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

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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What is the sum, of 'n' terms in the series : log m + log -Maths 9th

Description : What is the sum, of 'n' terms in the series : log m + log -Maths 9th

Last Answer : (d) log \(\bigg[rac{m^{(1+n)}}{n^{(n-1)}}\bigg]^{rac{n}{2}}\) S = log m + log \(rac{m^2}{n}\) + log \(rac{m^3}{n^2}\) + ...........n terms= log \(\bigg[\)m.\(rac{m^2}{n}\).\(rac{m^3}{n^2}\)........ ... 2}}}{n^{rac{n(n-1)}{2}}}\)\(\bigg]\) = log \(\bigg[rac{m^{(1+n)}}{n^{(n-1)}}\bigg]^{rac{n}{2}}\)

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

Description : 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 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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Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side -Maths 9th

Description : Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side -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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In Fig. 8.40, points M and N are taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AM = CN. Show that AC and MN bisect each other. -Maths 9th

Description : In Fig. 8.40, points M and N are taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AM = CN. Show that AC and MN bisect each other. -Maths 9th

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l,m and n are three parallel lines intersected by transversal p and q such that l,m and n cut-off equal intersepts AB and BC on p (Fig.8.55). Show that l,m and n cut - off equal intercepts DE and EF on q also. -Maths 9th

Description : l,m and n are three parallel lines intersected by transversal p and q such that l,m and n cut-off equal intersepts AB and BC on p (Fig.8.55). Show that l,m and n cut - off equal intercepts DE and EF on q also. -Maths 9th

Last Answer : Given:l∥m∥n l,m and n cut off equal intercepts AB and BC on p So,AB=BC To prove:l,m and n cut off equal intercepts DE and EF on q i.e.,DE=EF Proof:In △ACF, B is the mid-point of ... a triangle, parallel to another side, bisects the third side. Since E is the mid-point of DF DE=EF Hence proved.

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.

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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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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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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Find the sum of ‘n’ terms of the series : -Maths 9th

Description : Find the sum of ‘n’ terms of the series : -Maths 9th

Last Answer : (b) \(n\, ext{log}_2\big(rac{x}{y}\big)\)Given series= \( ext{log}_2\big(rac{x}{y}\big)\) + \( ext{log}_{2^2}\big(rac{x}{y}\big)^2\) + \( ext{log}_{2^3}\big(rac{x}{y}\big)^3\) + \( ext{log}_{2^4 ... \, ext{terms}\big)\)= \( ext{log}_2\big(rac{x}{y}\big)^n\) = \(n\, ext{log}_2\big(rac{x}{y}\big)\).

The sum of n terms of the series -Maths 9th

Description : The sum of n terms of the series -Maths 9th

Last Answer : (d) log \(\bigg(rac{2^{n+1}}{3^{n-1}}\bigg)^{rac{n}{2}}\) \(\displaystyle\sum_{x=1}^n\) log \(rac{2^x}{3^{x-1}}\) = log \(\big(rac{2^1}{3^0}\big)\) + log \(\big(rac{2^2}{3^1}\big)\) + log \(\big(rac{2^ ... }{2}}}{3^{rac{n(n-1)}{2}}}\bigg]\) = log \(\bigg[rac{2^{n+1}}{3^{n-1}}\bigg]^{rac{n}{2}}\)

How do you play What is inside the box from cool mth games?

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In Fig. 6.10, if m|n, then find the value of x. -Maths 9th

Description : In Fig. 6.10, if m|n, then find the value of x. -Maths 9th

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If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Description : If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Last Answer : Let l+m−2nlogx​=m+n−2llogy​=n+l−2mlogz​=k(say) So, we get logx=k(l+m−2n) ....... (i) logy=k(m+n−2l) ....... (ii) logz=k(n+l−2m) ....... (iii) ∴logx+logy+logz=k(l+m−2n)+k(m+n−2l)+k(n+l−2m) ⇒logx+logy+logz=kl+km−2kn+km+kn−2kl+kn+kl−2km ⇒log(xyz)=0 ⇒logxyz=log1 ⇒xyz=1

If 1/3 log3 M + 3 log3 N = 1 + log 0.008 5, then -Maths 9th

Description : If 1/3 log3 M + 3 log3 N = 1 + log 0.008 5, then -Maths 9th

Last Answer : (b) \(N^9=rac{9}{M}\)\(rac{1}{3}\) log3 M + 3 log3 N = 1 + log0.008 5⇒ log3 M1/3 + log3N3 = 1 + log0.0085 ⇒ log3 M1/3 N3 = 1 + log0.0085 ⇒ M1/3 N3 = 3(1 + log0.0085) ⇒ M1/3 N3 = 31 . 3log0.0085⇒ \(N^9=rac{27 ... ^9=rac{27}{M}\big(3^{log_{rac{1}{5}}5}\big)\) = \(rac{1}{M}\) (27)(3-1) = \(rac{9}{M}.\)

