JEE (Main) Mathematics - Binomial Theorem: General and Middle Term MCQs (31-45)

31. In the expansion of \( (x + 3)^4 \), the general term is:
    a) \( T_r = \binom{4}{r} x^{4-r} 3^r \)
    b) \( T_r = \binom{r}{4} x^r 3^{4-r} \)
    c) \( T_r = \binom{4}{r} x^{r} 3^{r} \)
    d) \( T_r = \binom{4}{r} x^{4-r} 3^{4-r} \)
    Answer: a) \( T_r = \binom{4}{r} x^{4-r} 3^r \)
32. The middle term in the expansion of \( (x + y)^9 \) is:
    a) \( \binom{9}{4} x^4 y^5 \)
    b) \( \binom{9}{5} x^5 y^4 \)
    c) \( \binom{9}{3} x^6 y^3 \)
    d) \( \binom{9}{4} x^5 y^4 \)
    Answer: b) \( \binom{9}{5} x^5 y^4 \)
33. In the expansion of \( (x - 2)^6 \), the term containing \( x^2 \) is:
    a) \( \binom{6}{2} x^2 (-2)^4 \)
    b) \( \binom{6}{4} x^2 (-2)^2 \)
    c) \( \binom{6}{4} x^2 (-2)^3 \)
    d) \( \binom{6}{2} x^2 (-2)^3 \)
    Answer: a) \( \binom{6}{2} x^2 (-2)^4 \)
34. In the expansion of \( (3x + y)^4 \), the coefficient of \( x^3 \) is:
    a) \( 81 \)
    b) \( 36 \)
    c) \( 54 \)
    d) \( 27 \)
    Answer: a) \( 81 \)
35. In the expansion of \( (a + b)^{12} \), the term containing \( a^5b^7 \) is:
    a) \( \binom{12}{5} a^5 b^7 \)
    b) \( \binom{12}{7} a^5 b^7 \)
    c) \( \binom{12}{5} a^7 b^5 \)
    d) \( \binom{12}{7} a^5 b^7 \)
    Answer: a) \( \binom{12}{5} a^5 b^7 \)
36. In the expansion of \( (2x + 3)^5 \), the second term is:
    a) \( \binom{5}{1} 2x 3^4 \)
    b) \( \binom{5}{2} 2^2 x^2 3^3 \)
    c) \( \binom{5}{2} 2x^3 3^2 \)
    d) \( \binom{5}{2} 2x^2 3^3 \)
    Answer: d) \( \binom{5}{2} 2x^2 3^3 \)
37. The number of terms in the expansion of \( (x + y)^7 \) is:
    a) 7
    b) 8
    c) 6
    d) 9
    Answer: b) 8
38. In the expansion of \( (x + y)^8 \), the coefficient of \( x^5 y^3 \) is:
    a) \( \binom{8}{3} \)
    b) \( \binom{8}{5} \)
    c) \( \binom{8}{4} \)
    d) \( \binom{8}{2} \)
    Answer: b) \( \binom{8}{5} \)
39. In the expansion of \( (a + b)^9 \), the third term is:
    a) \( \binom{9}{2} a^7 b^2 \)
    b) \( \binom{9}{3} a^6 b^3 \)
    c) \( \binom{9}{2} a^6 b^3 \)
    d) \( \binom{9}{3} a^7 b^2 \)
    Answer: b) \( \binom{9}{3} a^6 b^3 \)
40. In the expansion of \( (x + y)^6 \), the coefficient of \( x^3 y^3 \) is:
    a) \( \binom{6}{3} \)
    b) \( \binom{6}{2} \)
    c) \( \binom{6}{4} \)
    d) \( \binom{6}{5} \)
    Answer: a) \( \binom{6}{3} \)
41. The coefficient of the term containing \( x^4 \) in the expansion of \( (2x + 3)^6 \) is:
    a) \( \binom{6}{2} 2^4 3^2 \)
    b) \( \binom{6}{3} 2^3 3^3 \)
    c) \( \binom{6}{4} 2^2 3^4 \)
    d) \( \binom{6}{2} 2^3 3^3 \)
    Answer: a) \( \binom{6}{2} 2^4 3^2 \)
42. In the expansion of \( (x + 4)^6 \), the coefficient of \( x^2 \) is:
    a) \( \binom{6}{2} 4^4 \)
    b) \( \binom{6}{2} 4^3 \)
    c) \( \binom{6}{4} 4^2 \)
    d) \( \binom{6}{2} 4^5 \)
    Answer: a) \( \binom{6}{2} 4^4 \)
43. The term \( T_5 \) in the expansion of \( (x + y)^8 \) is:
    a) \( \binom{8}{5} x^5 y^3 \)
    b) \( \binom{8}{4} x^4 y^4 \)
    c) \( \binom{8}{3} x^3 y^5 \)
    d) \( \binom{8}{2} x^6 y^2 \)
    Answer: a) \( \binom{8}{5} x^5 y^3 \)
44. What is the 4th term in the expansion of \( (x + 2)^7 \)?
    a) \( \binom{7}{4} x^3 2^4 \)
    b) \( \binom{7}{4} x^4 2^3 \)
    c) \( \binom{7}{3} x^4 2^4 \)
    d) \( \binom{7}{3} x^3 2^5 \)
    Answer: b) \( \binom{7}{4} x^4 2^3 \)
45. The middle term in the expansion of \( (a + b)^8 \) is:
    a) \( \binom{8}{4} a^4 b^4 \)
    b) \( \binom{8}{3} a^5 b^3 \)
    c) \( \binom{8}{5} a^3 b^5 \)
    d) \( \binom{8}{4} a^5 b^3 \)
    Answer: a) \( \binom{8}{4} a^4 b^4 \)

   l    Next Page >>

Note/Caution: studentsbizz.com does not promise a job or an interview in exchange for money. Fraudsters may ask you to pay under the pretext of a registration fee or refundable fee, but please be aware that legitimate employers will not require such payments.

Join in Our Groups

Home Latest Jobs Syllabus Projects Previous Question Papers Entrance Exam Notifications Multiple Choice Question

@ 2025 Students Bizz Platform. All Rights Reserved.