i)

If 2x + 5y = 1 and 5x + 2y = 13, find the values of 7x + 7y and 3x + 3y.

ii)

The side of an equilateral triangle is 7 cm. Find its perimeter. Write down the ratio of its side to its perimeter.

iii)

If x µ and x = 15 when y = 3, find y when x = 9.

iv)

If 3 sin q = 4 cos q, find the value of tan q.

v)

Write the equation r² - r = 2r -5 in the form of ax² + bx + c = 0 and then write the value of a, b and c.

vi)

If cot A = , then find the value of cosec A.

vii)

Verify whether the expression (a-b) (c-b) (a-c) is cyclic.

Q.2.

Attempt any five of the following:

15

i)

Points (3,0) and (0,4) are on a line having equation Ax + By = 12.
Find the values of A and B.

ii)

If a natural number is added to its square, the sum is 56, find the number.

iii)

If , then find the value of .

iv)

Draw a histogram of the data. (Scale: 1 cm = 10)

v)

Show that:
(sin x + cosec x) ² + (cos x + sec x) ² = tan²x + cot² x +7.

vi)

Find the order relation between .

vii)

A piece of string 12 m in length was cut into pieces such that one piece is x metre and other is y metre. If y is 2 metres more than x, find the length of each piece.

a)

Solve any two of the following:

6

i)

The force of the attraction between two unlike magnetic poles varies inversely as the square of the distance between them. If the distance is 9 cm, then the force of attraction is 4 dyne. Find the force of attraction if the distance between the poles is 3 cm.

ii)

Solve: x² + 4x - 5 = 0

iii)

Show that + cos A = sec A

b)

Solve any one of the following:

4

i)

Solve: 23a - 25b = 215,
         25a - 23b = 217

ii)

If a, b, c are in continued proportion, show that .

a)

Solve any two of the following:

6

i)

Using formula, find factors of x² + 8x + 7.

ii)

Solve: x + 6y = 22, + y = 4.

iii)

The marks obtained by 40 students in a class are given below:

35, 15, 29, 40, 31, 07, 40, 11, 48, 01, 45, 03, 32, 43, 49, 18, 30, 24, 25, 29, 23, 12, 25, 09, 27, 41, 12, 13, 02, 44, 30, 48, 22, 49, 19, 13, 32, 39, 25, 03

Prepare a grouped frequency table.
(Take classes 1-10, 11-20, &..)

b)

Attempt any one of the following:

4

i)

Take 1 cm = 1 unit on both axes. Draw graph of y = x  1 and 2y = -x + 2 on the same graph paper. Write the coordinates of the point of intersection of the graphs.

ii)

Observe the given table and answer the questions below it:

Class (Age Group)      :    1-7        8-14       15-21        22-28

Frequency                     :     105        315         208            331
(No. of Persons)

1. Write the interval and the mid-point of the class 15-21.
2. Write true upper and true lower limil of class 22-28.
3. How many persons are of the age below 22 years?

Q.5.

Attempt any three of the following:

15

i)

Factorise: (x + y + z) ³ -x³ -y³ - z³.

ii)

A number formed by two digits exceeds the number formed by reversing the digits by 18, and three times the product of the digits exceeds five times the sum of the digits by 5. Find the number.

iii)

The following table shows percentage population of some nations with respect to the world population. Draw a pie-diagram representing the information. (Round off the measures of arcs of sectors, if necessary, to the nearest integer.)

Nations               :   A      B      C       D     Other Nations

Percentage          :   5       6     15     22            52
Population

iv)

Draw the graph of the following equations on the same coordinate system:
1) 4x + 3y = 18,
2) x + y = 5, 3) x = 5. State with reason, whether the graphs are concurrent.

Q.6.

Attempt any three of the following:

15

i)

The distance of horizon seen from a spot varies directly as the square root of the height of the spot. When a person descended 300 metres from a spot at a certain height, the distance of horizon appeared half of the original. When he further descended 19 metres more, the distance of horizon was 1.1 kilometer. Find the height of the spot where he was standing originally and the distance of horizon appeared to him from there.

ii)

A medicine has four ingredients A, B, C and D. The ratio of the masses of A and B is 3:2. The mass of C is 50% of B and the mass of D is of the mass of C. Find the mass, in milligrams, of each ingredient in a tablet of mass 1 gram.

iii)

Solve:

iv)

For acute angles A and B, the following relations are given to be true:

sin A > cos A, sin B < cos B
State with reasons, which of the following relations are true:

1. sin (A - B) > cos (A - B)
2. tan A > tan B

Further, if sin (A + B) = 1,
find the value of sin A cos B + cos A sin B.