Mathematics › Binomial Theorem
Binomial Theorem Questions
326 questions across 10 subtopics — with step-by-step solutions.
Binomial Theorem for Negative Index(5)
- If the expansion in powers of of the funct... | Mathematics | TestHub
- If then the value of is | Mathematics | TestHub
- The coefficient ofin the expansion ofis | Mathematics | TestHub
- Ifis very small as compared to the value o... | Mathematics | TestHub
- If the coefficients ofandinareandrespectiv... | Mathematics | TestHub
Comparison between two numbers(2)
General(179)
- The coefficients of and in the expansion o... | Mathematics | TestHub
- If the sum of the coefficients in the expa... | Mathematics | TestHub
- and are positive integers and coefficient... | Mathematics | TestHub
- If denotes the number of combination of th... | Mathematics | TestHub
- The number of integral terms in the expans... | Mathematics | TestHub
- If is positive, the first negative term in... | Mathematics | TestHub
- The coefficient of in expansion of is | Mathematics | TestHub
- The coefficient of the middle term in the... | Mathematics | TestHub
- If the coefficients of th, th and th terms... | Mathematics | TestHub
- If the coefficient of in equals the coeffi... | Mathematics | TestHub
- For natural numbers if , and then is | Mathematics | TestHub
- In the binomial expansion of , the sum of... | Mathematics | TestHub
- The letters of the word TOUGH are written... | Mathematics | TestHub
- With 17 consonants and 5 vowels the number... | Mathematics | TestHub
- For , let and denote, respectively, the co... | Mathematics | TestHub
- In the binomial , if the ratio of the seve... | Mathematics | TestHub
- The coefficient of in the expansion of is | Mathematics | TestHub
- The term independent of in the expansion o... | Mathematics | TestHub
- If , then the value of is given by | Mathematics | TestHub
- The middle term in the expansion of in pow... | Mathematics | TestHub
- If then the coefficient of in it is | Mathematics | TestHub
- The number of terms in the expansion of ,... | Mathematics | TestHub
- The coefficient of the middle term in the... | Mathematics | TestHub
- The ratio of the coefficient of to the ter... | Mathematics | TestHub
- If the 7th term in the binomial expansion... | Mathematics | TestHub
- If for positive integers , the coefficient... | Mathematics | TestHub
- The coefficients of three consecutive term... | Mathematics | TestHub
- If is expanded in the ascending powers of... | Mathematics | TestHub
- The coefficient of in the binomial expansi... | Mathematics | TestHub
- The number of terms in the expansion of in... | Mathematics | TestHub
- If the coefficients ofandin the expansion... | Mathematics | TestHub
- The coefficient ofin the expansion of(wher... | Mathematics | TestHub
- Coefficient ofin the expansion ofis | Mathematics | TestHub
- The term independent ofin the binomial exp... | Mathematics | TestHub
- If the coefficient of the three successive... | Mathematics | TestHub
- The coefficient ofin the expansion ofis | Mathematics | TestHub
- The sum of coefficients of integral powers... | Mathematics | TestHub
- If the coefficients ofand, in the expansio... | Mathematics | TestHub
- The value ofis equal to: | Mathematics | TestHub
- If, thensatisfies the equation: | Mathematics | TestHub
- The coefficient ofin the expansion ofis | Mathematics | TestHub
- The coefficient ofin the binomial expansio... | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- The coefficient ofin the expansion of the... | Mathematics | TestHub
- The coefficient ofinis | Mathematics | TestHub
- If is the degree of the polynomial, and is... | Mathematics | TestHub
- Ifis the degree of the polynomial,andis th... | Mathematics | TestHub
- The greatest term in the expansion ofis | Mathematics | TestHub
