Mathematics & Numerical Ability – Previous Year Questions
166 questions from past HTET Common Portion papers, each with the correct answer. Open any question for its explanation.
- If tan θ + sec θ = 4, then the value of cos θ is equal to :
- What is the smallest number by which 2880 must be divided in order to make it a perfect square ?
- P began a business with Rs. 45,000 and Q joined with Rs. 30,000 after some time. If the profit at the end of the year were divided among them in the ratio 2 : 1, when did Q join ?
- If three numbers are in the ratio 3 : 2 : 5 such that the sum of their squares is equal to 1862, the middle number is equal to :
- A, B and C together completed a work for Rs. 5,290. A and B together did 19/23 of the whole work. Amount received by C in Rs. is equal to :
- The difference between the compound interest and simple interest on a certain amount at 5% per annum for 2 years is Rs. 15. The principal amount is equal to :
- The radius of a circular field, whose area is equal to the sum of the area of the three circular fields having radii 8 m, 9 m and 12 m respectively, is equal to :
- A square and an equilateral triangle are inscribed in a circle. If a and b denote the lengths of their sides respectively, then which of the following is true ?
- The surface areas of the two spheres are in the ratio 1 : 2. The ratio of their volumes is :
- The volume of the metallic cylindrical pipe is 748 cm³. Its length is 14 cm and its external radius is 9 cm. The thickness of pipe is equal to :
- By selling an item for Rs. 153, a man gets loss of 10%. For how much should he sell them to get profit of 20% ?
- The diameter of a sphere whose volume is 1131/7 cubic metres is :
- If the diameter of a right circular cylinder is 28 cm and its height is 20 cm, then the total surface area is equal to :
- The perimeter of the rhombus is 52 cm. If one of the diagonal is 24 cm, the area of the rhombus is equal to :
- The radius and the height of right circular cone are in the ratio 5 : 12. If its volume is 314 metre3, the diameter of its base is equal to (π = 3.14) :
- The value of sec (90° – A) – cot A cos (90° – A) tan (90° – A) is :
- If the height of a tower is 2√3 metres and the length of its shadow is 2 metres, then the angle of elevation of sun is equal to :
- The least number of complete years, in which a sum of money put at 20% compound interest will be more than doubled, is :
- How many numbers from 11 to 50 are there which are exactly divisible by 7 but not by 3 ?
- The square root of [(1¾)4 − (2⅓)4] ÷ [(1¾)2 − (2⅓)2] is equal to :
- X can do a work in 6 days and Y can do same work in 8 days. With the help of Z, all three finished the work in 3 days. If they altogether got Rs. 2000 after completing the work, then Z gets :
- A boat goes 20 km downstream in one hour and the same distance upstream in two hours. The speed of the boat in still water is :
- The ratio of an interior angle to the exterior angle of a regular polygon is 7 : 2. The number of sides of the polygon is :
- Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then pipe B will fill the tank in :
- The radius of the circumcircle of the triangle made by x-axis, y-axis and 4x + 3y = 12 is :
- Find the least number which must be added to 15463 so that the resulting number is exactly divisible by 107 :
- What proportion of water must be added to milk to gain 20% by selling it at the cost price ?
- The ratio of compound interest and simple interest on a certain sum at the rate of 4% per annum for 2 years is :
- If A, B and C enter into a partnership with shares in the ratio 7/2 : 4/3 : 6/5. After 4 months, A increase his share by 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is :
- A man sold an article at a loss of 20%. If he sells the article for Rs. 12 more, he would have gained 10%. The cost price of an article is :