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

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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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.

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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​.

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

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The minimum value of the expression ((3b+4c)/a)+((4c+a)/3b)+((a+3b)/4c) -Maths 9th

Description : The minimum value of the expression ((3b+4c)/a)+((4c+a)/3b)+((a+3b)/4c) -Maths 9th

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Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

Description : Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

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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.

Show that If m > 1, then the sum of the mth powers of underline (n)even numbers is greater than n (n + 1)^m -Maths 9th

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Give three rational numbers lying between 1 / 3 and 1 / 2. -Maths 9th

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Last Answer : The rational numbers lying between is 1 / 3 and 1 / 2 . Therefore , 1 / 3 < 3 / 8 < 1 / 2. Now . the rational number lying between 1 / 3 and 5 / 12 is Therefore , 5 /12 < 11 / 24 < 1 / 2.

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

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Find three irrational numbers between 2 and 2.5 . -Maths 9th

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Find three rational numbers between -Maths 9th

Description : Find three rational numbers between -Maths 9th

Last Answer : Rational numbers

Give three rational numbers lying between 1 / 3 and 1 / 2. -Maths 9th

Description : Give three rational numbers lying between 1 / 3 and 1 / 2. -Maths 9th

Last Answer : The rational numbers lying between is 1 / 3 and 1 / 2 . Therefore , 1 / 3 < 3 / 8 < 1 / 2. Now . the rational number lying between 1 / 3 and 5 / 12 is Therefore , 5 /12 < 11 / 24 < 1 / 2.

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 three irrational numbers between 2 and 2.5 . -Maths 9th

Description : Find three irrational numbers between 2 and 2.5 . -Maths 9th

Last Answer : If a and b are any two distinct positive rational numbers such that ab is not a perfect square , then the irrational number √ab lies between a and b. ∴ Irrational number between 2 and 2.5 is √ 2 2.5 , i.e √5 Irrational number ... 2.5 are √5 , 2(1/2) 5(1/4) and (1/2) 5 3/4 21/2 .

Find three rational numbers between -Maths 9th

Description : Find three rational numbers between -Maths 9th

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A box contains 100 balls numbers from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability -Maths 9th

Description : A box contains 100 balls numbers from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability -Maths 9th

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If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th

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

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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 a point O lies between two points P and R such that PO=OR then prove that PO= 1/2PR. -Maths 9th

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Last Answer : THINGS WHICH ARE COINCIDE WITH EACH OTHER ARE EQUAL TO ONE ANOTHER PO+OR=PR 2PO=PR PO=OR PO=1/2PR HENCE PROVED

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If A, B and C are the angles of a triangle such that sec (A – B), sec A and sec (A + B) are in arithmetic progression then show that -Maths 9th

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