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Question 4

In the given figure, $\angle ABC={69}^{\circ },\angle ACB={31}^{\circ }.Find\angle BDC$

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see figure 10.25).

The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

The components of a segment of a circle are:

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In the given figure OA and OB are opposite rays:

i) If x = 75${}^{\circ }$, then what is the value of y?

ii) If y = 110${}^{\circ }$, then what is the value of x?

Evaluate :

$3\cos {80}^{\circ }cosec{10}^{\circ }+2\sin {59}^{\circ }\sec {31}^{\circ }$

A metal crystallises into two cubic phases, face-centred cubic(FCC) and body-centred cubic(BCC), whose unit cell lenghts are $3.5\stackrel{\circ }{\text{A}}\text{and}3.0\stackrel{\circ }{\text{A}}$, respectively. Calculate the ratio of the densities of FCC and BCC.

The matrix $X$ for which $\left[\begin{array}{cc}1& -4\\ 3& -2\end{array}\right]X=\left[\begin{array}{cc}-16& -6\\ 7& 2\end{array}\right],$ is

Choose the correct statement

Represent $\frac{4}{7}$ in decimal form.

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
$\begin{array}{ccccccc}\text{Political Party}& A& B& C& D& E& F\\ \text{Seats Won}& 75& 55& 37& 29& 10& 37\end{array}$
(i) Draw a bar graph to represent the polling results.

A survey was conducted to see what people like to do in their free time. 100 people were interviewed. 20 people said they watch TV, 32 said that they read, 27 said they surf the internet and the rest said they do other stuff. Based on the data, what is the probability that a person chose at random

1. likes watching TV
2. likes reading
3. likes surfing the nws
4. prefers to do something other than these activities. [4 MARKS]

The sides of a rectangle are in the ratio of $6:5$ and its area is $750m^2.$ Find the perimeter of rectangle (in $m$).

What is the approximate circumference of a circle that has a radius of 14 cm?

What is the formula of π? Why it is considered as a irrational number?

If A = 15°

Find 4 cos 2A . sin 4A .tan 3A - 1

If the height of a sphere is 20 cm, then the total surface area of the sphere is

What polynomial added to $2x^2–3$ gives the result as $3x^2-4$?​

In a study of diabetic patients in a village, the following observations were noted.
$\begin{array}{ccccccc}\text{Age in years}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Number of patients}& 2& 5& 12& 19& 9& 4\end{array}$
Represent the above data by a frequency polygon.

The ratio of surface areas of 1 cube of volume $64c{m}^3$ and 64 cubes of volume $1c{m}^3$ is

If the area of a rhombus-shaped box is $6\sqrt{7}{cm}^2$ and its one diagonal is $6cm$. Find the side of the rhombus.

The perimeter of a square is 80 units. Find its perimeter when the length of its side is doubled.

Question 1 (b)

State whether true or false.

(b) All rhombuses are parallelograms.

Which of the following rational numbers is a terminating decimal?

Find the values of x and y in the given pair of equations.

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

Factors of $x^6-y^6$ is:

The base of an isosceles trapezoidal prism has parallel sides measuring 7 cm and 9 cm. The non-parallel sides measure 6 cm each. What is the perimeter of the trapezoidal base?

Two fair dice are thrown together. The probability that the number 5 does not appear on any of them is: