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1. 45

Find the measure of the angle subtended by

arc (ACB) in the given figure.

Question 1 (i)

Write all the factors of the given number:

36

What is the inradius of an equilateral triangle the length of whose side is $6\sqrt{3}$?

A hemisphere made of lead of radius $7cm$ is cast into a right circular cone of height $49cm.$ Find the radius of the base of the cone.

In the given figure, a circle with cenre O has diameter 112 cm. Two equal circles whose diameter is half the diameter of the bigger circle are drawn inside the circle with centre O. If the shaded portion has been cut-out from the two smaller circles as shown in the figure, then the area of the remaining part of the circle is equal to

The heights (in cm) of 30 students of a class are given below:
161, 155, 159, 153, 150, 158, 154, 158, 160, 148, 149, 162, 163, 159, 148, 153, 157, 151, 154, 157, 153, 156, 152, 156, 160, 152,147,155,155,157.
Prepare a frequency table as well as a cumulative frequency table with 160-165 (165 not included) as one of the class intervals.

Find the zero of the polynomial in each of the following cases :



(i) p(x) = x + 5

(ii) p(x) = 2x + 5

1. 2

In the given figure, $AC||FD.IfBC=\frac{1}{4}ACandED=4BC,$ then the ratio of ar(∆ABE) to ar(∆BED) is equal to

The median for a data having 99 observations arranged in descending order is the _______________

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Question 36

State whether the given statement is True or False.

Two parallel lines meet each other at some point.

The points (5, - 2), (6, 4) and (7, - 2) are the vertices of an _________ triangle.

Compound interest on ₹ 18,000 for $2\frac{1}{2}$ years at 10% per annum, compounded annually is

A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.

PQRS is a parallelogram, if the two diagonals are equal, then the measure of DPQR is:

The height of the rectangle in a histogram is proportional to?

Evaluate ${\left(\frac{81}{49}\right)}^{-\frac{3}{2}}$

What is the solution of the following system of linear equations?

2x+3y=12

x-y=1

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& -2\\ a& 2& b\end{array}\right]$ is a matrix satisfying

$A{A}^T=9I_3$, then find the values of $a$ and $b$.

Question 82(ii)

Given below is a frequency distribution table. Read it and answer the questions that follow.

$\begin{array}{cc}Classinterval& Frequency\\ 10-20& 5\\ 20-30& 10\\ 30-40& 4\\ 40-50& 15\\ 50-60& 12\end{array}$

What is the upper limit of the last class interval ?

Two different families A and B are blessed with equal number of children. There are 3 tickects to be distributed among the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is $\frac{1}{12}$, then the number of children in each family is :

Find the value of the $\frac{sin{17}^{\circ }sec{73}^{\circ }-cose{c}^2{67}^{\circ }}{se{c}^2{45}^{\circ }-tan{23}^{\circ }tan{67}^{\circ }+co{t}^2{67}^{\circ }}$

Give zeroes of the polynomial p(x)=(x-1)(x-2)(x-3)(x-4)

What is frequency ?

Question 107

State whether the statement is True or False.

The sum of an integer and its additive inverse is zero (0).

The number $(\sqrt{2}{)}^5$ is

If $x\in R$ satisfies $(lo{g}_{10}100x{)}^2+(lo{g}_{10}10x{)}^2+lo{g}_{10}x\le 14$ then $x$ contains the interval

If two rational numbers $\frac{a}{b}and\frac{c}{d}$ are equal, then

For constructing angle ${75}^{\circ }$

Steps of construction are:

Step 1: Draw ray AB

Step 2: Construct $\angle BAC={60}^{\circ }$

Step 3: Construct .

Find the value of 'k' if 2x-3 is a factor of 2x3-ax2+x+k.

The sizes of shirts sold in a shop are as follows:

36, 38, 30, 40, 34, 42, 30, 46, 40, 38, 34, 40, 38, 40, 42, 30, 40, 38, 44, 40, 32, 40, 32, 44, 38

Compute the mean, median and mode. Among these, which is the most important one for the seller? Discuss.

What is the meanof the following data: 1, 4, 7, 3, 9, 5, 3, 2, 7, 5.