- The coefficient of in the expansion of is... | Mathematics | TestHub
- The term independent ofin the expansion of... | Mathematics | TestHub
- A ratio of theterm from the beginning to t... | Mathematics | TestHub
- If the third term in the binomial expansio... | Mathematics | TestHub
- If some three consecutive coefficients in... | Mathematics | TestHub
- The total number of irrational terms in th... | Mathematics | TestHub
- The coefficient ofin the productis | Mathematics | TestHub
- If the coefficients ofand, are both zero,... | Mathematics | TestHub
- If the fourth term in the Binomial expansi... | Mathematics | TestHub
- The sum of the co-efficient of all even de... | Mathematics | TestHub
- The smallest natural number, such that the... | Mathematics | TestHub
- If the coefficient ofandin the expansion o... | Mathematics | TestHub
- If the fourth term in the binomial expansi... | Mathematics | TestHub
- The sum of the real values of for which th... | Mathematics | TestHub
- In the expansion ofifis the least value of... | Mathematics | TestHub
- If the constant term in the binomial expan... | Mathematics | TestHub
- Letbe such that. If the maximum value of t... | Mathematics | TestHub
- The natural number, for which the coeffici... | Mathematics | TestHub
- If the term independent ofin the expansion... | Mathematics | TestHub
- If the number of integral terms in the exp... | Mathematics | TestHub
- If for some positive integer, the coeffici... | Mathematics | TestHub
- The coefficient ofin the expansion ofin po... | Mathematics | TestHub
- The maximum value of the term independent... | Mathematics | TestHub
- For the natural numbersifandthen the value... | Mathematics | TestHub
- The sum of all those terms which are ratio... | Mathematics | TestHub
- If the constant term, in binomial expansio... | Mathematics | TestHub
- If the sum of the coefficients in the expa... | Mathematics | TestHub
- The ratio of the coefficient of the middle... | Mathematics | TestHub
- If the co-efficient ofandin the expansion... | Mathematics | TestHub
- If the coefficients ofinandinare equal, th... | Mathematics | TestHub
- Ifis the number of irrational terms in the... | Mathematics | TestHub
- Coefficient of in the expansion of is | Mathematics | TestHub
- Ifis the term, independent ofin the binomi... | Mathematics | TestHub
- A possible value offor which the ninth ter... | Mathematics | TestHub
- The coefficient of the term independent of... | Mathematics | TestHub
- The term independent ofin the expansion of... | Mathematics | TestHub
- If the greatest value of the term independ... | Mathematics | TestHub
- The number of rational terms in the binomi... | Mathematics | TestHub
- The coefficient ofin the expansion ofis: | Mathematics | TestHub
- The term independent ofin the expansion of... | Mathematics | TestHub
- If the fourth term in the expansion ofisth... | Mathematics | TestHub
- Let the coefficients of third, fourth and... | Mathematics | TestHub
- Let be an integer. If and , then is equal to: | Mathematics | TestHub
- The term independent ofin the expression ofis | Mathematics | TestHub
- Let for theterm in the binomial expansion... | Mathematics | TestHub
- If the coefficient ofin the binomial expan... | Mathematics | TestHub
- If the coefficients ofandin the expansion... | Mathematics | TestHub
- Let the coefficients of the middle terms i... | Mathematics | TestHub
- Let the coefficients ofandin the expansion... | Mathematics | TestHub
- If the sum of the coefficients in the expa... | Mathematics | TestHub
- The number of positive integerssuch that t... | Mathematics | TestHub
- The number of terms in the expansion of , is | Mathematics | TestHub
- The coefficient ofin the expressionis | Mathematics | TestHub
