points of trisection of the line segment joining the points A(-4, 3) and B (2, -1).

If a tin of paint covers an area of 100 sq.metres, how many tins would you need to cover a square wall of length 10 m?

If $A=\left[\begin{array}{ccc}1& 0& 1\\ 0& 2& 0\\ 1& -1& 4\end{array}\right],A=B+C,B=B^T,C=-C^T$, then $C$ is equal to

Which of the following fractions can be expressed as recurring decimal ?

The diagonals of a parallelogram PQRS intersect at O. If ∠QOR = 90o and ∠QSR = 50o, then ∠ORS is:

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?

The factorisation of $a^6+b^6$ is equal to .

A hemisphere lead of radius 9 cm is cast into a right circular cone of height 72 cm. The radius of the base of cone is

Write the following in decimal form and say what kind of decimal expansion each has:

(i) (ii) (iii)

(iv) (v) (vi)

If ABCD is a cyclic quadrilateral in which $AD||BC$. Prove that $\angle B=\angle C$.

Find the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.

Which of the following is not a fraction equivalent to $\frac{21}{27}$?​