JEE Main Mathematics: Binomial Theorem Practice Questions

13 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$F in d t h ecoe f f i c i e n t o f x^{2} in t h ee x p an s i o n o f (1 + x)^{5} .$
Easy
Q2.
$Find the value of 4C0 + 4C1 + 4C2 + 4C3 + 4C4.$
Easy
Q3.
$W ha t i s t h e mi dd l e t er min t h ee x p an s i o n o f (x + 1)^{4} ?$
Easy
Q4.
$W ha t i s t h e n u mb er o f t er m s in t h ee x p an s i o n o f (x + y)^{1} 0 ?$
Easy
Q5.
$W ha t i s t h es u m o f t h e bin o mia l coe f f i c i e n t s in t h ee x p an s i o n o f (x + y)^{n} ?$
Easy
Q6.
$If the coefficients of three consecutive terms in the expansion of (1 + x) raised to the power of n are in the ratio 1:7:42, then find the value of n.$
Medium
Q7.
$If the sum of the coefficients in the expansion of (x - 2y + 3z) raised to the power of n is 128, then find the value of n.$
Medium
Q8.
$The value of the sum of the series 20C0 - 20C1 + 20C2 - ... + 20C20 is equal to what?$
Medium
Q9.
$Find the coefficient of x raised to the power of 7 in the expansion of (ax squared + 1/bx) raised to the power of 11.$
Medium
Q10.
$Find the term independent of x in the expansion of (x + 1/x raised to the power of 2/3 - x raised to the power of 1/3 + 1) - (x - 1/x raised to the power of 2/3$
Medium
Q11.
$I f t h es u m o f t h ecoe f f i c i e n t s in t h ee x p an s i o n o f (1 + 2 x)^{n} i s 6561, t h e n t h ecoe f f i c i e n t o f x^{4} in t h ee x p an s i o ni s :$
Hard
Q12.
$I f t h ecoe f f i c i e n t so f t h r eeco n sec u t i v e t er m s in t h ee x p an s i o n o f (1 + x)^{n} a r e in t h er a t i o 1 : 7 : 42, t h e nni se q u a l t o :$
Hard
Q13.
$The value of the sum of the series sum from r=0 to n of (r+1) * nCr is:$
Hard

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