If n is a positive integer, then the number of terms in the expansion of `(x+a)^n` is

If n is a positive integer, then the number of terms in the expansion of `(x+a)^n` is
by

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If n is a positive integer, then the number of terms in the expansion of `(x+a)^n` is
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If `a gt 0` and `n` is any positive integer, then the sign of `root(n)(a)` is _______.

Description : If `a gt 0` and `n` is any positive integer, then the sign of `root(n)(a)` is _______.

Last Answer : If `a gt 0` and `n` is any positive integer, then the sign of `root(n)(a)` is _______.

If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number . -Maths 9th

Description : If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number . -Maths 9th

Last Answer : We know that product of two rational number is always a rational number. Hence if a is a rational number then a2 = a x a is a rational number, a3 = 4:2 x a is a rational number. ∴ an = an-1 x a is a rational number.

If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number . -Maths 9th

Description : If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number . -Maths 9th

Last Answer : We know that product of two rational number is always a rational number. Hence if a is a rational number then a2 = a x a is a rational number, a3 = 4:2 x a is a rational number. ∴ an = an-1 x a is a rational number.

Consider the following statements : 1. a^n + b^n is divisible by a + b if n = 2k + 1, where k is a positive integer. -Maths 9th

Description : Consider the following statements : 1. a^n + b^n is divisible by a + b if n = 2k + 1, where k is a positive integer. -Maths 9th

Last Answer : Statement (1) is correct as for k = 1, n = 2 × 1 + 1 = 3. ∴ a3 + b3 = (a + b) (a2 + b2 – ab) which is divisible by (a + b), statement (2) is also correct as for k = 1, n = 2, ∴ a2 – b2 = (a – b) (a + b) which is divisible by (a – b).

The positive integer value of `n gt 3` satisfying the equation `(1)/(sin((pi)/(n)))=(1)/(sin((2pi)/(n)))+(1)/(sin((3pi)/(n)))` is

Description : The positive integer value of `n gt 3` satisfying the equation `(1)/(sin((pi)/(n)))=(1)/(sin((2pi)/(n)))+(1)/(sin((3pi)/(n)))` is

Last Answer : The positive integer value of `n gt 3` satisfying the equation `(1)/(sin((pi)/(n)))=(1)/(sin((2pi)/(n)))+(1)/(sin((3pi)/(n)))` is

Let `a`, `b`, `c`, `d` are positive integer such that `log_(a)b=3//2` and `log_(c)d=5//4`. If `a-c=9`, then value of `(b-d)` is equal to

Description : Let `a`, `b`, `c`, `d` are positive integer such that `log_(a)b=3//2` and `log_(c)d=5//4`. If `a-c=9`, then value of `(b-d)` is equal to

Last Answer : Let `a`, `b`, `c`, `d` are positive integer such that `log_(a)b=3//2` and `log_(c)d=5//4`. If `a-c=9` ... ` is equal to A. `20` B. `93` C. `10` D. `1`

The least positive integer x, which satisfies the inequality `log_(log(x/2)) (x^2-10x+22) > 0` is equal to

Description : The least positive integer x, which satisfies the inequality `log_(log(x/2)) (x^2-10x+22) > 0` is equal to

Last Answer : The least positive integer x, which satisfies the inequality `log_(log(x/2)) (x^2-10x+22) > 0` is equal to A. `3` B. `4` C. `7` D. `8`

If `a lt 0` and n is any odd integer, then the sign of `root(n)(a)` is _______

Description : If `a lt 0` and n is any odd integer, then the sign of `root(n)(a)` is _______

Last Answer : If `a lt 0` and n is any odd integer, then the sign of `root(n)(a)` is _______

Why is the following a poor definition for a whole number. A whole number is a positive integer.?

Description : Why is the following a poor definition for a whole number. A whole number is a positive integer.?

Last Answer : Zero is a whole number.

