CBSE Class 11 (Commerce) Binomial Theorem — practice questions
74 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 11 (Commerce) Binomial Theorem in the app →The expansion of $(a + b)^n$ contains how many terms?The general term in the expansion of $(x + 2)^{10}$ is:The angle 90° in radians is:The function f(x) = tan x has vertical asymptotes at:The number of terms in a binomial expansion is one more than the:How many terms are there in the expansion of a bracket squared?In successive terms, the powers of the first quantity:In successive terms, the powers of the second quantity:In every term of the expansion, the sum of the two indices equals the:The triangular array of binomial coefficients is named after:Pascal's triangle is also known in India as:Blaise Pascal lived during which years?The row of Pascal's triangle for index 5 reads:Why is Pascal's triangle awkward for a large index?The general rule for expansion is built using the concept of:In the first term of the expansion, the index of a is:In the first term of the expansion, the index of b is:In the last term of the expansion, the index of b is:How many terms are in the expansion of a bracket raised to five?How many terms are in the expansion of a bracket raised to twelve?In the expansion of a bracket raised to four, the sum of indices is:A binomial raised to the ninth power expands into how many terms?How many terms does the expansion of (2x + 5)^12 contain?In the expansion of (a + b)^n, the power of b in the first term isEvery term in the expansion of (x + y)^7 has a total degree ofIn (a + b)^3, the term containing a squared times b carries the numberAmong the entries 1, 4, 6, 4, 1 for index 4, the centre one isThe mathematician behind Pascal's triangle belonged to which country?In ancient Indian mathematics, Pascal's triangle was known asWhich ancient Indian scholar gave the Meru-Prastara arrangement of coefficients?Adding every number in the fifth-index row of Pascal's triangle givesWhich number multiplies x^5 once (2x + 3y)^5 is fully expanded?After expanding (2x + 3y)^5, the x^4 y term is multiplied byExpand (2x + 3y)^5; the number attached to x^3 y^2 isWhich number sits in front of y^5 when (2x + 3y)^5 is written out?Expanding (x + 2)^6 gives a cubic term whose multiplier isSetting x = 0 in (x + 2)^6 leaves the valueThe linear term of (x + 2)^6 has multiplierPutting x = 1 in (x + 2)^6, the sum of all its coefficients isFor (x - 2y)^5, find the multiplier of the x^3 y^2 termIn the expansion of (x - y)^n, the signs of successive termsThe value of 7C0 + 7C1 + 7C2 + ... + 7C7 isThe alternating sum nC0 - nC1 + nC2 - ... + (-1)^n nCn is equal toThe sum of the binomial coefficients 10C0 + 10C1 + ... + 10C10 isEvaluate 3C0 + 3 x 3C1 + 9 x 3C2 + 27 x 3C3.Computing 102 cubed as (100 + 2)^3 givesComputing 101 to the fourth power as (100 + 1)^4 givesIn showing (1.01)^1000000 > 10,000, the term 1000000C1 x 0.01 equalsWhen 6^n - 5n is divided by 25, the remainder is alwaysFor every positive integer n, 9^(n+1) - 8n - 9 is divisible byFor distinct integers a and b, a^n - b^n always has which factor?Using the result for (a + b)^4 - (a - b)^4, (sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4 equalsThe value of (sqrt2 + 1)^6 + (sqrt2 - 1)^6 isUsing the first three terms of its expansion, (0.99)^5 is approximatelyChu-shi-kie of China wrote the coefficient triangle inWho first introduced the term binomial coefficients, around 1544?Oughtred listed binomial coefficients for n = 1 to 10 in which year?Bombelli (1572) gave the coefficients of (a + b)^n up to which n?Pingla wrote his book Chhanda shastra aroundPascal's treatise containing the binomial theorem was published posthumously inIn what year did the French thinker Blaise Pascal pass away?The standard proof of the binomial theorem for positive integers n usesIn the inductive step, kCr + kC(r-1) is replaced byFor any non-negative integer n, the value of nC0 isThe combination nCr is defined asHow many binomial coefficients appear in the expansion of (a + b)^20?In summation form, (a + b)^n is the sum over k ofWriting (x^2 + 3/x)^4 out, the leading term isIn (x^2 + 3/x)^4, the term in x^5 has multiplierThe final term of (x^2 + 3/x)^4 isWriting (1 - x)^6 out, the x term has multiplierUsing the first two terms of (1 + 0.1)^10000, the partial sum isThe binomial theorem for a finite expansion of (a + b)^n needs n to be aExpanded fully, (2x - 3)^6 begins with