- Let the ratio of the fifth term from the b... | Mathematics | TestHub
- If the maximum value of the term independe... | Mathematics | TestHub
- If occurs in the rth term in the expansion... | Mathematics | TestHub
- If the coefficient ofin the expansion ofis... | Mathematics | TestHub
- The coefficient ofin the expansion ofis | Mathematics | TestHub
- If the co-efficient ofinand the co-efficie... | Mathematics | TestHub
- If the constant term in the binomial expan... | Mathematics | TestHub
- If the coefficients of in and in are equal... | Mathematics | TestHub
- The coefficient ofin the expansion ofis | Mathematics | TestHub
- Let he sum of the coefficient of first thr... | Mathematics | TestHub
- Letdenote the greatest integer. if the con... | Mathematics | TestHub
- Let the coefficients of three consecutive... | Mathematics | TestHub
- If theterm from the end in the binomial ex... | Mathematics | TestHub
- The absolute difference of the coefficient... | Mathematics | TestHub
- If the ratio of the fifth term from the be... | Mathematics | TestHub
- Let, be the smallest number such that the... | Mathematics | TestHub
- The middle term in the expansion of is | Mathematics | TestHub
- If the coefficient ofinand the coefficient... | Mathematics | TestHub
- Let the sixth term in the binomial expansi... | Mathematics | TestHub
- The coefficient of, in the expansion of, is | Mathematics | TestHub
- if the coefficients of three consecutive t... | Mathematics | TestHub
- The sum of the coefficients of three conse... | Mathematics | TestHub
- If the term withoutin the expansion ofis,... | Mathematics | TestHub
- Letbe the constant term in the binomial ex... | Mathematics | TestHub
- The largest natural numbersuch thatdividesis | Mathematics | TestHub
- Letandbe two nonzero real numbers. If the... | Mathematics | TestHub
- The number of integral terms in the expans... | Mathematics | TestHub
- Number of integral terms in the expansion... | Mathematics | TestHub
- If the coefficient ofin the expansion ofis... | Mathematics | TestHub
- If the term independent of in the expansio... | Mathematics | TestHub
- The coefficient ofin the expansion ofis eq... | Mathematics | TestHub
- Let . If , then is equal to: | Mathematics | TestHub
- The coefficient of the highest power of in... | Mathematics | TestHub
- Letand. Then : | Mathematics | TestHub
- If the second, third and fourth terms in t... | Mathematics | TestHub
- If the coefficients of and in the expansio... | Mathematics | TestHub
- The coefficient of in is . Then a possible... | Mathematics | TestHub
- The coefficient of term in the binomial ex... | Mathematics | TestHub
- If the constant term in the expansion of i... | Mathematics | TestHub
- The number of integers, between 100 and 10... | Mathematics | TestHub
- Let be the coefficients of seventh and thi... | Mathematics | TestHub
- The coefficient of in the expansion of is | Mathematics | TestHub
- In the expansion of, the sum of the coeffi... | Mathematics | TestHub
- Supposeare the coefficient of four consecu... | Mathematics | TestHub
- The sum of the coefficient of and in the b... | Mathematics | TestHub
- If the constant term in the expansion of ,... | Mathematics | TestHub
- Suppose A and B are the coefficients of an... | Mathematics | TestHub
- The least value of n for which the number... | Mathematics | TestHub
- For an integer , if the arithmetic mean of... | Mathematics | TestHub
- Let the coefficients of three consecutive... | Mathematics | TestHub
- If then is equal to | Mathematics | TestHub
- Let and be the coefficients of and respect... | Mathematics | TestHub
- The sum of all rational terms in the expan... | Mathematics | TestHub
- For some , let the coefficients of the 5 t... | Mathematics | TestHub
