If a1, a2, ....., an are distinct positive real numbers such that a1 + a2 + ..... + an = 1, then -Maths 9th

If a1, a2, ....., an are distinct positive real numbers such that a1 + a2 + ..... + an = 1, then -Maths 9th
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Let a1, a2, ..... an be positive real numbers such that a1a2a3 ...... an = 1. Then (1 + a1) (1 + a2) ..... (1 + an) is -Maths 9th

Description : Let a1, a2, ..... an be positive real numbers such that a1a2a3 ...... an = 1. Then (1 + a1) (1 + a2) ..... (1 + an) is -Maths 9th

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If a1, a2, a3 ....... an are positive real numbers whose product is a fixed number ‘c’, then the minimum value of a1 + a2 ..... + an–1 + 2an is -Maths 9th

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If a1, a2, .... an are positive numbers such that a1.a2.a3 .... an = 1, then their sum is -Maths 9th

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If a, b, c, d are four distinct positive real numbers and if 3s = a + b + c + d, then -Maths 9th

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If x, y, z are distinct positive numbers different from 1, such that -Maths 9th

Description : If x, y, z are distinct positive numbers different from 1, such that -Maths 9th

Last Answer : (d) 1logy x. logz x - logx x = \(rac{ ext{log}\,x}{ ext{log}\,y}\) . \(rac{ ext{log}\,x}{ ext{log}\,z}\) - 1 = \(rac{ ext{(log}\,x^2)}{ ext{log}\,y.\, ext{log}\,z}\) - 1Similarly, logx y.logz y - logy y = ... log z = 0 (if a + b + c = 0, then a3 + b3 + c3 = 3abc) ⇒ log xyz = 0 ⇒ xyz = 1.

For three distinct positive numbers p, q and r, if p + q + r = a, then -Maths 9th

Description : For three distinct positive numbers p, q and r, if p + q + r = a, then -Maths 9th

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If a, b, c are positive real numbers such that a + b + c = p, then 1/a+1/b+1/c is greater than -Maths 9th

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If three positive real numbers, a, b, c are such that a + b + c = 1, then the minimum value of -Maths 9th

Description : If three positive real numbers, a, b, c are such that a + b + c = 1, then the minimum value of -Maths 9th

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Description : Two ores A1 and A2 of a metal M show the following reactivity: `A_(1)=CuCo_(3).Cu(OH)_(3),S=Cu` `P=Cu_(2)I_(2): G=SO_(2)` . Then `A_(2)` is

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If a1 and a2 are the relative volatilities when the pressure in the distillation column is 1 and 2 atm respectively. Pick out the correct statement. (A) a1 = a2 (B) a1 = 2a2 (C) a1 = 0.5 a2 (D) None of these

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Description : The average marks scored by two Class A1 and A2 students are 120 and 130 respectively. If 8 students are moved from Class A2 to Class A1 and the average marks of the two Class get interchanged. Find the total number ... average marks scored by the 8 students who moved is 150 A) 25 B) 30 C) 35 D) 40

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For positive real numbers a, b, c, the least value of a^(logb – logc) + b^(logc – loga) + c^(loga – logb) is -Maths 9th

Description : For positive real numbers a, b, c, the least value of a^(logb – logc) + b^(logc – loga) + c^(loga – logb) is -Maths 9th

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If x, y, z are three positive numbers, then the minimum value of -Maths 9th

Description : If x, y, z are three positive numbers, then the minimum value of -Maths 9th

Last Answer : hope its clear and understandable

Let a, b, c be positive numbers, then a/(b+c) + b/(c+a) + c/(a+b) is -Maths 9th

Description : Let a, b, c be positive numbers, then a/(b+c) + b/(c+a) + c/(a+b) is -Maths 9th

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Let a, b, c be positive numbers lying in the interval (0, 1], then a/(1+b+ca)+b/(a+c+ab)+c/(1+a+bc) is -Maths 9th

Description : Let a, b, c be positive numbers lying in the interval (0, 1], then a/(1+b+ca)+b/(a+c+ab)+c/(1+a+bc) is -Maths 9th

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If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 +c2. -Maths 9th

Description : If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 +c2. -Maths 9th

Last Answer : Find a2 + b2 +c2.

If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 +c2. -Maths 9th

Description : If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 +c2. -Maths 9th

Last Answer : Find a2 + b2 +c2.

If a,b,c are all non-zero and a + b + c = 0, prove that a2/bc + b2/ca+ c2/ab = 3. -Maths 9th

Description : If a,b,c are all non-zero and a + b + c = 0, prove that a2/bc + b2/ca+ c2/ab = 3. -Maths 9th

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The product (a + b) (a – b) (a2 – ab + b2) (a2 + ab + b2) is equal to (a) a6 + b6 (b) a6 – b6 (c) a3 – b3 (d) a3 + b3 -Maths 9th

Description : The product (a + b) (a – b) (a2 – ab + b2) (a2 + ab + b2) is equal to (a) a6 + b6 (b) a6 – b6 (c) a3 – b3 (d) a3 + b3 -Maths 9th

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If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2 -Maths 9th

Description : If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2 -Maths 9th

Last Answer : (a+b+c)2=a2+b2+c2+2ab+2bc+2ca =a2+b2+c2+2(ab+bc+ca) Given, ⇒92=a2+b2+c2+2(23) ⇒81−46=a2+b2+c2 ∴a2+b2+c2=35

If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c. -Maths 9th

Description : If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c. -Maths 9th

Last Answer : ( a + b + c )^2 = a^2 + b^2 + c^2 + 2( ab + bc + ca ) => ( a + b + c )^2 = 16 + 2×10 => ( a + b + c )^2 = 36 => a + b + c = Root 36 = 6

Prove that a2 + b2 + c2 – ab – bc – ca is always non-negative for all values of a, b and c. -Maths 9th

Description : Prove that a2 + b2 + c2 – ab – bc – ca is always non-negative for all values of a, b and c. -Maths 9th

Last Answer : Sol-2(a2+b2+c2-ab-bc-ca)/2 multiplying & dividing by 2 ...

