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The two parallel sides and the distance between them are in the ratio 3 : 4 : 2. If the area of the trapezium is 175 cm2; find its height.

In what time will Rs 64000 amount to Rs 68921 at 5% p.a, interest being compounded half-yearly?

In general, if a natural number m can be expressed as $n^2$, where n is also a natural number, then m is a __________.

What should be added to $\frac{-8}{9}$ to get $\frac{-1}{6}$

A cuboid of length 10cm and breadth 5 cm is melted and cast into identical cubes of side 2cm. What would have been the height of the cuboid if the number of cubes cast = 50.

Each angle of an equilateral triangle measures ________ .

Factorise:
$a^8-2a^4{b}^4+b^8$

An isosceles trapezium has an area of $36c{m}^2$, the parallel sides are $12cm$ and $6cm$ respectively. The perimeter of the trapezium is

If U = {a, e, d}, A = {a, e} and B’ = { a, d}, then A’ $\cap$ B’ = ___.

Study the pie – chart carefully to answer the following questions.
The pie-chart shows the percentage of students studying different specialisations in a management institute. The total number of students is 4500.

Ratio of men to women in each specialisation
$\begin{array}{ccc}\text{Specialisation}& \text{Men}& \text{Women}\\ \text{HR}& \text{2}& \text{3}\\ \text{Marketing}& \text{7}& \text{5}\\ \text{International Business}& \text{5}& \text{1}\\ \text{Banking}& \text{17}& \text{10}\\ \text{IT}& \text{1}& \text{2}\\ \text{Finance}& \text{5}& \text{4}\end{array}$

(A) What is the total number of men studying in the institute?
(B) The number of women studying Marketing is approximately what percent of the total number of students in the institute?

Question 91

The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also, find its weight if the metal weighs 8 g per $c{m}^3$.

Length of tape required to cover the edges of a semi-circular disc of radius $10cm$ is

(a) $62.8cm$
(b) $51.4cm$
(c) $31.4cm$
(d) $15.7cm$

From the given ogive, which of the following can be determined?

A path of uniform width, 3 m, runs around the outside of a square field of side 21 m. Find the area of the path.

Question 28

Fill in the blanks to make the statements true.

The square of 500 will have ___ zeroes.

The additive inverse of $\frac{3}{5}$ is

V = 3 + 9t if t < 9

V= 8 - 2t if t =10

Find the value of v (m/s) when t = 10

Construct a triangle ABC in which BC is 5 cm, Angle B is ${120}^{\circ }$ and AB+AC=17cm [3 MARKS]

Opposite sides are not equal in

Which of the following correctly represents the units digit of any perfect square number.

Divide

i) $48x^4$ by $12x^{2}y$

ii) $24a^2{b}^{2}c$ by $4ab$ [2 MARKS]

There is a box containing 15 ping pong balls of 3 different colors red, green and blue. There are 7 red balls and 3 green balls. What is the probability of getting a blue ball in the first attempt?

When $x^4+x^3-2x^2+x+1$ is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

What is the error in the area of a rectangle?

Given: L=5 $\pm$ 1 units

B= 4$\pm$2 units

Observe the pictograph. Find which of the following is the most favorite colour amongst the students?

Find the area of a trapezium if the distance between its parallel sides is 26 cm and one of the parallel sides is 84 cm, the other parallel side is half of the perpendicular distance between the parallel sides.

A man borrowed $Rs.3125$ on compound interest which amounted to $Rs.4500$ in $2$ years. What was the rate of interest per annum?

If the sides of ractangle are 8 cm and 15 cm, then the length of its diagonal is

A line graph can be :

Draw the frequency polygon representing the following frequency distribution.

$\begin{array}{ccccccc}\text{Class interval}& 30-34& 35-39& 40-44& 45-49& 50-54& 55-59\\ \text{Frequency}& 12& 16& 20& 8& 10& 4\end{array}$
[4 MARKS]

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}$

(ii) $\frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9}$

(iii) $\frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3}$

(iv) $\frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21}$

Find the distance travelled with the following pairs of monomials as their speed and time respectively:

$\left(i\right)(25a^2{b}^2,50b)$

$\left(ii\right)(12abc,23cde)$

$\left(iii\right)(5c^2{d}^2,4a^2{b}^2)$ [3 MARKS]

The diagonals of a rhombus are 18 cm and 24 cm. Find ;

(i) its area

(ii) length of its sides

(iii) its perimeter

Question 26

The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 sq cm. The volume of the solid (in cubic cm) is
a) 192
b) 384
c) 480
d) 2592

1. 14

Write the prime factor form of the following:
(i) 70
(ii) 105
(iii) 150
(iv) 810 [3 MARKS]

Vignesh has two angles, $\angle$A and $\angle$B. He arranged those two angles on a paper such that they are supplementary. Which of the following arrangements did he make?

The point (5, -2) and (-2, -5) lie in?

Find the square root of each of the following correct to two decimal places :

(i) $3\frac{4}{5}$ (ii) $6\frac{7}{8}$

Statement 1: Histograms are used to show the distribution of variables.

Statement 2: Bar graphs are used to compare variables.