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

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

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

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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.

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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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

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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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If a, b, c are positive real numbers, then show that (a + 1)^7 (b + 1)^7 (c + 1)^7 > 7^7 a^4b^4c^4. -Maths 9th

Description : If a, b, c are positive real numbers, then show that (a + 1)^7 (b + 1)^7 (c + 1)^7 > 7^7 a^4b^4c^4. -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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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 a, b, c, d are four distinct positive real numbers and if 3s = a + b + c + d, then -Maths 9th

Description : 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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For three distinct positive real numbers a, b, c (1 + a^3) (1 + b^3) (1 + c^3) is greater than -Maths 9th

Description : For three distinct positive real numbers a, b, c (1 + a^3) (1 + b^3) (1 + c^3) is greater than -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

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

Description : 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 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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Let N be the set of natural numbers. Describe the following relation in words giving its domain -Maths 9th

Description : Let N be the set of natural numbers. Describe the following relation in words giving its domain -Maths 9th

Last Answer : The given relation stated in words is R = {(x, y) : x is the fourth power of y; x ∈ N, y ∈ {1, 2, 3, 4}}.

On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

Description : On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

Last Answer : (c) Symmetric only Let a ∈N. Then (a, a) ∉R as the GCD of a' and a' is a' not 2. R is not reflexive Let a, b ∈N. Then, (a, b) ∉R ⇒ GCD of a' and b' is 2 ⇒ GCD of b' and a' is 2 ⇒ (b, a) ∈R ∴ R ... , let a = 4, b = 10, c = 12 GCD of (4, 10) = 2 GCD of (10, 12) = 2 But GCD of (4, 12) = 4.

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.

The relation ‘is less than’ on a set of natural numbers is -Maths 9th

Description : The relation ‘is less than’ on a set of natural numbers is -Maths 9th

Last Answer : (c) Only transitiveLet N be the set of natural numbers. Then R = {(a, b) : a < b, a, b ∈N}A natural number is not less than itself ⇒ (a, a)∉R where a ∈N ⇒ R is not reflexive V a, b ∈N, (a, b) ∈R ⇒ a < b \( ot\ ... ∈N, (a, b) ∈R and (b, c) ∈R ⇒ a < b and b < c ⇒ a < c (a, c) ∈R ⇒ R is transitive.

What is the probability that a number selected at random from the set of numbers {1, 2, 3, …, 100} is a perfect cube? -Maths 9th

Description : What is the probability that a number selected at random from the set of numbers {1, 2, 3, …, 100} is a perfect cube? -Maths 9th

Last Answer : (a) \(rac{1}{25}\) Let us assume S as the sample space in all questions. S means the set denoting the total number of outcomes possible. Let S = {1, 2, 3, , 100} be the sample space. Then, n(S) = 100 Let A : ... ∴Required probability P(A) = \(rac{n(A)}{n(S)}\) = \(rac{4}{100}\) = \(rac{1}{25}\)

If x is real and x^2 + 3x + 2 > 0, x^2 – 3x – 4 < 0, then which of the following is correct? -Maths 9th

Description : If x is real and x^2 + 3x + 2 > 0, x^2 – 3x – 4 < 0, then which of the following is correct? -Maths 9th

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If the roots of the equation x^2 – 2ax + a^2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ? -Maths 9th

Description : If the roots of the equation x^2 – 2ax + a^2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ? -Maths 9th

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The number of real solutions of the equation 2|x|^2 – 5|x| + 2 = 0 is : -Maths 9th

Description : The number of real solutions of the equation 2|x|^2 – 5|x| + 2 = 0 is : -Maths 9th

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Find the solution set of x^2 – 5x + 6 > 0. -Maths 9th

Description : Find the solution set of x^2 – 5x + 6 > 0. -Maths 9th

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The set of values of x for which the inequalities x^2 – 3x – 10 < 0, 10x – x^2 – 16 > 0 hold simultaneously is -Maths 9th

Description : The set of values of x for which the inequalities x^2 – 3x – 10 < 0, 10x – x^2 – 16 > 0 hold simultaneously is -Maths 9th

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In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Description : In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Last Answer : Following are the rational numbers which represent irrational numbers .