- The least value of n for which the number... | Mathematics | TestHub
- The sum of all rational terms in the expan... | Mathematics | TestHub
- Let be real numbers such that for every re... | Mathematics | TestHub
- In the expansion of , if the ratio of term... | Mathematics | TestHub
- If in the expansion of , the coefficients... | Mathematics | TestHub
- If in the expansion of , the coefficients... | Mathematics | TestHub
- The term independent of in the expansion o... | Mathematics | TestHub
- The largest such that divides 50 ! is: | Mathematics | TestHub
- For some , let the coefficients of the 5 t... | Mathematics | TestHub
- The sum of all rational terms in the expan... | Mathematics | TestHub
- The number of integral terms in the expans... | Mathematics | TestHub
- Let the coefficients of three consecutive... | Mathematics | TestHub
- If , where , then is equal to : | Mathematics | TestHub
- The remainder, when is divided by 23 , is... | Mathematics | TestHub
- Let and be the coefficients of and respect... | Mathematics | TestHub
- Suppose A and B are the coefficients of an... | Mathematics | TestHub
- In the expansion of , if the ratio of term... | Mathematics | TestHub
- The number of irrational terms in the expa... | Mathematics | TestHub
- Number of irrational terms in the expansio... | Mathematics | TestHub
- The greatest integer less than or equal to... | Mathematics | TestHub
- Let n be an odd natural number greater tha... | Mathematics | TestHub
- Let \left(1+x+x^{2}\right)^{20}(2 x+1)=a_{... | Mathematics | TestHub
- Find the maximum value of \left(\log _{2^{... | Mathematics | TestHub
- In the expansion of (1+x)^{m}(1-x)^{n} , t... | Mathematics | TestHub
Integral and Fractional Part of a Number(8)
- The positive integer just greater than is | Mathematics | TestHub
- The positive integer just greater than is | Mathematics | TestHub
- If is a positive integer, then is | Mathematics | TestHub
- Letand. Ifdenotes the greatest integer, then | Mathematics | TestHub
- The sum of all rational terms in the expan... | Mathematics | TestHub
- The number of integral terms in the expans... | Mathematics | TestHub
- Let n \in \mathbb{N} and (3 \sqrt{3}+5)^{2... | Mathematics | TestHub
- Find the greatest integer less than the nu... | Mathematics | TestHub
Logarithmic and Exponential series(31)
- If then | Mathematics | TestHub
- Let m be the smallest positive integer suc... | Mathematics | TestHub
- If, thenequal to | Mathematics | TestHub
- Let, then the value of is | Mathematics | TestHub
- Supposeholds for some positive integerThen... | Mathematics | TestHub
- The value ofis equal to: | Mathematics | TestHub
- If the sum of the coefficients of all even... | Mathematics | TestHub
- Letthenis equal to | Mathematics | TestHub
- Letdenote greatest integer less than or eq... | Mathematics | TestHub
- Letbe a positive integer. Let. Ifthenis eq... | Mathematics | TestHub
- If the sum of the coefficients of all the... | Mathematics | TestHub
- Ifis equal to, whereis odd, thenis equal t... | Mathematics | TestHub
- If the sum of the co-efficients of all the... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- If then is equal to | Mathematics | TestHub
- Letbe the sum of the coefficients of the o... | Mathematics | TestHub
- The mean of the coefficients ofin the bino... | Mathematics | TestHub
- The sum, of the coefficients of the firstt... | Mathematics | TestHub
- The sum of the series , is equal to | Mathematics | TestHub
- If , then the distance of the point from t... | Mathematics | TestHub
- If , where , then is equal to : | Mathematics | TestHub
- If , then is equal to ______ | Mathematics | TestHub
- If then is equal to | Mathematics | TestHub
- If , then is equal to _______ | Mathematics | TestHub