If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Description : If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Last Answer : (b) 1Let \(rac{ ext{log}\,x}{l+m-2n}\) = \(rac{ ext{log}\,y}{m+n-2l}\) = \(rac{ ext{log}\,z}{n+l-2m}\) = k. Thenlog x = k(l + m – 2n), log y = k(m + n – 2l); log z = k(n + l – 2m) ⇒ log x + log y + log z = k(l + m – 2n) + k(m + n – 2l) + k(n + l – 2m)⇒ log(xyz) = 0 ⇒ log(xyz) = log 1 ⇒ xyz = 1.

If (1+cos A)/(1-cos A) = m^2/n^2 , then tan A is equal to -Maths 9th

Description : If (1+cos A)/(1-cos A) = m^2/n^2 , then tan A is equal to -Maths 9th

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If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

Description : If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

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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.

In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m. -Maths 9th

Description : In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m. -Maths 9th

Last Answer : Given, In the figure AP|| BQ, AP and BQ are the bisectors of alternate interior angles ∠CAB and ∠ABF. To show l || m Proof Since, AP|| BQ and t is transversal, therefore ∠PAB = ∠ABQ [alternate interior angles] ⇒ 2 ∠PAB = 2 ∠ABQ [multiplying both sides by 2]

In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m. -Maths 9th

Description : In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m. -Maths 9th

Last Answer : Given, In the figure AP|| BQ, AP and BQ are the bisectors of alternate interior angles ∠CAB and ∠ABF. To show l || m Proof Since, AP|| BQ and t is transversal, therefore ∠PAB = ∠ABQ [alternate interior angles] ⇒ 2 ∠PAB = 2 ∠ABQ [multiplying both sides by 2]

The sum of the first n even natural numbers is ___________

Description : The sum of the first n even natural numbers is ___________

Last Answer : The sum of the first n even natural numbers is ___________

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}}.

Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Description : Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Last Answer : Take a = (2+ √3) and b =(2 - √3 ); a and b are irrational numbers, but their product = 4-3 = 1, is a rational number. Take c = √3 and d = -√3; c and d are irrational numbers. but their product = -3, is a rational number.

Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Description : Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Last Answer : Take a = (2+ √3) and b =(2 - √3 ); a and b are irrational numbers, but their product = 4-3 = 1, is a rational number. Take c = √3 and d = -√3; c and d are irrational numbers. but their product = -3, is a rational number.

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

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Description : If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Last Answer : (d) Let the angles of a AABC be ∠A, ∠B and ∠C. Given, ∠A = ∠B+∠C …(i) InMBC, ∠A+ ∠B+ ∠C-180° [sum of all angles of a triangle is 180°]…(ii) From Eqs. (i) and (ii), ∠A+∠A = 180° ⇒ 2 ∠A = 180° ⇒ 180° /2 ∠A = 90° Hence, the triangle is a right triangle.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Description : If one angle of a triangle is equal to the sum of the other two angles, then the triangle is -Maths 9th

Last Answer : (d) Let the angles of a AABC be ∠A, ∠B and ∠C. Given, ∠A = ∠B+∠C …(i) InMBC, ∠A+ ∠B+ ∠C-180° [sum of all angles of a triangle is 180°]…(ii) From Eqs. (i) and (ii), ∠A+∠A = 180° ⇒ 2 ∠A = 180° ⇒ 180° /2 ∠A = 90° Hence, the triangle is a right triangle.

If the sum as well as the product of roots of a quadratic equation is 9, then the equation is: -Maths 9th

Description : If the sum as well as the product of roots of a quadratic equation is 9, then the equation is: -Maths 9th

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If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

Description : If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

Last Answer : Given equation: ax2+bx+c=0 Let α and β be the roots of given quadratic equation Sum of the roots i.e. α+β=a−b Product of roots i.e. αβ=ac It is given that, Sum of the roots = Sum of squares of the roots i ... )2−2αβ i.e. a−b =(a−b )2−a2c i.e. −ab=b2−2ac i.e. ab+b2=2ac Hence, C is the correct option.

If the sum and difference of two expressions are 5a^2 – a – 4and a^2 + 9a – 10 respectively, then what is their LCM ? -Maths 9th

Description : If the sum and difference of two expressions are 5a^2 – a – 4and a^2 + 9a – 10 respectively, then what is their LCM ? -Maths 9th

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If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (–a, 0) be 2b^2, then which of the following is correct ? -Maths 9th

Description : If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (–a, 0) be 2b^2, then which of the following is correct ? -Maths 9th

Last Answer : (d) (0, 0)Let the vertices of Δ ABC be given as: A(0, 0), B(3, 0) and C(0, 4) The orthocentre O is the point of intersection of the altitudes drawn from the vertices of Δ ABC on the opposite sides. Slope of BC = \(rac{ ... ⇒ y = 0 ...(ii) From (i), \(x\) = 0 Hence, the orthocentre is (0, 0).