Let x and y be rational and irrational numbers, respectively. -Maths 9th

Description : Let x and y be rational and irrational numbers, respectively. -Maths 9th

Last Answer : Yes, (x + y) is necessarily an irrational number.

Find which of the variables x, y, z and u represent rational numbers and which irrational numbers. -Maths 9th

Description : Find which of the variables x, y, z and u represent rational numbers and which irrational numbers. -Maths 9th

Last Answer : Rational number and irrational number

In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Description : In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Last Answer : Following are the rational numbers which represent irrational numbers .

Let x and y be rational and irrational numbers, respectively. -Maths 9th

Description : Let x and y be rational and irrational numbers, respectively. -Maths 9th

Last Answer : Yes, (x + y) is necessarily an irrational number.

Find which of the variables x, y, z and u represent rational numbers and which irrational numbers. -Maths 9th

Description : Find which of the variables x, y, z and u represent rational numbers and which irrational numbers. -Maths 9th

Last Answer : Rational number and irrational number

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.

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

Find three rational numbers lying between 0 and 0.1 . -Maths 9th

Description : Find three rational numbers lying between 0 and 0.1 . -Maths 9th

Last Answer : The three rational numbers lying between 0 and 0.1 are 001,005,009. The twenty rational numbers between 0 and 0.1 are 0.001 , 0.002, 0.003, 0.004,--- 0.011, 0.012,--- 0.099. To determine any ... 0 and 0.1 insert the square root of its product. i.e. The rational numbers between a and b is √a b .

Find two irrational numbers between 0.1 and 0.12. -Maths 9th

Description : Find two irrational numbers between 0.1 and 0.12. -Maths 9th

Last Answer : The two irrational numbers between 0.1 and 0.12 are 0.1 010010001--- and 0.1101001000100001 -----

Give two rational numbers lying between 0.232332333233332---- and 0.21211211121111---- -Maths 9th

Description : Give two rational numbers lying between 0.232332333233332---- and 0.21211211121111---- -Maths 9th

Last Answer : The two rational numbers are 0.222. and 0.221

Find three rational numbers lying between 0 and 0.1 . -Maths 9th

Description : Find three rational numbers lying between 0 and 0.1 . -Maths 9th

Last Answer : The three rational numbers lying between 0 and 0.1 are 001,005,009. The twenty rational numbers between 0 and 0.1 are 0.001 , 0.002, 0.003, 0.004,--- 0.011, 0.012,--- 0.099. To determine any ... 0 and 0.1 insert the square root of its product. i.e. The rational numbers between a and b is √a b .

Find two irrational numbers between 0.1 and 0.12. -Maths 9th

Description : Find two irrational numbers between 0.1 and 0.12. -Maths 9th

Last Answer : The two irrational numbers between 0.1 and 0.12 are 0.1 010010001--- and 0.1101001000100001 -----

Give two rational numbers lying between 0.232332333233332---- and 0.21211211121111---- -Maths 9th

Description : Give two rational numbers lying between 0.232332333233332---- and 0.21211211121111---- -Maths 9th

Last Answer : The two rational numbers are 0.222. and 0.221

Express the following numbers in the form of p/q.(1)0.15 (2)0.00026 (3)23.434343434343...... (4)0.6666666.... -Maths 9th

Description : Express the following numbers in the form of p/q.(1)0.15 (2)0.00026 (3)23.434343434343...... (4)0.6666666.... -Maths 9th

Last Answer : (i) 0.15 = 15/100 = 3/20 (ii) 0.00026 = 26/100000 = 13/50000 (iii) 23.43434343.... Let p/q = 23.434343...... - (i) Multiply both side by 100:- 100 * p/q = 100 * 23.434343...... 100p/q = 2343. ... .434343...... 99p/q = 2320.0 p/q = 2320/99 (iv) 0.6666.... = 6/9 Proceed same as question no. (iii)

