Eamcet - Maths - Binomial Theorem Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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2.C2+6.C3+12.C4+……….+n(n-1)Cn =

  

  

  

  

If (3 + 4i) is a root of x2+px+q=0, then (p, q) is:

  

  

  

  

Which term of (2x-3y)12 when x=1, y=5/2 numerically greatest?

  

  

  

  

If the third term in the expansion of (1/x+ xlog10 x)5 is 1, then x=

  

  

  

  

1.nC0+41.nC1+42.nC2+43.nC3+……..+4n.nCn =

  

  

  

  

mCr+ mCr-1nC1+mCr-2. nC2+………..+ nCr =

  

  

  

  

3.C0-5.C1+7.C2-9.C3+…………(n+1) terms =

  

  

  

  

If the sum of the coefficients of (1+2x)n is 6561, then the greatest coefficient is

  

  

  

  

The coefficient of x10 in 1-2x+3x2/1-x is

  

  

  

  

The coefficient of xn in(1+x)2/(1-x)2 is

  

  

  

  

C2+C4+C6+……….. =

  

  

  

  

If n is odd then C02-C12+C22-……….+(-1)n Cn2 =

  

  

  

  

The coefficient of x2 in (1+x)2(8-x)-1/3 is

  

  

  

  

The number of non-zero terms in the expansion of (1+3√2x)9+(1+3√2x)9is equal to:

  

  

  

  

The coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:7:42, then n=

  

  

  

  

x2n-1+y2n-1 is divisible by x+y if n is

  

  

  

  

The number of non zero terms in the expansion of (a+b)20 – (a-b)20 is

  

  

  

  

C1/1 – C2/2 + C3/3 – C4/4 +………. +(-1)n-1 Cn/n =

  

  

  

  

The coefficient of xk in the expansion of E=1+(1+x)+(1+x)2+……..+(1+x)n is

  

  

  

  

If nεN, n is odd then n(n2-1) is divisible by

  

  

  

  

Coefficient of x50 in (1+x)1000+2x(1+x)999+3x2(1+x)998+……..+1001x1000 is

  

  

  

  

The term independent of x in the expansion of (1+x+2x3)(3x2/2-1/3x/)9 is

  

  

  

  

The general term of (2a-3b)-1/2 is

  

  

  

  

The 4th term of (1-2x)-1 when x=1/3 is

  

  

  

  

If the sum of odd terms and the sum of even terms in the expansion of (x+a)n are p and q respectively then p2+q2=

  

  

  

  

The number of non zero terms in the expansion of (8+2)101 - (8-2)101 is

  

  

  

  

The ratio of the coefficient of x15 to the term independent of x in (x2+2/x)15 is

  

  

  

  

The coefficient of x2 in1+x2/(1-x)3 is

  

  

  

  

If the coefficients of (2r+1)th term and (4r+5)th term in the expansion of (1+x)10 are equal then r=

  

  

  

  

The coefficient of x7 in (1-2x+3x2-4x3+……..∞)-4 is

  

  

  

  

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