A number with both integer and a fractional part has digits raised to both positive and negative powers of 2 in a decimal number system. a) True b) False

Description : A number with both integer and a fractional part has digits raised to both positive and negative powers of 2 in a decimal number system. a) True b) False

Last Answer : Answer: b Explanation: In a decimal number system, a number with both integer and a fractional part has digits raised to both positive and negative powers of 10 and not 2. e.g. 22.34 = 2 * 101 + 2 * 100 + 3 * 10-1 + 4 * 10-2

What is the remainder when positive integer ‘p’ is divided by 3? (A) ‘p’ is an even number (B) ‘p’ is a perfect square a) If statement (A) alone is sufficient to answer the question but statement (B) alone is not sufficient.

Description : What is the remainder when positive integer p' is divided by 3? (A) p' is an even number (B) p' is a perfect square a) If statement (A) alone is sufficient to answer the ... sufficient to answer the question e) If the two statements taken together are still not sufficient to answer the question.

Last Answer : Using (A), we can have p' as 2/4/6/8 etc. we cant determine remainder when divided by 3. Using (B), we can have p' as 1/4/9/16 etc. we cant determine remainder when divided by 3. Using ... be 1/0 (4/16 leave remainder 1, 36 remainder 0). So, we cant determine using both statements. Answer: e)

Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Description : Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Last Answer : Let f(x) = xn + an x + a will be the factor of xn + an if f(-a) = 0 Now f(-a) = (-a)n + an = 0 (since n is a odd +ve integer) Thus (x +a) is a factor of xn + an .

Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Description : Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Last Answer : Let f(x) = xn + an x + a will be the factor of xn + an if f(-a) = 0 Now f(-a) = (-a)n + an = 0 (since n is a odd +ve integer) Thus (x +a) is a factor of xn + an .

2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Description : 2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Last Answer : Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r

Use Euclid’s Division Lemma to show that the cube of any positive integer is either of the form 9m, 9m + 1 or 9m + 8 -Maths 10th

Description : Use Euclid’s Division Lemma to show that the cube of any positive integer is either of the form 9m, 9m + 1 or 9m + 8 -Maths 10th

Last Answer : Let us consider a and b where a be any positive number and b is equal to 3. According to Euclid's Division Lemma a = bq + r where r is greater than or equal to zero and less than b (0 ≤ r < b) a = 3q + r so ... 8 Where m = (3q3 + 6q2 + 4q)therefore a can be any of the form 9m or 9m + 1 or, 9m + 8.

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Description : Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. -Maths 10th

Last Answer : Let a' be any positive integer and b = 6. ∴ By Euclid's division algorithm, we have a = bq + r, 0 ≤ r ≤ b a = 6q + r, 0 ≤ r ≤ b [ ∵ b = 6] where q ≥ 0 and r = 0,1, 2, 3, 4, ... numbers. Therefore, any odd integer can be expressed is of the form 6q + 1, or 6q + 3, or 6q + 5 where q is some integer

An integer is chosen at random from the first two hundred positive integers. What is the probability that the integer chosen is divisible by 6 or 8 ? -Maths 9th

Description : An integer is chosen at random from the first two hundred positive integers. What is the probability that the integer chosen is divisible by 6 or 8 ? -Maths 9th

Last Answer : As there are 200 integers, total number of exhaustive, mutually exclusive and equally likely cases, i.e, n(S) = 200 Let A : Event of integer chosen from 1 to 200 being divisible by 6⇒ n(A) = 33 \(\bigg(rac{200}{6}=33rac{1}{3}\ ... (rac{25}{200}\) - \(rac{8}{200}\) = \(rac{50}{200}\) = \(rac{1}{4}\).

