JEE Main · MathematicsEasy

$Find the coefficient of x^{2} in the expansion of (1 + x)^{5} .$

A. $5$
B. $10$
C. $15$
D. $20$

Show correct answer & step-by-step solution

Correct answer: B — $10$

Solution

The general term in the expansion of (1 + x)^{n} is given by^{n} C_{r} x^{r} . For r = 2 and n = 5, the coefficient is^{5} C_{2}, which equals \frac{5 \times 4}{2 \times 1} = 10 .

Attempt this question & track your score

Sign up free to answer, get instant scoring, and let SolveGini track which Mathematics topics you need to revise.

Attempt & Track Free →

More Binomial Theorem practice questions

$W ha t i s t h es u m o f t h e bin o mia l coe f f i c i e n t s in t h ee x p an s i o n o f (x + y)^{n} ?$
$W ha t i s t h e n u mb er o f t er m s in t h ee x p an s i o n o f (x + y)^{1} 0 ?$
$Find the value of 4C0 + 4C1 + 4C2 + 4C3 + 4C4.$
$W ha t i s t h e mi dd l e t er min t h ee x p an s i o n o f (x + 1)^{4} ?$
$The value of the sum of the series 20C0 - 20C1 + 20C2 - ... + 20C20 is equal to what?$
$Find the coefficient of x raised to the power of 7 in the expansion of (ax squared + 1/bx) raised to the power of 11.$
$Find the term independent of x in the expansion of (x + 1/x raised to the power of 2/3 - x raised to the power of 1/3 +$
$If the coefficients of three consecutive terms in the expansion of (1 + x) raised to the power of n are in the ratio 1:7$
$If the sum of the coefficients in the expansion of (x - 2y + 3z) raised to the power of n is 128, then find the value of$
$The value of the sum of the series sum from r=0 to n of (r+1) * nCr is:$
$I f t h es u m o f t h ecoe f f i c i e n t s in t h ee x p an s i o n o f (1 + 2 x)^{n} i s 6561, t h e n t h ecoe f f i c i e n t o f x^{4} in t h ee x p an s i o ni s :$
$I f t h ecoe f f i c i e n t so f t h r eeco n sec u t i v e t er m s in t h ee x p an s i o n o f (1 + x)^{n} a r e in t h er a t i o 1 : 7 : 42, t h e nni se q u a l t o :$

View all Binomial Theorem questions →