Q1.On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs16.Find the sum lent out, if the rate of interest in both cases is 8 %.
Q2. Mr. Smith has a two years recurring deposit account in State Bank of India and deposits Rs.1500 per month. If he receives Rs.37, 875 at the time of maturity, find the rate of interest.
Q3. A man bought 200 shares each of face value Rs.10 at Rs.12 per share. At the end of the year, the company from which he bought the shares declares a dividend of 15%. Calculate:
(i) The amount of money invested by the man
(ii) The amount of dividend he received
(iii) The percentage return on his outlay.
Q4. An integer is chosen at random from 1 to 50. Find the probability that the number is:
(i) Divisible by 5
(ii) A perfect cube
(iii) A prime number.
Q5. Mr. Sharma wishes to start a 200 meter square rectangular vegetable garden. Since he has only 50 meter barbed wire, he fences three sides of the rectangular garden letting his house compound wall act as the fourth side of the fence. Find the dimensions of the garden.
Q6. Construct a triangle ABC, with AB = 6 cm, BC = 7 cm and angle ABC = 60.
Locate by construction the point P such that:
(i) P is equidistant from B and C.
(ii) P is equidistant from AB and BC
(iii) Measure and record the length of PA.
Q7. A fair dice is rolled. Find the probability of getting
(i) 3 on the face of the dice
(ii) An odd number on the face of the dice
(iii) A number greater than 1 on the face of the dice.
Q8. A (4, 2), B (6, 8) and C (8, 4) are the vertices of a triangle ABC. Write down the equation of the median of the triangle through A.
Q9.The angle of elevation of an aero plane from a point P on the ground is 60 Degree. After 12 seconds from the same point P, the angle of elevation of the same plane changes to 30 degree. If the plane is flying horizontally at a speed of 600km/ hr, find the height at which the plane is flying.
Q10. Construct a triangle ABC, given that AB = 6 cm, BC = 8 cm and median AD = 5 cm. Construct an in-circle to triangle ABC and measure its radius.
Q11. The manufacturer sold a washing Machine to a wholesaler for Rs.7000. The wholesaler sold it to a trader at a profit of Rs.1000. If the trader sold it to the customer at a profit of Rs.1500, find:
(i) The total VAT (value added tax) collected by the state government at the rate of 5%.
(ii) The amount that the customer pays for the TV.
Q12. A (4, 2), B (6, 8) and C (8, 4) are the vertices of a triangle ABC. Write down the equation of the median of the triangle through A.
Q13. Prove that A (2, 1), B (0, 3) and C (-2, 1) are the three vertices of an isosceles right angled triangle. Hence find the coordinates of a point D, if ABCD is a square.
Q14. Plot the points A(9,6) and B(5,9) on the graph paper. These two points are the vertices of a figure ABCD which is symmetrical about x = 5 and y = 6. Compl