Comp. Mathematics Test -01

All questions are compulsory.

[ Q. No. 1 ]
a) If S = { letters needed to spell the word ‘donkey’ } and A = { m, o, n, y } then,
i) Show S and A in a Venn-diagram. [1]
ii) Find the number of subsets of A. [1]

b) If P = { even number less than 10 } and B = { 1, 3, 5, 7 } then,
i) List the elements of P. [1]
ii) What type of set are set P and B ? Why are they called so ? [1+1]

[ Q. No. 2]
a) If A = { a, b, c, d } and B = { c, d, e, f }, find B – A and shade it in a Venn-diagram. [1+1]

b) In a group of students, it was found that 60 like to listen poem, 45 like to listen story, 25 like both of them and 8 like neither of them.
i) Find how many students were in the survey. [1]
ii) Find number of students who like to listen only poems. [1]
iii) Show the above information in Venn-diagram. [1]

[ Q. No. 3 ] Scientific notation can help express huge numbers easily using certain mathematical form.
i) Write the general form in which scientific notation is expressed. [1]
ii) The tallest mountain in the world, Mount Everest, is over 8848860 mm. Write it in scientific notation. [1]
iii) The mass of the Sun is approximately 1.989 × 10³⁰ kg. Rewrite it in usual/standard notation. [1]
iv) A rocket travels 5 × 10³ km in one hour. The distance of Mars from the earth is 7.8 × 10⁷ km. In how many hours the rocket can reach the mars planet? [2]

[ Q. No. 4 ] Ratio of two quantities of the same kind and in the same unit is the fraction that one quantity is of the other.
i) What are the antecedent and the consequent in the ratio 3 : 4. [1]
ii) Find the ratio of 32 min to 1 hour. [1]
iii) Find a : c if a : b = 2 : 3 and b : c = 4 : 5. [1]
iv) A map was drawn to the scale 1 : 20000. If the distance between two places in the map is 10 cm, find the actual distance ( in km ) between the two places. [2]

[ Q. No. 5 ] Four numbers a, b, c and d are said to be in proportion, if a : b = c : d which is mathematically expressed as a : b :: c : d.
i) Determine whether 2 cm, 3 cm, 4 cm and 6 cm are in proportion or not. [1]
ii) If yes, write the extremes and means. If no, state why not ? [1]
iii) Determine the mean proportion between 0.4 and 0.9. [1]
iv) Divide Rs. 9350 into three parts such that half of the 1st part, one-third of the 2nd and one-sixth of the 3rd part are equal. [2]

[ Q. No. 6 ] A gain is made when the selling price of an item is more than its cost price.
a) Write the formula to find gain percent. [1]
b) Ram bought a cap at Rs. 150 and sold it to Shyam for Rs. 200.
i) Does Ram bear loss or profit ? By what amount ? [1]
ii) Find the loss or gain percent made by Ram in the transaction . [1]

c) When a pack of noodle is sold for Rs. 23, there is a profit of 15%.
i) Find its cost price. [1]
ii) At what price must it be sold to make a profit of 10%. [1]

[ Q. No. 7 ] Discount is the amount reduced from the marked price of an article.
a) Write the formula to find discount percent. [1]
b) A discount of 15% is allowed on a table whose marked price is Rs. 8000.
i) Find the discount amount. [1]
ii) Find the selling price of the table. [1] ]
c) A mobile set was bought for Rs. 9600.
i) At what labelled price should it be sold to gain 33.3% after allowing 20% discount ? [1]
ii) What was the selling price of the mobile set ? Find. [1]

[ Q. No. 8 ]

[ Q. No. 9 ]

[ Q. No. 10 ]

[ Q. No. 11 ]
a) Write the exponent and base in x⁵. [1]
b) If x⁴ = 81, what is the value of x ? [1]
c) Write the simplified form of p³ × p⁴ × p⁵. [1]
d) Consider an expression (a²b)² × (ac²)² × (b²c)³.
i) Simplify it using the law of indices. [1]
ii) If a = -1, b = 1 and c = 2, find the value of the above expression. [1]

[ Q. No. 12 ]

* Best Of Luck *