If the number of terms in the expansion of is 28, then the sum of the coefficients of all the terms in this expansion is
64
2187
243
243
Statement − 1: For every natural number n ≥ 2
Statement −2: For every natural number n ≥ 2,
Statement −1 is false, Statement −2 is true
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
If A = and I = , then which one of the following holds for all n ≥ 1, by the principle of mathematical induction
An = nA – (n – 1)I
An = 2n-1A – (n – 1)I
An = nA + (n – 1)I
An = nA + (n – 1)I
Let S(K) = 1 +3+5+..... (2K-1) = 3+K2. Then which of the following is true?
S(1) is correct
Principle of mathematical induction can be used to prove the formula
S(K) ≠S(K+1)
S(K) ≠S(K+1)
The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8 m/s2. The time taken by the particle to move the second metre is
(√2-1)/2 S
(√2+1)/2 S
(1 + √2)S
(√2-1)S
Prove by induction that for n N, n2 + n is an even integer (n 1)
n = 1, n2 + n = 2 is an even integer
Let for n = k, k2 + k is even
Now for n = k + 1.
(k + 1)2 + (k + 1) - (k2 + k)
= k2 + 2k + 1 + k + 1 - k2 - k = 2k + 2
which is even integer, also k2 + k is integer
Hence (k + 1)2 + (k + 1) is also an even integer.
Hence n2 + n is even integer for all n N.
A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t - 6t2 + t3. Its acceleration will be zero at
t = 1 unit time
t = 2 unit time
t = 3 unit time
t = 4 unit time