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
A^{n} = n^{A} – (n – 1)I
A^{n} = 2^{n-1}A – (n – 1)I
A^{n} = nA + (n – 1)I
A^{n} = nA + (n – 1)I
Let S(K) = 1 +3+5+..... (2K-1) = 3+K^{2}. 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)
Maximum sum of coefficient in the expansion of (1 – x sinθ + x^{2} )^{n} is
1
2^{n}
3^{n}
3^{n}
The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8 m/s^{2}. 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
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 - 6t^{2} + t^{3}. Its acceleration will be zero at
t = 1 unit time
t = 2 unit time
t = 3 unit time
t = 4 unit time