- Coefficient of x^{10} in the expansion of... | Mathematics | TestHub
- \sum_{n=1}^{\infty} \frac{2 n^{2}+n+1}{n!}= | Mathematics | TestHub
- If |x|<1 and y=x-\frac{x^{2}}{2}+\frac{x^{... | Mathematics | TestHub
- The sum of the series 1+\frac{1}{4.2!}+\fr... | Mathematics | TestHub
- \sum_{\mathrm{k}=1}^{\infty} \frac{1}{\mat... | Mathematics | TestHub
- \frac{1^{2}}{1!}+\frac{1^{2}+2^{2}}{2!}+\f... | Mathematics | TestHub
- The coefficient of x^{4} in \left(e^{x}-1\... | Mathematics | TestHub
Miscellaneous/Mixed(10)
- The coefficient of in the expansion of is | Mathematics | TestHub
- If the sum of odd numbered terms and the s... | Mathematics | TestHub
- If the third term in the expansion of is t... | Mathematics | TestHub
- Let, wheredenote binomial coefficients. Th... | Mathematics | TestHub
- For nonnegative integersand, let. For posi... | Mathematics | TestHub
- \sum_{K=1}^{10}\frac{(-1)^{K-1}}{K}\cdot\l... | Mathematics | TestHub
- In the expansion of \left(7^{\frac{1}{3}}+... | Mathematics | TestHub
- The last two digits of the number (23)^{14... | Mathematics | TestHub
- For the following questions, match the ite... | Mathematics | TestHub
- Consider \mathrm{S}=\{1,2,3,4, \ldots \ldo... | Mathematics | TestHub
Multinomial theorem(14)
- The term independent of in the expansion ofis | Mathematics | TestHub
- The coefficient of in the expansion of is | Mathematics | TestHub
- In the expansion of, the coefficient ofis | Mathematics | TestHub
- LetThenis equal to ______ | Mathematics | TestHub
- If the coefficient ofin the expansion ofis... | Mathematics | TestHub
- If the constant term in the expansion ofis... | Mathematics | TestHub
- Let. Ifand, thenis equal to | Mathematics | TestHub
- The constant term in the expansion ofis __... | Mathematics | TestHub
- The coefficient ofinis __________ . | Mathematics | TestHub
- Let . If , then k is equal to . | Mathematics | TestHub
- The coefficient of x^{6} in the expansion... | Mathematics | TestHub
- The sum of all the coefficient of those te... | Mathematics | TestHub
- If \left(x^{2}+2 x+4\right)^{n}=\sum_{r=0}... | Mathematics | TestHub
- For the multinomial expansion (2 x-3 y+z)^... | Mathematics | TestHub
Properties of Binomial coefficients(38)
- Match the following sums with their correc... | Mathematics | TestHub
- If denote the binomial coefficientsin the... | Mathematics | TestHub
- If represent the terms in the expansion of... | Mathematics | TestHub
- The number of values of satisfying the equ... | Mathematics | TestHub
- Ifandare in A.P., thencan be | Mathematics | TestHub
- If a, b, c are three natural numbers in AP... | Mathematics | TestHub
- The number of ordered pairsfor whichwherei... | Mathematics | TestHub
- Ifandare the greatest values ofandrespecti... | Mathematics | TestHub
- Ifandthen the value ofis equal to: | Mathematics | TestHub
- Ifthen the ratiois | Mathematics | TestHub
- If, thenis equal to : | Mathematics | TestHub
- If the and the terms in the expansion of a... | Mathematics | TestHub
- If , then is equal to : | Mathematics | TestHub
- The coefficient of x^{50} in the expansion... | Mathematics | TestHub
- The Coefficient of x^{9} in \left(x-{ }^{2... | Mathematics | TestHub
- The value of { }^{12} \mathrm{C}_{2}+{ }^{... | Mathematics | TestHub
- Match List - I with List - II: LIST ILIST... | Mathematics | TestHub
- If \{x\} represents the fractional part of... | Mathematics | TestHub
- Match the values of the following expressi... | Mathematics | TestHub
- If \mathrm{a}_{\mathrm{n}}=\sum_{\mathrm{r... | Mathematics | TestHub
- If C_{r}=\binom{n}{r} , then sum of the se... | Mathematics | TestHub
- In the expansion of (1+x)^{70} , the sum o... | Mathematics | TestHub
- \sum_{r=0}^{n} \frac{n-3 r+1}{n-r+1} \frac... | Mathematics | TestHub
