SECTION A

Question 1

Represent |x-3|<2 on the number line.

Evaluate |3|+|-2-3| -3-|-7|.

Express 3/2 Ö(8) as pure surel of order 4.

Ö(a²-b²) + a + Ö(a²+b²) - b
------------------- ------------. Simplify
Ö(a²+b²) + b aÖt(a²-b²)

Find the value of a if x-2 is a factor of x⁵-3x⁴-ax³+3ax²+2ax+4.

Resolve into factors (x+2)(x²+25)+10 x² + 20 x.

Using factor theorem, show that a-b, b-c and c-a are the factors of a (b²-c²) + b (c²-a²) + c (a²-b²).

Solve x²+5x+4 = 3
           x²+3x+2     2

Solve 2x-3 + x+3 = 4x+1
             5           4           7

Simplify [81/16]^-3/4 . [25/9]^-3/2 ÷ [5/2]^-3.

If log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8457, find the value of log 42.

Show that 2 (Cos⁴ 60° + Sin⁴ 30° ) - (tan² 60° + Cot² 45° ) + 3 Sec² 30 = 1/4.

If x = 30°, Verify that Sin x = Ö(1-Cos 2x)/2.

The class marks of a distribution are 47, 52, 57, 62, 72. Determine the class zise, the class limits and the true class limits.

ABC is a right triangle, right angled at C. If A=30 ° and AB=40 units, find the remaining two sides and ÐB pf Triangle ABC.

SECTION B

Question 16

Simplify If 7Ö(3) - 5Ö(2)/Ö(48) + Ö(18) = a+b Ö(6), Find the values of A and B.

Factorize x³-9x²+27x-27.

The length of a rectangle is 4 cm. more than the breadth, and the perimeter is 11 cm more than the breadth. Find the length and breadth of the rectangle.

A boy is now one - third as old as his father. Twelve years hence he will be half as old as his father. Determine the present age of the boy and that of his father.

Evaluate (73.56)³ x (0.0371)² / 68.21 Using Logarithms.

In a rectangle ABCD, AB = 20 cm, Ang BAC = 60 °. Calculate side BC and diagonals.

An observer 1m. tall is 2m. away from a pole of height 3m. Find the angle of elevation of the top of the pole as observed by him.

A ladder 10 m long reaches a point on a wall which is 10 m. from the top of the wall. The angle of depression of the foot of the ladder as observed from the top of the wall is 60 °. Find the height of the wall.

Draw a Histogram and a frequency polygon for the following data.

A pharamaist needs to strengthen a 15 % alcohol solution to one of 32% alcohol. How much pure alcohol should be added to 400 ml of the 15 % of solution.

Rationalize the denominator                 1                       
                                               root(7)+ root(6) - root(13).

A man invested Rs 35000/- a part of it at an annual rate of 12 % and the rest at 14% if he received a total annual interest of Rs 4460, how much did he invest at each rate?

The value of a macine depreciates 10% annually. Its present value is Rs 45450/-. Find is value of 5 years ago.

The angle of depression of the foot of a 9 m. high pole from the top of a building is 60°. and the anlge of depression of the foot of the building at the top of the pole is 30°. Find the height of the building.

How many kilograms of tea at Rs. 50/- per Kg should be mixed with 35 Kg of tea costing Rs 60/- per Kg So as to Sell the mixture at Rs 57/- per kg without gaining or loosing any thing in the transaction.