If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + be + ca. -Maths 9th

Description : If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + be + ca. -Maths 9th

Last Answer : (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca = a2 + b2 + c2 + 2(ab + bc + ca) 0 = 16 + 2(ab + bc + ca) 2(ab + bc + ca) = - 16 (ab + bc + ca) = -8

If a, b, c, d are positive reals such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the relation -Maths 9th

Description : If a, b, c, d are positive reals such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the relation -Maths 9th

Last Answer : answer:

On the set R of all real numbers, a relation R is defined by R = {(a, b) : 1 + ab > 0}. Then R is -Maths 9th

Description : On the set R of all real numbers, a relation R is defined by R = {(a, b) : 1 + ab > 0}. Then R is -Maths 9th

Last Answer : (a) Reflexive and symmetric only(a, a) ∈ R ⇒ 1 + a . a = 1 + a2 > 0 V real numbers a ⇒ R is reflexive (a, b) ∈ R ⇒ 1 + ab > 0 ⇒ 1 + ba > 0 ⇒ (b, a) ∈ R ⇒ R is symmetricWe observe that \(\big(1,rac{1}{2}\big) ... }{2},-1\big)\) ∈ Rbut (1, - 1) ∉ R as 1 + 1 (-1) = 0 \( ot>\) 0 ⇒ R is not transitive.

If a, b, c, x, y, z are all positve real numbers, then -Maths 9th

Description : If a, b, c, x, y, z are all positve real numbers, then -Maths 9th

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If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

Description : If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

Last Answer : (d) An equivalence relationWe can check the given properties as follows: Reflexive: Let (a, b) ∈ N x N. Then (a, b) ∈ N ⇒ a + b = b + a (Communtative law of Addition) ⇒ (a, b) R (b, a) ⇒ (a, b) R (a, ... , f) ⇒ (a, b) R (e, f) on N x N so R is transitive.Hence R is an equivalence relation on N N.

If r is real number such that |r| < 1 and if a = 5 (1 – r), then -Maths 9th

Description : If r is real number such that |r| < 1 and if a = 5 (1 – r), then -Maths 9th

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If cell range A1 : A5 contain the numbers 20, 16, 5, 35 and 7 then = AVERAGE(A1 : A5, 50) will display. -Technology

Description : If cell range A1 : A5 contain the numbers 20, 16, 5, 35 and 7 then = AVERAGE(A1 : A5, 50) will display. -Technology

Last Answer : The correct answer is(a) 22.167

If p, q, r are positive and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are real for : -Maths 9th

Description : If p, q, r are positive and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are real for : -Maths 9th

Last Answer : Given p,q,r are in A.P. then q=2p+r​.....(1). Now px2+qx+r=0 will have real root then q2−4pr≥0. or, 4(p+r)2​−4pr≥0 or, p2+r2−14pr≥0 or, r2−14rp+49p2≥48p2 or, (r−7p)2≥(43​p)2 or, (pr​−7)2≥(43​)2 [ Since p=0 for the given equation to be quadratic] or, ∣∣∣∣∣​pr​−7∣∣∣∣∣​≥43​.

Let ABCD be a parallellogram. Let m and n be positive integers such that n < m < 2n. Let AC = 2 mn -Maths 9th

Description : Let ABCD be a parallellogram. Let m and n be positive integers such that n < m < 2n. Let AC = 2 mn -Maths 9th

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Is ax + by + c = 0, where a, b and c are real numbers, a linear equation in two variables? Give reason. -Maths 9th

Description : Is ax + by + c = 0, where a, b and c are real numbers, a linear equation in two variables? Give reason. -Maths 9th

Last Answer : Solution :-

Consider the following relations R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; -Maths 9th

Description : Consider the following relations R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; -Maths 9th

Last Answer : (c) S is an equivalence relation but R is not an equivalence relationR = {(x, y) | x, y ∈ R, x = wy, w is a rational number} Reflexive: x R x ⇒ x = wx ⇒ w = 1, (a rational number) Hence R is reflexive. Symmetric ... \(rac{r}{s}\) ⇒ \(rac{m}{n}\) S \(rac{r}{s}\) (True)∴ S is an equivalence relation.

The solution set for the inequality 2x – 10 < 3x – 15 over the set of real numbers is -Maths 9th

Description : The solution set for the inequality 2x – 10 < 3x – 15 over the set of real numbers is -Maths 9th

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The set of all real numbers x, for which x^2 – |x + 2| + x > 0, is -Maths 9th

Description : The set of all real numbers x, for which x^2 – |x + 2| + x > 0, is -Maths 9th

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The minimum value of the sum of real numbers a^(–5), a^(–4), 3a^(–3), 1, a^8 and a^10 with a > 0 is -Maths 9th

Description : The minimum value of the sum of real numbers a^(–5), a^(–4), 3a^(–3), 1, a^8 and a^10 with a > 0 is -Maths 9th

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