If g = 10100 and H = 10g, then in which interval does g! = 1 . 2 .3 ........ 10100 lie?
A. | 10H < g! < H |
B. | H < g! < 10^{H} |
C. | 10H < g! < 10 |
D. | 10H < g! <10^{H} |
Option: D Explanation :
Choose k, so that 10^{H} = g^{λ}= 10^{100k} Click on Discuss to view users comments. |
What is the harmonic mean of two numbers whose geometric mean and arithmetic mean is 8 and 5 respectively?
A. | 12.8 |
B. | 12 |
C. | 13.5 |
D. | 14.6 |
Option: A Explanation :
(GM)^{2}= HM x AM Click on Discuss to view users comments. |
Anil wants to divide Rs.100 into a number of bags so that one can ask for any amount between Rs.1 and Rs.100, he can give the proper amount by giving certain number of these bags without taking out the amount from them. What is the minimum number of bags he will require if each bag has whole number of rupees?
A. | 5 |
B. | 6 |
C. | 7 |
D. | 8 |
Option: C Explanation : If Anil has to give 1 rupee he needs a bag with Re.1. For 2 rupees he had two bags with Re.1 each or Rs.2. bag. To have minimum bags, he has a bag with Rs. 2. Now with the two bags he can give Rs.3. So next he will require a bag with Rs.4. With these three he can give Rs.5. Rs.6 and Rs.7 and next bag will be one containing Rs.8 and so on. Thus he would have bags with Re.1. 2. 4. 8. 16. 32. Sum of which is 63 and remaining 37 can be put in the last bag. So total number of bags is 7. Click on Discuss to view users comments. |
When x + y + z = 9 and xy + yz + zx = 11, then x3 - y3 - z3 - 3xyz equals
A. | 384 |
B. | 192 |
C. | 432 |
D. | 48 |
Option: C Explanation : x^{3} - y^{3} - z^{3 }- 3xyz = (x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx) = 9[(x + y + z)2 - 3(xy + yz + zx)] = 9(81 - 33) = 432. Click on Discuss to view users comments. |
HCF and LCM of two numbers is given. It is possible to ind out the two numbers uniquely if
I. either sum or difference between the two numbers is known.
II. HCF of two numbers = LCM of two numbers.
III. (LCM/HCF)= Prime number.
A. | I and II only |
B. | II only |
C. | II and III only |
D. | I, II and III |
Option: D Explanation :
Let HCF be h and LCM be l. Click on Discuss to view users comments. |