AISSEE-MATHEMATICS (2020)

Questions in this test

1. Find the compound interest on 1,25,000 for 9 months at 8% per annum, compounded quarterly:
2. The value of $\left(-\frac{3}{2}\times \frac{4}{5}\right)+\left(\frac{9}{5}\times \frac{-10}{3}\right)-\left(\frac{1}{2}\times \frac{3}{4}\right)$?
3. The abscissa of a point is its distance from the :
4. What is the value of m, if $\left(\frac{2}{9}\right)^3\times \left(\frac{2}{9}\right)^{-6}=\left(\frac{2}{9}\right)^{2m-1}$
5. “If a number when divided by 4 leaves remainder 2 or 3", then which one is the correct statement?
6. The value of $\frac{\sqrt{0.2304}+\sqrt{0.1764}}{\sqrt{0.2304}\ +\sqrt{0.1764}}$
7. Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. The numbers are:
8. Find the least square number divisible by each one of 8, 9 and 10:
9. If $\overline{148101a095}$ is a multiple of 11, where a is a digit, the value of a is:
10. Find the value of A and B in B A
11. Find the value of Z for which the number 471Z8 is divisible by 9:
12. If the area of an equilateral triangle is 64√3 cm², then the side of the triangle is :
13. The value of $\frac{4m^2-a^2+2ab-b^2}{2m+a-b}$
14. The ratio between the speeds of two trains A and B is 3:5. If train B runs 300 km in 4 hours, the speed of train A will be:
15. Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. The present age of son and Dilip are:
16. The probability of getting a 7 in a single throw of a dice is:
17. A's income is 60% more than that of B. By what percent is B's income less than A's?
18. By joining $(-3, 2)$, $(-3,-3)$ and $(-3, 4)$, which of the following is obtained?
19. The number of times a particular observation occurs in a given data is called its :
20. By selling 33 m of cloth, a draper loses an amount equal to the selling price of 3 m of cloth. Find his gain or loss percent
21. Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is :
22. Find the single discount equivalent to two successive discounts of 20% and 10%
23. Which of the following is not a case of direct variation?
24. If a+b+c= 9 and ab + bc + ca = 23, then the value of a² +b² + c² equals to :
25. On dividing 200 into two parts, $1/3$ of the first part and $1/2$ the second part are equal. The larger of the parts is:
26. On selling a fan for ₹810, Sunil gains 8%. For how much did he purchase it?
27. Find the value of $x:3^{2x}\times 3^{x+3}\times 3^{4-x}=\left(\sqrt{3}\right)^{10}$
28. $\sqrt[3]{\frac{\left(-a^4\times b^3\times c^{21}\right)}{c^9\times a^{21}}}\ =\ _{_{_{ }}}$ ________
29. If n is a perfect cube, then every prime factor of 'n' occurs
30. Find the greatest number of four digits which is a perfect square
31. If the ratio of the ages $(in$ $years)$ of x and y, 8 years ago is 7:6, then which of the following can be the sum of their ages 8 years from now?
32. The age of the boy is one-fifth of the age of his mother and sum of the ages of the son and the mother is equal to the age of the father. After 15 years, the sum of the ages of the son and his mother will be four-third of his father's age. Find the ratio of the present ages of son, mother and father respectively.
33. The ratio of the income of P and Q is 5:4. The ratio of expenditure is 4:3. The saving of P is more than that of Q by $16\frac{2}{3}$%. What % of his income does P spend?
34. Mohan invested a sum of ₹12,500 at 12% per annum compound interest. He received an amount of 15,680 after x Year Then the value of x is ____
35. Pipe A can fill a tank in 12 hours and pipe B can empty the tank in 18 hours. Both pipes are opened at 6 AM and after some time, pipe B is closed and the tank is full at 8 PM. At what time was pipe B closed?
36. A car covers 300 kms at a constant speed. If its speed was 10 kmph more, it would have taken 1 hour less to travel the same distance. Find the speed of the car.
37. Two trains are travelling in opposite direction with speed of 25 m/s and 30 m/s respectively. If the length of one train is 300 m and that of the other train is 250 m, then find the time taken by the trains to cross each other.
38. The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number then the digits get reversed. Find the number.
39. There are some four wheelers and six-wheelers in a garage. The total number of wheels of these vehicles is 120. The number of four-wheelers is 3/2 times the number of six-wheelers. Find the number of six wheelers in the garage.
40. What is the minimum interior angle possible for a regular polygon?
41. What is the number of diagonals in a hexagon?
42. In the adjacent figure, the bisectors of <A and < B meet at a point P. If<C=100° and <D=60° find the measure of <APB.
43. A square and a rectangle each have a perimeter of 40 m. The difference between area of the two figures is 9 m². What are the possible dimensions of the rectangle?
44. In a parallelogram ABCD, AB = 6 cm, BC = 5 cm and AC = 7 cm. Find the perpendicular distance between $\overline{AB}\ and\ \overline{CD}$.
45. Some cubic metres of earth is dug out to sink a well which is 16 m deep and which has a radius of 3.5 m. If that amount of earth when taken out is spread over a rectangular plot of dimensions 25 m × 16 m, what is the height of the platforms so formed ?
46. What is the difference between the total surface area and curved surface area of a cylinder whose radius is equal to 10 cm?
47. The mean of six numbers is 15. If 2 is taken away from every number, the new mean would be:
48. The sides of the triangle are 45 cm, 60 cm and 75 cm. Find the length drawn to the longest side from its opposite vertex.
49. In the following figure, find the value of Y.
50. A cylindrical tank has a capacity of 5632 $m^3$. If the diameter of its base is 16m, find its depth.