Express the following numbers in the form of p/q.(1)0.15 (2)0.00026 (3)23.434343434343...... (4)0.6666666.... -Maths 9th

Description : Express the following numbers in the form of p/q.(1)0.15 (2)0.00026 (3)23.434343434343...... (4)0.6666666.... -Maths 9th

Last Answer : (i) 0.15 = 15/100 = 3/20 (ii) 0.00026 = 26/100000 = 13/50000 (iii) 23.43434343.... Let p/q = 23.434343...... - (i) Multiply both side by 100:- 100 * p/q = 100 * 23.434343...... 100p/q = 2343. ... .434343...... 99p/q = 2320.0 p/q = 2320/99 (iv) 0.6666.... = 6/9 Proceed same as question no. (iii)

How many different numbers greater than 60000 can be formed with the digits 0, 2, 2, 6, 8? -Maths 9th

Description : How many different numbers greater than 60000 can be formed with the digits 0, 2, 2, 6, 8? -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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show the following numbers on the number line. (a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5 -Maths 9th

Description : show the following numbers on the number line. (a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5 -Maths 9th

Last Answer : (a) 0.2 lies between the points 0 and 1 on the number line. The space between 0 and 1 is divided into 10 equal parts. Therefore each equal part will be equal to one-tenth. 0.2 is the second point ... parts. Therefore each equal part will be equal to one-tenth. 2.5 is the fifth point between 2 and 3

Find the range of values of x for which (x^2+x+1)/(x^2+2)<1/3, x being real. -Maths 9th

Description : Find the range of values of x for which (x^2+x+1)/(x^2+2)

Last Answer : answer:

Find the range of real values of x for which (x-1)/(4x+5)<(x-3)/(4x-3). -Maths 9th

Description : Find the range of real values of x for which (x-1)/(4x+5)

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What are the number of solutions for real x, which satisfy the equation -Maths 9th

Description : What are the number of solutions for real x, which satisfy the equation -Maths 9th

Last Answer : log2 x>0 2log2 log2 x+log21 log2 (22 x)=1 ⇒2log2 log2 x−log2 log2 (22 x)=1[∵loga1 b=−loga b] $$\Rightarrow \log _{ 2 }{ \left[ \dfrac { { \left( \log _{ 2 }{ x } \right) }^{ 2 } }{ \log_{ 2 } ... log2 (22 )2=log2 8=log2 23=3] ⇒t=3,−1=log2 x ⇒x=2−1or 23 That is x=21 or 8 Hence, the answer is 8.

Let u = (log2x)^2 – 6(log2x) + 12, where x is a real number. Then the equation x^u = 256 has : -Maths 9th

Description : Let u = (log2x)^2 – 6(log2x) + 12, where x is a real number. Then the equation x^u = 256 has : -Maths 9th

Last Answer : ⇒ u=(log2 x)2−log2 x+12 ⇒ We can take log2 x=y ⇒ Then equation becomes y2−6y+12=u ⇒ Given that xu=256 Applying log we get, ⇒ ulog2 x=8 ∴ u=log2 x8 =y8 So our equation becomes, ⇒ y2−6y+12=y8 ⇒ ... We get y=2 ⇒ So, log2 x=2 ⇒ x=22 ∴ x=4 ∴ The given equation has exactly one solution for x

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 X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. -Maths 9th

Description : Let X be the set of all graduates in India. Elements x and y in X are said to be related, if they are graduates of the same university. -Maths 9th

Last Answer : R = {(x, y)}: x and y are graduates of same university, x, y ∈ {All graduates of India}. R is reflexive as (x, x) ∈ R, since x and x are graduates from the same university. R ... graduates from the same university ⇒ (x, z) ∈ R. R being reflexive, symmetric and transitive is an equivalence relation.