Q1) The areas of the ends of a frustum of a pyramid are P and Q where P < Q and H is its thickness. What is the volume of the frustum. Q2) P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersects the circle at points A and B in such a way that PA = 9 cm and AB = 7 cm. The radius of the circle is 1) 4 cm 2) 4.5 cm 3) 5 cm 4) 5.5 cm Q3) The diagonals AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then it is always true that 1) AP.CP = BP.DP 2) AP.BP = CP.DP 3) AP.CD = AB.CP 4) BP.AB = CD.CP Q4) ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then, AP:AB is 1) 3:5 2) 4:1 3) 2:3 4) 1:4 Q5) ABCD is a rhombus. AB is produced to F and BA is produced to E such that AB = AE = BF, then 1) ED^{2} + CF^{2} = EF^{2} 2) ED is parallel to CF 3) ED > CF 4) ED is perpendicular to CF Q6) If the graph of the equation 2x + 3y = 6 form a triangle with coordinate axis, then the area of triangle will be 1) 3 sq units 2) 1 sq units 3) 2 sq units 4) 6 sq units Q7) The area of the region bounded by y = |x| - 5 with the coordinate axis is 1) 25 sq units 2) 50 sq units 3) 52 sq units 4) 20 sq units Q8) What is the remainder when 19^{100} is divided by 20 1) 0 2) 19 3) 1 4) 3 Q9) A man reads 3/8 of a book on a day and 4/5 of the remaining on the second day. If the number of pages still unread are 40, then how many pages did the book contain? 1) 300 2) 320 3) 360 4) 500 Q10) If p + q = 10 and pq = 5 then the value of 1) 18 2) 20 3) 16 4) 22 Q11) An article is sold for Rs 300 at a profit of 20%. Had it been sold for Rs 235, the loss percentage would have been 1) 3% 2) 6% 3) 5% 4) 16% Q12) If P^{2} + 4Q^{2} = 4PQ then find the ratio of P:Q 1) 1:3 2) 1:2 3) 3:1 4) 2:1 Q13) In an examination, a student scores 4 marks for every correct answer and losses 1 mark for every wrong answer. A student attempted all the 200 questions and scored 200 marks. Find the number of questions, he answered correctly. 1) 80 2) 60 3) 82 4) 68 Q14) If find the value of 1) 0 2) 1 3) 2 4) 3 Q15) If the side of a square is increased by 25%, then the area of the square will be increased by 1) 125% 2) 56.25% 3) 50% 4) 25% Q16) A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30 m/min, then the radius of the circular ground is 1) 10.5 m 2) 7.5 m 3) 3.5 m 4) 5.5 m Q17) If tan8θ = cot2θ where 0 < 8θ < π/2 then what is the value of tan5θ 1) 0 2) 1 3) 1.732 4) 0.577 Q18) What part of a ditch 48 m long, 16.5 m broad and 4 m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 m and length 56 m? 1) 1/9 2) 8/9 3) 7/9 4) 2/9 Q19) A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between 1) 370 cu cm and 380 cu cm 2) 380 cu cm and 390 cu cm 3) 390 cu cm and 400 cu cm 4) 360 cu cm and 370 cu cm Q20) If the sides of a quadrilateral ABCD touch a circle and AB = 6 cm, CD = 5 cm, BC = 7 cm, then the length of AD (in cm) is 1) 4 2) 9 3) 8 4) 6 1) 3 2) 3 3) 2 4) 4 5) 4 6) 1 7) 1 8) 3 9) 2 10) 1 11) 2 12) 4 13) 1 14) 4 15) 2 16) 3 17) 2 18) 4 19) 1 20) 1
1) Area of first end = P = |
SCORE | PERFORMANCE |
---|---|
18-20 | Excellent |
15-17 | Good |
11-14 | Satisfactory |
1-10 | Poor |