- Match the binomial and counting results. C... | Mathematics | TestHub
- If a, b, c form an A.P., find the sum of c... | Mathematics | TestHub
- Statement I: For positive integer n<20, n!... | Mathematics | TestHub
- The value of the expression { }^{10} C_{0}... | Mathematics | TestHub
- Match the values of the following expressi... | Mathematics | TestHub
- Match the binomial and counting results. C... | Mathematics | TestHub
- The sum S_{n}=\sum_{k=0}^{n}(-1)^{k}\cdot{... | Mathematics | TestHub
- If \left(1+x+x^{2}\right)^{25}=a_{0}+a_{1}... | Mathematics | TestHub
- If \sum_{r=0}^{n}\left\{\frac{{ }^{n} C_{r... | Mathematics | TestHub
- If are the binomial coefficients in the ex... | Mathematics | TestHub
- The greatest binomial coefficient in (1+x)... | Mathematics | TestHub
- For 0 \leq i<j \leq n , let S=\sum \sum(i+... | Mathematics | TestHub
- If \sum_{r=0}^{n} \frac{r}{\binom{n}{r}}=\... | Mathematics | TestHub
- If \sum_{\mathrm{r}=0}^{\mathrm{n}-1}\left... | Mathematics | TestHub
- Let S=\sum_{n=1}^{\infty} \frac{n^{2}}{\su... | Mathematics | TestHub
Remainder and Divisibility Problems(32)
- The remainder left out when is divided by... | Mathematics | TestHub
- The general solution of is | Mathematics | TestHub
- For is divisible by | Mathematics | TestHub
- Ifis divided by, then the remainder is | Mathematics | TestHub
- If the fractional part of the numberisthen... | Mathematics | TestHub
- Ifdenotes the fractional part of the numbe... | Mathematics | TestHub
- If the remainder whenis divided byis, then... | Mathematics | TestHub
- Ifis divided bythen the remainder is _______. | Mathematics | TestHub
- when divided byleaves the remainder | Mathematics | TestHub
- The remainder whenis divided byis | Mathematics | TestHub
- The remainder whenis divided byis | Mathematics | TestHub
- The remainder whenis divided byis | Mathematics | TestHub
- The remainder on dividingbyis _____. | Mathematics | TestHub
- The remainder whenis divided byis _____ . | Mathematics | TestHub
- The remainder whenis divided byis | Mathematics | TestHub
- If, then the remainder whenis divided byis | Mathematics | TestHub
- The remainder on dividingbyis _____ . | Mathematics | TestHub
- Among the statements : is divisible by . i... | Mathematics | TestHub
- is divisible by | Mathematics | TestHub
- The remainder whenis divided by, is _____ . | Mathematics | TestHub
- root of a numberisandroot of another numbe... | Mathematics | TestHub
- The remainder whenis divided byis | Mathematics | TestHub
- Fractional part of the number is equal to | Mathematics | TestHub
- Let the numberleave the remainderwhen divi... | Mathematics | TestHub
- The remainder, whenis divided byis | Mathematics | TestHub
- The remainder when is divided by 21 is____... | Mathematics | TestHub
- Remainder whenis divided byis equal to _____. | Mathematics | TestHub
- The remainder when is divided by 7 is equa... | Mathematics | TestHub
- The remainder, when is divided by 23 , is... | Mathematics | TestHub
- The product of the last two digits of is | Mathematics | TestHub
- Statement I: \binom{30}{15}-1 is divisible... | Mathematics | TestHub
- Statement I: \binom{30}{15}-1 is divisible... | Mathematics | TestHub
Specific Terms(7)
- Coefficient of x^{2009} in \left(1+x+x^{2}... | Mathematics | TestHub
- Coefficient of x^{6} in \left((1+x)\left(1... | Mathematics | TestHub
- Statement I: The constant term of \left(x+... | Mathematics | TestHub
- In (2 x+3 y)^{12}=T_{1}+\cdots+T_{13} , pu... | Mathematics | TestHub
- The coefficient of the term independent of... | Mathematics | TestHub
- In the expansion of \left(\sqrt[3]{\frac{a... | Mathematics | TestHub
- The ratio of the second to third term in (... | Mathematics | TestHub
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