How many pairs of integer (a, b) are possible such that a2 – b2 = 288?
Solve the inequality x3 – 5x2 + 8x – 4 > 0.
x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.
What is the sum of 12 + 32 + 52 …….312?
What is the remainder when x4 + 5x3 – 3x2 + 4x + 3 is divided by x + 2?
If x4 – 8x3 + ax2 – bx + 16 = 0 has positive real roots, find a – b.
4x3 + ax2 – bx + 3 divided by x – 2 leaves remainder 2, divided by x + 3 leaves remainder 3. Find remainder when it is divided by x + 2.
How many of the following are factors of 3200 – 5100?
1. 7
2. 16
3. 53
4. 12
x3 – 18x2 + bx – c = 0 has positive real roots, p, q and z. If geometric mean of the roots is 6, find b.
What is the value of 27x3 + 18x2y + 12xy2 + y3 when x = 4, y = – 8?
A sequence of numbers is defined as 2 = an – an-1. Sn is sum upto n terms in this sequence and a3 = 5. How many values m, n exist such than Sm – Sn = 65?
6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to?
1(1!) + 2(2!) + 3(3!) + 4(4!)………….50(50!) is a multiple of prime P. P lies in the range........?
What is the sum of ?
2 + 6 + 10 + 14 ………..upto n term is given by Sn. How many of the following statements are true?
1. S2m – S2k could be a multiple of 16
2. 18Sn is a perfect square for all n
3. S2n > 2Sn for all n > 1
4. Sm+n > Sm + Sn for all m, n > 1
What is the sum of all numbers less than 200 that are either prime or have more than 3 factors?
What is the sum of .... 19 terms or 7 + 13 + 21 + 31 + 43 + 57 + 73... 19 terms?
= ?
x3 – 4x2 + mx – 2 = 0 has 3 positive roots, two of which are p and . Find m.
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