The values of the remainder r, when a positive integer a is divided by 3 are (a) 0, 1, 2(b) Only 1 (c) Only 0 or 1 (d) 1, 2

Description : The values of the remainder r, when a positive integer a is divided by 3 are (a) 0, 1, 2(b) Only 1 (c) Only 0 or 1 (d) 1, 2

Last Answer : (a) 0, 1, 2

In the expansion of various power of `(x+y)^(n)` if the expansion contains 49 times, then it is the expansion of ___________

Description : In the expansion of various power of `(x+y)^(n)` if the expansion contains 49 times, then it is the expansion of ___________

Last Answer : In the expansion of various power of `(x+y)^(n)` if the expansion contains 49 times, then it is the expansion of ___________

A number n is a perfect cube only if there is an integer m such that n=__________

Description : A number n is a perfect cube only if there is an integer m such that n=__________

Last Answer : A number n is a perfect cube only if there is an integer m such that n=__________

n2 – 1 is divisible by 8, if n is (a) an integer (b) a natural number (c) an odd integer (d) an even integer

Description : n2 – 1 is divisible by 8, if n is (a) an integer (b) a natural number (c) an odd integer (d) an even integer

Last Answer : (c) an odd integer

Suppose the function y and a fuzzy integer number around -4 for x are given as y=(x-3)2+2 Around -4={(2,0.3), (3,0.6), (4,1), (5,0.6), (6,0.3)} respectively. Then f(Around - 4) is given by: (A) {(2,0.6), (3,0.3), (6,1), (11,0.3)} (B) {(2,0.6), (3,1), (6,1), (11,0.3)} (C) {(2,0.6), (3,1), (6,0.6), (11,0.3)} (D) {(2,0.6), (3,0.3), (6,0.6), (11,0.3)}

Description : Suppose the function y and a fuzzy integer number around -4 for x are given as y=(x-3)2+2 Around -4={(2,0.3), (3,0.6), (4,1), (5,0.6), (6,0.3)} respectively. Then f(Around - 4) is given by: (A) {(2,0.6), (3,0.3), ... 6), (3,1), (6,0.6), (11,0.3)} (D) {(2,0.6), (3,0.3), (6,0.6), (11,0.3)}

Last Answer : (C) {(2,0.6), (3,1), (6,0.6), (11,0.3)}

Aromatic molecules contain __________ π electrons. (a) no (b) 4n + 2 (with n being an integer) (c) 4n + 2 (with n being 0.5) (d) 4n (with n an integer)

Description : Aromatic molecules contain __________ π electrons. (a) no (b) 4n + 2 (with n being an integer) (c) 4n + 2 (with n being 0.5) (d) 4n (with n an integer)

Last Answer : 4n + 2 (with n being an integer)

If there are n integers to sort, each integer has d digits and each digit is in the set {1,2, ..., k}, radix sort can sort the numbers in: (A) O(d n k) (B) O(d nk) (C) O((d+n)k) (D) O(d(n+k))

Description : If there are n integers to sort, each integer has d digits and each digit is in the set {1,2, ..., k}, radix sort can sort the numbers in: (A) O(d n k) (B) O(d nk) (C) O((d+n)k) (D) O(d(n+k))

Last Answer : (D) O(d(n+k))

Find the middle term or terms of the expansion of `(x+5y)^(9)`

Description : Find the middle term or terms of the expansion of `(x+5y)^(9)`

Last Answer : Find the middle term or terms of the expansion of `(x+5y)^(9)`

Write the first, the middle and the last terms in the expansion of `(x^(2)+1)^(3)`

Description : Write the first, the middle and the last terms in the expansion of `(x^(2)+1)^(3)`

Last Answer : Write the first, the middle and the last terms in the expansion of `(x^(2)+1)^(3)`

Is the speed of the ship related to the number of terms in the Taylor series expansion of a function?

Description : Is the speed of the ship related to the number of terms in the Taylor series expansion of a function?

Last Answer : I sat here with an answer and realised I totally misread your question! The direct answer to your question is Yes, but the conditions in which a ship sails is so varied that to try to give a ship a ... though. I can see you were trying to give a certain mpg' rating but it isn't relevant enough.

