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

  

  

  

  

k.C0+k2.C1/2+K2. C2/3+.…………+kn+1.Cn/n+1 =

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If the first three terms of (1+ax)n are 1,6x,6x2 then (a,n)=

  

  

  

  

(2-)5 + (2+)5 =

  

  

  

  

The coefficient of x6 in (1+x+x2+x3+x4+x5)6 is

  

  

  

  

If the 3rd, 4th and 5th terms of (x+a)n are 60, 160 and 240 respectively then (x,a,n)=

  

  

  

  

The positive integer which is just greater than (1+0.0001)10000 is

  

  

  

  

The coefficient of x5 in the expression of (1+x)21+(1+x)22+……+(1+x)30 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 (x+a)100 + (x-a)100 is

  

  

  

  

If Tr+1 is the term independent of x in (3x-5/x3)8 then r=

  

  

  

  

Larger of 199100+200100and 201100 is

  

  

  

  

C2+C4+C6+……….. =

  

  

  

  

The 3rd term of 4 (3x-y3)is

  

  

  

  

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

  

  

  

  

The point which divides the line segment joining the points( 1,-1,2), (2,3,7) in the ratio -2:3 is

  

  

  

  

C0+C1/2+C3/3+ …………Cn/n+1+ =

  

  

  

  

Sum of the last 20 coefficients in the expansion of (1+x)39, when expanded in ascending powers of x, is

  

  

  

  

Middle term in the expansion of (2x-3/x)15is

  

  

  

  

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

  

  

  

  

The sum of the coefficients of even powers of x in the expansion of (1+x+x2)15 is

  

  

  

  

(1.03)19 =

  

  

  

  

C0+4.C1+7.C2+……(n+1) terms =

  

  

  

  

2.C0+22.C1/2+23.C3/3+……..+2n+1.Cn/n+1 =

  

  

  

  

The 4th term of 6(x+2/x2)6 is

  

  

  

  

If the coefficients of 2nd, 3rd, 4th terms in the expansion of (1+x)2n are in A.P. then

  

  

  

  

C0+C1/2+C2/22+C3/23+.....Cn/2n

  

  

  

  

(2n+1)C0-(2n+1)C1+…………. -(2n+1)C2n =

  

  

  

  

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