Questions 45 to 66 carry 3 marks each.
Q. 1.
Let an and bn two sequences such that an = 13 + 6 (n ‒ 1) and bn = 15 + 7 (n ‒ 1) for all natural numbers n then the largest threes digit integer that is common to both these sequences is
Questions 45 to 66 carry 3 marks each.
Q. 2.
If p2 + q2 ‒ 29 = 2pq ‒20 = 52 ‒ 2pq, then the difference between the maximum and minimum possible value of (p3 ‒ q3) is
- A).
189
- B).
243
- C).
486
- D).
378
Questions 45 to 66 carry 3 marks each.
Q. 3.
Let both the series a1, a2, a3,….. and b1, b2, b3,… be in arithmetic progression such that the common differences of both the series are prime numbers, if a5 = b9, a19 = b19 and b2 = 0 then a11 equals.
- A).
79
- B).
84
- C).
86
- D).
83
Questions 45 to 66 carry 3 marks each.
Q. 4.
The area of the quadrilateral bounded by Y-axis, the line x = 5, and the lines |x ‒ y| ‒ |x ‒ 5| = 2 is
Questions 45 to 66 carry 3 marks each.
Q. 5.
In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the ï¬gures ABP, APQ, and AQCD are in geometric progression. If the area of the ï¬gure AQCD is four times the area of triangle ABP, then BP : PQ : QC is
- A).
1 : 2 : 4
- B).
1 : 2 : 1
- C).
2 : 4 : 1
- D).
1 : 1 : 2
Questions 45 to 66 carry 3 marks each.
Q. 6.
A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ration a:b if the radius of the circle is r, then the area of the triangle is
- A).
abr2/2(a2 + b2)
- B).
abr2/a2 + b2
- C).
2abr2/a2 + b2
- D).
4abr2/a2 + b2
Questions 45 to 66 carry 3 marks each.
Q. 7.
If a certain amount of money is divided equally among n persons, each one receives Rs 352. However if two persons receives Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330. Then the maximum possible value of n is
Questions 45 to 66 carry 3 marks each.
Q. 8.
A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is
Questions 45 to 66 carry 3 marks each.
Q. 9.
Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a ï¬xed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total proï¬t of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
Questions 45 to 66 carry 3 marks each.
Q. 10.
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is
- A).
1620000
- B).
1296000
- C).
972000
- D).
1944000
Questions 45 to 66 carry 3 marks each.
Q. 11.
Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the ï¬rst year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to
- A).
33130
- B).
40991
- C).
45311
- D).
51311
Questions 45 to 66 carry 3 marks each.
Q. 12.
In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is
- A).
6:5
- B).
5:6
- C).
5:4
- D).
4:5
Questions 45 to 66 carry 3 marks each.
Q. 13.
Pipes A and C are ï¬ll pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to ï¬ll the empty tank. When pipes A, B and C are turned on together, the empty tank is ï¬lled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to ï¬ll the remaining tank. If Pipe A can ï¬ll the empty tank in less than ï¬ve hours, then the time taken, in minutes, by Pipe C to ï¬ll the empty tank is.
- A).
120
- B).
60
- C).
90
- D).
75
Questions 45 to 66 carry 3 marks each.
Q. 14.
Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% proï¬t. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total proï¬t made by Minu from all her transactions is Rs.500, then the percentage of proï¬t made by Minu when she sold the pair of sunglasses to Tanu is
- A).
26%
- B).
31.25%
- C).
52%
- D).
35.42%
Questions 45 to 66 carry 3 marks each.
Q. 15.
Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is
- A).
58.8
- B).
61.6
- C).
64.4
- D).
62.2
Questions 45 to 66 carry 3 marks each.
Q. 16.
Let k be the largest such that equation (x ‒ 1)2+ 2kx + 11 = 0 has no real roots. If y is apossible real number then the least possible value k/4y + 9y is
Questions 45 to 66 carry 3 marks each.
Q. 17.
Questions 45 to 66 carry 3 marks each.
Q. 18.
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
Questions 45 to 66 carry 3 marks each.
Q. 19.
Let a, b, m and n be natural numbers such that a > 1 and b >1. If am bn = 144145, then the largest possible value
- A).
580
- B).
289
- C).
290
- D).
579
Questions 45 to 66 carry 3 marks each.
Q. 20.
For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor
- A).
2m and n
- B).
2m and 3n
- C).
m and n
- D).
m and 2n
Questions 45 to 66 carry 3 marks each.
Q. 21.
Any non zero reaL number x,y such that y ≠ 3 and x/y < x + 3/y ‒ 3, will satisfy the condition.
- A).
x/y < y/x
- B).
If x < 0, then ‒x< y
- C).
If y > 10, then ‒x > y
- D).
If y < 0, then ‒x < y
Questions 45 to 66 carry 3 marks each.
Q. 22.
The sum of all possible value of x satisfying the equation 24x2 ‒2 2x2+x+16 +2 2x+30 = 0, is
- A).
3
- B).
5/2
- C).
3/2
- D).
1/2