In the expansion of `(x+y)^(n)` , if the exponent of x in second term is 10, what is the exponent of y in 11th term.

Description : In the expansion of `(x+y)^(n)` , if the exponent of x in second term is 10, what is the exponent of y in 11th term.

Last Answer : In the expansion of `(x+y)^(n)` , if the exponent of x in second term is 10, what is the exponent of y in 11th term.

In the expansion of `(x+y)^(n),T_(r+1)`= __________

Description : In the expansion of `(x+y)^(n),T_(r+1)`= __________

Last Answer : In the expansion of `(x+y)^(n),T_(r+1)`= __________

The correct way to round off a floating number x to an integer value is (A) y = (int)(x+0.5) (B) y = int(x+0.5) (C) y = (int)x+0.5 (D) y = (int)((int)x+0.5)

Description : The correct way to round off a floating number x to an integer value is (A) y = (int)(x+0.5) (B) y = int(x+0.5) (C) y = (int)x+0.5 (D) y = (int)((int)x+0.5)

Last Answer : (A) y = (int)(x+0.5)

Workdone in a free expansion process is  A.zero  B.minimum  C.maximum  D.positive

Description : Workdone in a free expansion process is  A.zero  B.minimum  C.maximum  D.positive

Last Answer : Answer: A

Let R be a relation on the set of integers given by a = 2^k .b for some integer k. Then R is -Maths 9th

Description : Let R be a relation on the set of integers given by a = 2^k .b for some integer k. Then R is -Maths 9th

Last Answer : (c) equivalence relationGiven, a R b = a = 2k .b for some integer. Reflexive: a R a ⇒ a = 20.a for k = 0 (an integer). True Symmetric: a R b ⇒ a = 2k b ⇒ b = 2-k . a ⇒ b R a as k, -k are both ... = 2k1 + k2 c, k1 + k2 is an integer. ∴ a R b, b R c ⇒ a R c True ∴ R is an equivalence relation.

If Ram knows that y is an integer greater than 2 and less than 7 and Hari knows that y is an integer greater than 5 and less than 10, then they may correctly conclude that (A) y can be exactly determined (B) y may be either of two values (C) y may be any of three values (D) there is no value of y satisfying these conditions

Description : If Ram knows that y is an integer greater than 2 and less than 7 and Hari knows that y is an integer greater than 5 and less than 10, then they may correctly conclude that (A) y can be exactly ... two values (C) y may be any of three values (D) there is no value of y satisfying these conditions

Last Answer : (A) y can be exactly determined

In backward areas, term loans for expansion or setting up a new unit are available at __________ . A. concessional terms. B. differential terms. C. standard terms. D. specific terms.

Description : In backward areas, term loans for expansion or setting up a new unit are available at __________ . A. concessional terms. B. differential terms. C. standard terms. D. specific terms.

Last Answer : A. concessional terms.

If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Description : If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Last Answer : answer:

Solve for `x` (where `[*]` denotes greatest integer function and `{*}` represent fractional part function) `(i) [2x]=1` `(ii) {x}^(2)+[x]=2` `(iii) 6{

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Solve the following inequalities (where `[*]` denotes greatest integer function and `{*}` represent fractional part function) `(i) [x+[x]] lt 0` `(ii)

Description : Solve the following inequalities (where `[*]` denotes greatest integer function and `{*}` represent fractional part function) `(i) [x+[x]] lt 0` `(ii)

Last Answer : Solve the following inequalities (where `[*]` denotes greatest integer function and `{*}` represent fractional part ... `(iii) {x} lt (1)/(2)`

Solve the following equations (where `[*]` dentoes greatest integer function and `{*}` represent fractional part function) `(i) 2[x]+3[x]=4x-1` `(ii)

Description : Solve the following equations (where `[*]` dentoes greatest integer function and `{*}` represent fractional part function) `(i) 2[x]+3[x]=4x-1` `(ii)

