Comp. Mathematics Test -02

All questions are compulsory.

[ Q. No. 1 ]
If U = { x : x € N, x < 11 } is a universal set, A = { y : y is an even number } and B = { z : z is a prime number },
a) List the elements of U. [1]
b) List the elements of A. [1]
c) List the elements of B. [1]
d) Is there any common elements in A and B ? Write in set notation. [1]
e) Show the above data in a Venn-diagram. [1]

[ Q. No. 2]
The capacities of two tanks were measured and found as below :
Capacity of Tank A – 3.2 × 10³ litre
Capacity of Tank B – 3.5 × 10³ litre
a) Express the capacities of each tanks in usual form. [1+1]
b) Calculate the total capacity of the tanks in usual form. [1]
c) Rewrite the total capacity in standard form. [1]
d) By how much is the capacity of tank B more than that of tank A ? Calculate and express in scientific notation. [1]

[ Q. No. 3 ] The ratio of present ages of Ram and Shyam is in the ratio of 5 : 4.
a) If Ram is 25 years old, what is the age of Shyam ? [1]
b) Find the ratios of their ages after 5 years. [1]
c) Find the ratios of their ages before 5 years. [1]
d) In how many years, the ratio of their ages will be 7 : 6 ? Find. [2]

[ Q. No. 4 ]
a) Find the mean proportion between 5/2 and 5/8. [1]
b) If A : B = 2 : 3 and A : C = 8 : 15, find B : C. [2]
c) In an exam, A obtained twice of marks obtained by B. Likewise, B obtained three times the marks obtained by C.
i) Find the ratio of marks obtained by A and B. [1]
ii) Find the ratio of marks obtained by B and C. [1]

[ Q. No. 5 ] Due to bad weather, a fruit seller had to sell his fruits at a loss of 8%. If he bought the fruits for Rs. 225 a dozen,
a) Find the cost price of 40 fruits. [1]
b) Find the loss in 40 fruits. [2]
c) Find the selling price of 40 fruits. [2]

[ Q. No. 6 ] The marked price of a watch is Rs. 2,800 which was 40% above the cost price. If it was sold by allowing 20% discount,
a) Find the cost price. [1]
b) Find the discount amount. [1]
c) Find the selling price of the watch. [1]
d) What will be the profit or loss percent ? Find. [2]

[ Q. No. 7 ] Reema took a loan of Rs. 80,000 from a money lender, who charged interest at the rate of 10% per annum. After 5 years, she paid him Rs. 50,000 and a laptop to clear the debt.
a) Find the interest after 5 years. [2]
b) What will be the amount after 5 years ? [2]
c) Estimate the price of the laptop. [1]

[ Q. No. 8 ] A rectangular field has the same area as that of a square field of side 60 m. If the breadth of the rectangular field is 32 m,
a) Find the area of the rectangular field. [1]
b) Find the length of the rectangular field. [2]
c) If the length and width of the rectangular field are doubled, what would be the new area of the field ? [2]

[ Q. No. 9 ] A circular garden has radius 49 m.
a) Find the diameter of the garden. [1]
b) Find the circumference of the garden. [1]
c) Calculate the area of the garden. [1]
d) Find the cost of gardening at Rs. 150 per sq. meter. [1]
e) If the area of the garden is 154 m², what will be the new radius of the garden ? [1]

[ Q. No. 10 ] The yearly income of Dolma, Rambilash and Sonam are in the ratio of 4: 5: 6. If the sum of the incomes is Rs 1,20,000 then answer the following questions.
(a) Express the income in scientific notation. [1]
(e) What is the ratio of income of Dolma and Sonam. [1]
(b) Find the income of Dolma and Sonam. [1]
(d) If Rambilash deposits his income in a bank for 5 years at the rate of 10% per annum, what amount will he make after 5 years? [2]

[ Q. No. 11 ]
a) Write any two laws of indices. [1]
b) For what value of x will the value of 2 raised to the power of x is 1 ? [1]
c) Write the simplified form of a² × a⁴ ÷ a³. [1]
d) Consider an expression (xy²)³ × (xz²)³ × (yz)².
i) Simplify it using the law of indices. [1]
ii) If x = -1, y = 1 and c

= 2, find the value of the above expression. [1]

[ Q. No. 12 ]

* Best Of Luck *