TEST PAPER -- 1(S)

            TEST PAPER - 1

             ( Marks 90)         

                  Section A

                   Attempt all 

1). (1x10= 10)

a) Express 15/56 as a decimal, correct to four decimal places.

b) Express 3.146146146.... as a vulgar fraction.

c) If √2= 1.414 and √3= 1732. Find the value of√72

d) What percentage of 2.5 is 1.21

e) If C. P=₹112, overheads= ₹14 and S. P=₹94.50. find Profit.

f) Factorize: 5a(b+c) -7b(b+c)

g) Insert a rational number between 3/5 and 5/7

h) Every real number is rational. True//false

i) x% of y = ?

j) 9x - 7= 6x +14

              SECTION- B.  

         Attempt all (10x2= 20)

2)

A) Show that √2 is not a rational number.

B) If 35% of a number is 26.6, what is 20% of that number?

C) If oranges are bought at 11 for ₹30 and sold at 10 for ₹31, find the loss or gain percentage.

D) At what rate percentage p.a. simple interest, would a sum double itself in 6 years?

E) Expand: (2x+ 1/3x)²

F) Solve: 7/(x-4) = 5/(x+2)

G) Simplify: (a+b)⁻¹ . (a⁻¹+b⁻¹)

H) Find the length of the longest rod that can be placed in a room 16m long, 12m broad and 32/3 m high.

I) Expand: (2p - 3q)³

J) Represent rational number on real line of - 1/4

              Section - C

    Attempt any six (6x5= 30)

3) A businessman sold 2/3 of his stock at a gain of 20% and the rest at a gain of 14%. Find the overall percentage of gain to the businessmen.

4) After getting two successive discount, a shirt with a list price of ₹150 is available at ₹105. If the second discount is 25/2%, find the first discount.

5) At a certain rate of simple interest, a sum amounts to ₹4760 in 3 years and Rs 5600 in 5 years. Find the sum and the rate percentage per annum.

6) Find the amount and the Compound Interest on ₹10000 for 4 years, if intrest is 5% p.a payable yearly.

7) If x - 1/x = 4, find

A) x² + 1/x². B) x⁴ + 1/x⁴

8) Factorize:

A) 3x² - 4x -7

B) 3x² - 48x

9) Solve: (5y-11)/4 + (3y-7)/2 = (4y-7)/3 + y - 1

10) A room is half as long again as it is broad. The cost of carpeting the room at ₹18 per m² is ₹972 and the cost of white washing the four walls at ₹ 6 per m² is ₹1080. Find the dimensions of the room.

                    Section - D

      Attempt any five (6x5= 30)

11) The dimensions of a metallic cuboid are 100cmx80cmx64cm. It is melted and recast into a cube. Find:

A) the edge of the cube

B) the surface area of the cube.

12) 

A) Simplify: {7²ⁿ⁺³ - (49)ⁿ⁺²}/[(343)ⁿ⁺¹]²⁾³

B) If 1960=2 ᵃ x 5ᵇ x 7ᶜ, find the values of a, b, c. Hence, Calculate the value of 1/(2 ᵃ x 5ᵇ x 7ᶜ)

13) If x = (k+1), find the value of k when, 1/2 (5x -3) - 1/2 (2+9k) = 1/4.

14) a) If a - 1/a =√5, find the value of I) a+ 1/a. II) a³ + 1/a³

15) The population of a town is 1764000. If it increases at the rate of 5% per annum, its population:

A) 2 years hence

B) 2 years ago

16) A man spends 80% of his income. His income increases by 20% and he increases his expenditure by 15%. Find the percentage increasein his savings.

17) a) Rationalize the denominator:

(√3+√2)/(√3 - √2)

b) Insert six rational numbers between 3 and 4.