Last Answer : Solve the following equations (where `[*]` dentoes greatest integer function and `{*}` represent fractional part function) ... }` `(iii) [x]+2{-x}=3x`

A three dimensional array in ‘C’ is declared as int A[x][y][z]. Here, the address of an item at the location A[p][q][r] can be computed as follows (where w is the word length of an integer): (A) &A[0][0][0]+w(y*z*q+z*p+r) (B) &A[0][0][0]+w(y*z*p+z*q+r) (C) &A[0][0][0]+w(x*y*p+z*q+r) (D) &A[0][0][0]+w(x*y*q+z*p+r)

Description : A three dimensional array in C' is declared as int A[x][y][z]. Here, the address of an item at the location A[p][q][r] can be computed as follows (where w is the word length of an integer): (A) &A[0][0][0]+w(y*z*q+z*p+r) (B) &A ... *q+r) (C) &A[0][0][0]+w(x*y*p+z*q+r) (D) &A[0][0][0]+w(x*y*q+z*p+r)

Last Answer : Answer: B

Which of the following terms denotes the polar molecules or negative ions clustered about a central positive ion? w) ligands x) isomers y) complex ions z) dipoles

Description : Which of the following terms denotes the polar molecules or negative ions clustered about a central positive ion? w) ligands x) isomers y) complex ions z) dipoles

Last Answer : ANSWER: W -- LIGAND

The value of n = 1 in the polytropic process indicates it to be  (a) reversible process  (b) isothermal process  (c) adiabatic process  (d) irreversible process  (e) free expansion process.

Description : The value of n = 1 in the polytropic process indicates it to be  (a) reversible process  (b) isothermal process  (c) adiabatic process  (d) irreversible process  (e) free expansion process.

Last Answer : Answer : b

The solution to a transportation problem with ‘m’ rows and ‘n’ columns is feasible if the number of positive allocations are: a. m + n b. m x n c. m +n – 1 d. m +n + 1

Description : The solution to a transportation problem with ‘m’ rows and ‘n’ columns is feasible if the number of positive allocations are: a. m + n b. m x n c. m +n – 1 d. m +n + 1

Last Answer : c. m +n – 1

If `""^(12)C_(r)(4)^(12-r)(x)^(12-3r)` is a contant term in an expansion, then r = __________

Description : If `""^(12)C_(r)(4)^(12-r)(x)^(12-3r)` is a contant term in an expansion, then r = __________

Last Answer : If `""^(12)C_(r)(4)^(12-r)(x)^(12-3r)` is a contant term in an expansion, then r = __________

Write the given sets in roster form: (a). P = {y: y is an integer and -4 < y < 6}. (b). Q = {y: y is a natural number which is <8} (c). R = {y: y is a 2 digit natural number in which the sum of its digits is 9} -Other

Description : Write the given sets in roster form: (a). P = {y: y is an integer and -4 < y < 6}. (b). Q = {y: y is a natural number which is

Last Answer : (i) A = {x: x is an integer and †3 < x < 7} The elements of this set are †2, †1, 0, 1, 2, 3, 4, 5, and 6 only. Therefore, the given set can be written in roster form as A = {†2, †... and 80 only. Therefore, this set can be written in roster form as C = {17, 26, 35, 44, 53, 62, 71, 80}}.

Is 9.9 a natural,whole,integer, rational,irrational, or real number?

Description : Is 9.9 a natural,whole,integer, rational,irrational, or real number?

Last Answer : rational

Is the integer 2 the only even prime number?

Description : Is the integer 2 the only even prime number?

Last Answer : What is the answer ?

Is -0.462 a whole number or integer?

Description : Is -0.462 a whole number or integer?

Last Answer : Neither because it is a decimal number

A number is between -1 and -5 what is least possible integer value of its opposite?

Description : A number is between -1 and -5 what is least possible integer value of its opposite?

Last Answer : 4