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Indians, Egyptians, Europeans and Australians are resided in a village of area 200$k{m}^2$. If the area is equally divided among the four civilizations, what is the probability that a particular person lands on the land occupied by Indians or Europeans?

Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 3.5 cm.

Figure shows a relation between set P and Q such that x $\in$ P, y $\in$ Q. What is the relation, domain and range?

The locus of the point which moves in such a way that its distance from the line $x=6$ is always equal to 2 units is

If the probability of winning a game is 0.7, what is the probability of losing it?

The area of a square is the same as the area of a circle.The perimeters of the circle and square are in the ratio ___.

The square of a number is decreased by 15 which is twice the original number. What are the numbers?

If the total surface area of a solid hemisphere is $462c{m}^2$, find its volume.

Express 7429 as a product of its prime factors.

A tent consists ofa frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of the canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of the surmounted conical portion are equal.)

Two vertices of a triangle are (3, –5) and (–7,4). If its centroid is (2, –1), find the third vertex.

In the given figure PQ is a diameter of a circle with centre O and PT is a tangent at P. QT meets the circle at R. If ∠POR = ${72}^{\circ }$, find $\angle$PTR.

The decimal expansion of the number $\frac{14753}{1250}$ will terminate after

(a) one decimal place (b) two decimal places

(c) three decimal places (d) four decimal places

What least number of must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion ?

Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of a parallelogram. Is this figure a rectangle ?

If sec 4A = cosec (A - ${10}^o$) an 4A is acute then $\angle$ A = ?

(a) ${20}^o$ (b) ${30}^o$ (c) ${40}^o$ (d) ${50}^o$

If PA and PB are tangents from an outside point P. such that PA =10 cm and $\angle APB={60}^{\circ }$. Find the length of chord AB.

Find the next number in the sequence 0, 2, 24, 252, ______

If a, b and c are in A. P. show that :

(i) 4a , 4b and 4c are in A.P.

(ii) a + 4, b +4 and c + 4 are in A.P.

Find the values of p for which the quadratic equation $(p+1)x^2-6(p+1)x+3(p+9)=0,p\ne -1$ has equal roots. Hence, find the roots of the equation.

Solve each of the following systems of equations by the method of cross-multiplication:

$\frac{b}{a}x+\frac{a}{b}y=a^2+b^2$

$x+y=2ab$

Question 8 (i)
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
$\begin{array}{cccccccccc}1& 6& 2& 3& 5& 12& 5& 8& 4& 8\\ 10& 3& 4& 12& 2& 8& 15& 1& 17& 6\\ 3& 2& 8& 5& 9& 6& 8& 7& 14& 12\end{array}$
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10.

Find the value of a, if (x-a) is a factor of x³- a²x + x+ 2

Factorise: $z-7+7xy-xyz$

Question 3
In a “magic square”. The sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?
$\begin{array}{ccc}\frac{4}{11}& \frac{9}{11}& \frac{2}{11}\\ \frac{3}{11}& \frac{5}{11}& \frac{7}{11}\\ \frac{8}{11}& \frac{1}{11}& \frac{6}{11}\end{array}$
$\left(\text{Along the first row}\frac{\text{4}}{\text{11}}+\frac{9}{11}+\frac{2}{11}=\frac{15}{11}\right)$

State the conjugate surd of 9+root7.

Which symbol replaces the ‘?’. Figure below represent a balance.

The quadratic equation 2x² - 3x + 5 = 0 has

A bank gives 10% S.I on deposits for senior citizens. Draw the graph for the relation between the sum deposited and the interest earned in one year. Hence, find

(i) The interest on the deposit of Rs. 650

(ii) The amount to be deposited to earn an interest of Rs. 45.

Two friends Rajat and Rajesh are 12.5 km apart. If they travel in opposite directions, they meet each other after half an hour and if they travel in the same direction, the meet after 2.5 hours. If Rajeh travels faster , what is his speed?

The sum of $1$st, $3$rd and $17$th term of AP is $216.$ find the sum of the first $13$ terms of the AP.

On simplifying $\frac{1}{tanA+cotA}$, we get

If A = $\left[\begin{array}{ccc}2& 4& 8\\ 6& 9& 1\\ 8& 7& 5\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then find the third element of the first row of A - B.

1. 5

$Inthegivenfigure,△ABCisinscribedinacircle.Thebisectorof\angle BACmeetsBCatDandthecircleatE,ifECisjoinedthen\angle ECD={30}^0.Find\angle BAC.$

Given that sin(A+B)=sinA cosB+cosA sinB,find the value of sin75°

A cone of height 8 metre has a curved surface area 188.4 square metres then its volume is what ?

Find the unknown length 'Z' of the following figure when BC = 4 cm, CD = 3 cm, and ED = 13 cm.

The first term of an arithmetic sequence is 200. The common difference is -10. Find the value of ${20}^{th}$ term.

Solve the following pair of equations:
7x - 15y = 2 ; x + 2y = 3.
Hence find 'm' in y = mx - 30/29

1/2x-2x²

Solve for x

Question 56

Of the 288 persons working in a company, 112 are men and the remaining are women. Find the ratio of the number of:
(a) men to that of women.
(b) men to the total number of persons.
(c) women to the total number of persons.

Matrix A has x rows and x + 5 columns. Matrix B has y rows and 11 - y columns. Both AB and BA exist.Then, the value of x and y is

In the figure, $\angle ADC={130}^{\circ }$ and chord $BC=$ chord $BE.$ Find $\angle CBE$

The angle opposite to the base edge of a square pyramid on its lateral face is 60${}^{\circ }$. If the slant height of the pyramid is 40$cm$, what is the lateral surface area of the pyramid?

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from $(n+1{)}^{th}to(2n{)}^{th}$ term is $\frac{1}{r^n}$.