Q. If a = x+y, b = x-y, c = x+2y, then a2+b2+c2-ab-bc-ca is
1) 4y2
2) 5y2
3) 6y2
4) 7y2
Q. The graphs of the equations 25x + 75y = 225 and x = 9 meet at the point
1) (0, 9)
2) (9, 0)
3) (3, 0)
4) (0, 3)
Q. The perimeter of a semicircular path is 36m. find the area of this semicircular path.
1) 42 sq. m
2) 54 sq. m
3) 63 sq. m
4) 77 sq. m
Q. The ratio of sides of triangle is 3 : 4 : 5 and area of the triangle is 72 square unit. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is
1) 32√3 square unit
2) 48√3 square unit
3) 96 square unit
4) 60√3 square unit
Q. A right circular cylinder and a sphere have same radius and same volume. The ratio of their surface ara is
1) 8 : 3
2) 9 : 4
3) 4 : 3
4) 7 : 6
Q. A sphere and a hemisphere have the same volume. The ratio of their radii is
1) 1 : 2
2) 1 : 8
3) 1 : √2
4) 1 : 3√2
Q. Two circles with centres A and B and radius 2 nunits touch each other externally at `C'. A third circle with centre `C' and radius `2' units meets other two at D & E. Then the area of the quadrilateral ABDE is
1) 2√2 sq. unit
2) 3√3 sq. unit
3) 3√2 sq. unit
4) 2√3 sq. unit
Q. If two adjacent sides of a rectangular parallelepiped are 1 cm and 2 cm and the total surface area of the parallelepiped is 22 square cm, then the diagonal of the parallelepiped is
1) √ 10 cm
2) 2√3 cm
3) √ 14 cm
4) 4 cm
Q. The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10,000, the present population is
1) 4600
2) 6400
3) 7600
4) 6000
Q. A person who pays income tax at the rate of 4 paise per rupee, finds that a fall of interest rate from 4% to 3.75% diminishes his net yearly income by Rs. 48. What is his capital?
1) Rs. 24,000
2) Rs. 25,000
3) Rs. 20,000
4) Rs. 18,000
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