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

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

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

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

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

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

If `0.2 y + 10.2 gt 11, " then " y gt` _______

Description : If `0.2 y + 10.2 gt 11, " then " y gt` _______

Last Answer : If `0.2 y + 10.2 gt 11, " then " y gt` _______

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).

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`

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

Number of positive integral solution of the equation `|x^(2)-3x-3| gt |x^(2)+7x-13|` is/are

Description : Number of positive integral solution of the equation `|x^(2)-3x-3| gt |x^(2)+7x-13|` is/are

Last Answer : Number of positive integral solution of the equation `|x^(2)-3x-3| gt |x^(2)+7x-13|` is/are A. `0` B. `1` C. `2 D. `3`

If the sum of the roots of a quadratic equation, is positive and product of the roots is negative, the numerically greater root has `"_____"` sign. [p

Description : If the sum of the roots of a quadratic equation, is positive and product of the roots is negative, the numerically greater root has `"_____"` sign. [p

Last Answer : If the sum of the roots of a quadratic equation, is positive and product of the roots is negative, ... root has `"_____"` sign. [positive/negative]

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)

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 \(\bigg(rac{200}{6}=33rac{1}{3}\ ... (rac{25}{200}\) - \(rac{8}{200}\) = \(rac{50}{200}\) = \(rac{1}{4}\).

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)

If `Delta G^(@)gt 0` for a reaction then :

Description : If `Delta G^(@)gt 0` for a reaction then :

Last Answer : If `Delta G^(@)gt 0` for a reaction then : A. `K_(P) gt 1` B. `K_(P) lt 1` C. The products predominate in the equilibrium mixture D. None

If `(x^(y))^z =2^(8)`then find the maximum possible value of (x)(y)(z) where x,y,z`gt`0

Description : If `(x^(y))^z =2^(8)`then find the maximum possible value of (x)(y)(z) where x,y,z`gt`0

Last Answer : If `(x^(y))^z =2^(8)`then find the maximum possible value of (x)(y)(z) where x,y,z`gt`0 A. 16 B. 12 C. 256 D. 24

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 .

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

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))

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)}

if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive root

Description : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive root

Last Answer : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the ... `1` D. third term is `(-1+sqrt(11))/(2)`

Statement -I: If `alpha gt beta gt 1`, then `(alpha^(sqrt(log_(alpha)beta)))/(beta^(sqrt(log_(beta)alpha)))` is greater than 1. Statement-2 : `log_(c)

Description : Statement -I: If `alpha gt beta gt 1`, then `(alpha^(sqrt(log_(alpha)beta)))/(beta^(sqrt(log_(beta)alpha)))` is greater than 1. Statement-2 : `log_(c)

Last Answer : Statement -I: If `alpha gt beta gt 1`, then `(alpha^(sqrt(log_(alpha)beta)))/(beta^(sqrt(log_( ... . D. Statement -1 is false, statement -2 is ture.

Two parallel long wires carry currents `i_(1) "and" i_(2)` with `i_(1) gt i_(2)`.When the currents are in the same direction then the magnetic field m

Description : Two parallel long wires carry currents `i_(1) "and" i_(2)` with `i_(1) gt i_(2)`.When the currents are in the same direction then the magnetic field m

Last Answer : Two parallel long wires carry currents `i_(1) "and" i_(2)` with `i_(1) gt i_(2)`.When the currents are in the same ... 4` B. `5:3` C. `7:11` D. `11:7`

Find the maximum value of the function `(log x)/x " when "x gt 0`.

Description : Find the maximum value of the function `(log x)/x " when "x gt 0`.

Last Answer : Find the maximum value of the function `(log x)/x " when "x gt 0`.

Number of solution of `sinx cosx-3cosx+4sinx-13 gt 0` in `[0,2pi]` is equal to

Description : Number of solution of `sinx cosx-3cosx+4sinx-13 gt 0` in `[0,2pi]` is equal to

Last Answer : Number of solution of `sinx cosx-3cosx+4sinx-13 gt 0` in `[0,2pi]` is equal to A. `0` B. `1` C. `2` D. `4`

Solve the following inequalities `(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1` `(iii)log_((x-1)/(x-5))(x-2) gt 0` `(iv) log_(

Description : Solve the following inequalities `(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1` `(iii)log_((x-1)/(x-5))(x-2) gt 0` `(iv) log_(

Last Answer : Solve the following inequalities `(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1` ... gt 0` `(iv) log_(x)(x^(3)-x^(2)-2x) lt 3`

If `Delta H gt 0` and `Delta S gt 0`, the reaction proceeds spontaneously when :-

Description : If `Delta H gt 0` and `Delta S gt 0`, the reaction proceeds spontaneously when :-

Last Answer : If `Delta H gt 0` and `Delta S gt 0`, the reaction proceeds spontaneously when :- A. `Delta H gt 0` B. ... Delta S` C. `Delta H = T Delta S` D. None

How many grams of LiOH is formed from 25.0 g of CaOH given the following equation... Ca(OH)2 plus Li2CO3 ----- and gt CaCO3 plus 2Li(OH) What is the answer and how did you get it?

Description : How many grams of LiOH is formed from 25.0 g of CaOH given the following equation... Ca(OH)2 plus Li2CO3 ----- and gt CaCO3 plus 2Li(OH) What is the answer and how did you get it?

Last Answer : The chemical reaction is:Li2CO3 + Ca(OH)2 = 2 LiOH + CaCO3Molar maass of LiOH is 23,95 g; molar mass of calcium hydroxide is 74,093 g.74,093 g Ca(OH)2----------------2.23,95 g LiOH25 g Ca(OH)2----------------------xx = (25 x 2 x 23,95)/74,093 = 16,2 g LiOH

If x^2 + mx + n = 0 and x^2 + px + q = 0 have a common root, then the common root is -Maths 9th

Description : If x^2 + mx + n = 0 and x^2 + px + q = 0 have a common root, then the common root is -Maths 9th

Last Answer : Let α be the common root ∴α2+pα+q=0 ...........(1) and α2+qα+p=0 ........ (2) Solving (1) & (2), we get, p2−q2α2​=q−pα​=q−p1​∴α=q−pp2−q2​ and α=1 ⇒q−pp2−q2​=1 ⇒p2−q2=q−p (or) (p2−q2)+(p−q)=0 ⇒(p−q)[p+q+1]=0 ⇒p−q=0 or p+q+1=0

If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

Description : If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

Last Answer : If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

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

If `a^(p/q)=root(q)(k)`, then `k=` _______.

Description : If `a^(p/q)=root(q)(k)`, then `k=` _______.

Last Answer : If `a^(p/q)=root(q)(k)`, then `k=` _______.

Point of contra-flexure is a (a) Point where Shear force is maximum (b) Point where Bending moment is maximum (c) Point where Bending moment is zero (d) Point where Bending moment=0 but also changes sign from positive to negative

Description : Point of contra-flexure is a (a) Point where Shear force is maximum (b) Point where Bending moment is maximum (c) Point where Bending moment is zero (d) Point where Bending moment=0 but also changes sign from positive to negative

Last Answer : (d) Point where Bending moment=0 but also changes sign from positive to negative

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 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)`

What integer would represent ten degrees below 0?

Description : What integer would represent ten degrees below 0?

Last Answer : -10

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

Is 0.36 a integer?

Description : Is 0.36 a integer?

Last Answer : Yo mum

If a is an integer variable, a=7/3; will return a value A) 2.5 B) 3 C) 0 D) 2

Description : If a is an integer variable, a=7/3; will return a value A) 2.5 B) 3 C) 0 D) 2

Last Answer : D) 2