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In the figure below, all the vertices of the small triangle are on the circle and all the sides of the larger triangle touch the circle at these points.

Find all angles of the small triangle.

Two dice are thrown simultaneously. Find the probability of obtaining the sum as 6 or same number on both the dice.

(vi) Which term of the A.P. –7, –12, –17, –22,... will be –82? Is –100 any term of the A.P?

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Using the table find the Modal Class.

The volume of a right circular cone of radius r and height h is directly proportional to

From a rectangular board of length 8 centimetres and breadth 3 centimetres, a small rectangular piece is cut off.

One side of the piece cut off is of length 3 centimetres itself. Denoting the length of the other side as x, write down an algebraic expression which gives the area of the remaining piece.

Three numbers are in the ratio of $3:4:5$ and their $\text{L.C.M.}$ is $2400.$ Their $\text{H.C.F.}$ is

The table below shows the daily expenditure on food of 30 households in a locality:
$\begin{array}{cc}\text{Daily expenditure (in Rs.)}& \text{Number of households}\\ 100-150& 6\\ 150-200& 7\\ 200-250& 12\\ 250-300& 3\\ 300-350& 2\end{array}$
Find:

(a) mean of daily expenditure on food.

(b) median of daily expenditure on food.

A fraction becomes $\frac{4}{5}$ if one is added to both numerator and denominator. If 5 is subtracted from the numerator and denominator, the resultant fraction becomes $\frac{1}{2}$. Find the fraction.

If the areas of the three adjacent face of a cuboidal box are 120 cm${}^2$, 72 cm${}^2$ and 60 cm${}^2$ respectively, then find the volume of the box.

Question 10

In algebra $a\times b$ means ab but in arithmetic $3\times 5$ is

(a) 35

(b) 53

(c) 15

(d) 8

The sum of the digits of a two-digit number is 11. If the digits of the number are interchanged, we get a number which 27 more than the original number. What is the number?

A man ,after tour ,finds that he had spent every day as many rupees as the number of days he had been on tour . How long did his tour last , if he had spent in all Rs. 1296?

Consider two squares with 4 cm side each. Then which of the following is/are true?

Prove that two isosceles triangles having an angle of one equal to the corresponding angle of the other are similar.

A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)

The surface area of a sphere is 32π cm${}^2$. Find the radius and volume of this sphere?

There is a box containing 10 ping pong balls of 3 different colours red, green and blue. There are 2 red balls and 3 green balls. What is the probability of getting a blue ball in the first attempt?

Divide 56 in four parts in A.P. such that the ratio of the product of their extremes to the prodcut of their means in 5:6.

Which of the following is an AP?
1) 2, 3 ,4, 5,…
2) 9, 7, 6, 5...

1. 360

The principal value of ${\tan }^{-1}\left[2\cos \left[2{\sin }^{-1}\frac{1}{2}\right]\right]$ is

Sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25th term.

If AB is a chord of a circle with centre O. If $\angle AOB={50}^{\circ }$ and AB = 18 cm, then find the diameter of the circle. $sin{25}^{\circ }=0.42$

Question 11.

$(x^2+1{)}^2-x^2=0$ has:

(a) four real roots

(b) two real roots

(c) no real roots

(d) one real roots

Find the value of k so that the area of the triangle with vertices A(k+1,1),B(4,-3) and C(7, -k) is 6 square units.

Question 110

Solve the following question:

Find the length of the side of a square, if the length of its diagonal is 10 cm.