Math Chapter Wise

EnglishEMRS PGT-2023

Q01.The greatest positive integer k, for which 49k + 1 is a factor of the sum 49125 +49124 +.... +492 +1 is:

A60 B63 C65 D32

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EnglishEMRS PGT-2023

Q02.If three consecutive coefficients in the binomial expansion of (x + 1)n in power of x are in the ratio 2:15: 70, then the average of these three coefficients is:

A227 B232 C625 D964

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EnglishEMRS PGT-2023

Q03.The coefficient of x7 in the expansion (1+x)10 + x(1+x)9 + x2 (1+x)8 +...+x10 is:

A330 B210 C120 D440

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EnglishEMRS PGT-2023

Q04.The coefficient of xn in the expansion of (1+x) (1–x)n is:

A(–1)n/(1–n) B(–1)n–1/(n–1)2 C(–1)n–1/n Dn–1

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EnglishEMRS PGT-2023

Q05.The two successive terms in the expansion of () 24 1+ x whose coefficients are in the ratio 1: 4 are:

A3rd/and 4th B4th/and 5th C5th/and 6th D2nd/and 3rd

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EnglishBihar (TRE 2.0)-2023

Q06.The fourth term in the binomial expansion 6 1 x + x of is

A2 15 x B20x2 C20x DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q07.The value of (99)5 is

A9509901999 B9509900499 C9909500495 DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q08.If n is a positive integer and n k k C = C, then 2 n 3 k k =1 k–1 C k C ∑ ∑ equal:

A() () 2 1 n n 1 n 2 12 + + B()() 2 1 n n 1 n 2 12 + + C()() 2 1 n n 1 n 2 12 + + D()() 1 n n 1 n 2 12 + +

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EnglishEMRS TGT-2023

Q09.If () n n r r r =0 1+ x = C x, ∑ ∑ then 1 2 0 1 C C 1+ 1+ C C... 3 n 2 n C C 1+ 1+ C C –1 is equal to:

A() n–1 n 1 n –1! + B() n n 1 n! + C() n 1 n! + D() n–1 n n –1!

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EnglishKVS PGT 2023

Q10.If the rth term in the expansion of 12 2 1 2x x − is without x, then r is:

A7 B8 C9 D10

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EnglishKVS PGT 2023

Q11.If the coefficients of (r - 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1: 3: 5 then value of n is:

A8 B4 C3 D7

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EnglishKVS PGT 2023

Q12.The coefficients of xn in the expansion of (1 + x)2n and (1 + x)2n - 1 are in the ratio:

A1: 2 B2: 1 C3: 1 D1: 3

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EnglishNVS PGT 2022

Q13.If (1 + x)n = C0 + C1x + C2x2 +.... + Cnxn, then value of 0 1 2 n C C C C + + +...+ 2 3 4 n + 2 is equal to:

A() n 2 1 n n 1 + B()() n 2 1 n 1 n 2 + + + C()() n 1 n.2 1 n 1 n 2 + + + D() n n 1 2 n n 1 − +

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EnglishNVS PGT 2022 OAVS TGT 2022

Q14.The term independent of ‘x’ in 9 2 1 x − is:

A84 B–84 C126 D–126

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EnglishKVS PGT 2022

Q15.The term without x in the expansion of 6 2 3 1 x 2 3x − is: 6 2 3 1 x 2 3x −

A20/3 B5/24 C5/12 D135/4

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EnglishKVS PGT 2022

Q16.The total number of terms in the expansion of (x+a)100 +(x −a)100 after simplification is:

A202 B51 C50 D52

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EnglishOAVS TGT 2022

Q17.The sum of the coefficients in the expansion of (x + 1)5 is:

A32 B40 C22 D20

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EnglishRPSC PGT 2022

Q18.If (1 + a)12 = C0+C1a+C2a2 +……+ C12a12, then value of 2. C C C C 3 2 4 12 + 3. + 4. +... + 12. C C C C 1 2 3 11 is

A66 B55 C78 D77

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EnglishDSSSB PGT 2021

Q19.The sum of coefficients of integral power of x in the binomial expansion of () 50 1 – 2 x is-

A() 50 1 30 –1 2 B() 50 1 2 1 2 + C() 50 1 3 –1 2 D() 50 1 3 2

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EnglishOAVS TGT 2019

Q20.The value of a if 17th and 18th terms in the expansion of (2+a)50 are equal is:

A1 B0 C2 D–1

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