If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Description : If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Last Answer : p(x) = (k2 – 14) x2 – 2x – 12 Here a = k2 – 14, b = -2, c = -12 Sum of the zeroes, (α + β) = 1 …[Given] ⇒ − = 1 ⇒ −(−2)2−14 = 1 ⇒ k2 – 14 = 2 ⇒ k2 = 16 ⇒ k = ±4

If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. -Maths 9th

Description : If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k. -Maths 9th

Last Answer : Here a = 3, b = -k, c = 6 Sum of the zeroes, (α + β) = − = 3 …..(given) ⇒ −(−)3 = 3 ⇒ k = 9

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 .

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Description : Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Last Answer : Let f(x)=xn+an. In order to prove that x+a is a factor of f(x) for any odd positive integer n, it is sufficient to show that f(−a)=0. f(−a)=(−a)n+an=(−1)nan+an f(−a)=(−1+1)an [ n is odd positive integer ] f(−a)=0×an=0 Hence, x+a is a factor of xn+an, when n is an odd positive integer.

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Description : Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Last Answer : This answer was deleted by our moderators...

If R is a relation in N × N defined by (a, b) R (c, d) if and only if ad = bc, show that R is an equivalence relation. -Maths 9th

Description : If R is a relation in N × N defined by (a, b) R (c, d) if and only if ad = bc, show that R is an equivalence relation. -Maths 9th

Last Answer : (i) R is reflexive. For all (a, b) ∈ N N we have (a, b) R (a, b) because ab = ba ⇒ R is reflexive. (ii) R is symmetric. Suppose (a, b) R (c, d) Then (a, b) R (c, d) ⇒ ... ) R (e, f) ⇒ R is transitive. Since R is reflexive, symmetric and transitive, therefore, R is an equivalence relation on N N.

In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

Description : In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

Last Answer : Join OE. In ΔOME and ΔONE, OM =ON [equal chords are equidistant from the centre] ∠OME = ∠ONE = 90° OE =OE [common sides] ∠OME ≅ ∠ONE [by SAS congruency] ⇒ ME = NE [by CPCT] In quadrilateral OMEN, ... =ON , ME = NE and ∠OME = ∠ONE = ∠MEN = ∠MON = 90° Hence, OMEN is a square. Hence proved.

l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see figure). -Maths 9th

Description : l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see figure). -Maths 9th

Last Answer : Though E, draw a line parallel to p intersecting L at G and n at H respectively. Since l | | m ⇒ AG | | BE and AB | | GE [by construction] ∴ Opposite sides of quadrilateral AGEB are ... ∠DGE = ∠FHE [alternate interior angles] By ASA congruence axiom, we have △DEG ≅ △FEH Hence, DE = EF

In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

Description : In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

Last Answer : Join OE. In ΔOME and ΔONE, OM =ON [equal chords are equidistant from the centre] ∠OME = ∠ONE = 90° OE =OE [common sides] ∠OME ≅ ∠ONE [by SAS congruency] ⇒ ME = NE [by CPCT] In quadrilateral OMEN, ... =ON , ME = NE and ∠OME = ∠ONE = ∠MEN = ∠MON = 90° Hence, OMEN is a square. Hence proved.

l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see figure). -Maths 9th

Description : l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see figure). -Maths 9th

Last Answer : Though E, draw a line parallel to p intersecting L at G and n at H respectively. Since l | | m ⇒ AG | | BE and AB | | GE [by construction] ∴ Opposite sides of quadrilateral AGEB are ... ∠DGE = ∠FHE [alternate interior angles] By ASA congruence axiom, we have △DEG ≅ △FEH Hence, DE = EF

Two lines l and m are perpendicular to the same line n.Are l and m perpendicular to each other ? -Maths 9th

Description : Two lines l and m are perpendicular to the same line n.Are l and m perpendicular to each other ? -Maths 9th

Last Answer : Solution :- No, they are parallel.

PQ and RS are two equal and parallel line segments.Any points M not lying on PQ or RS is joined to Q and S and lines through P parallel to SM meet at N.Prove that line segments MN and PQ are equal and parallel to each other. -Maths 9th

Description : PQ and RS are two equal and parallel line segments.Any points M not lying on PQ or RS is joined to Q and S and lines through P parallel to SM meet at N.Prove that line segments MN and PQ are equal and parallel to each other. -Maths 9th

Last Answer : hope its clear

If m parallel lines in a plane are intersected by a family of n parallel lines, find the number of parallelograms formed? -Maths 9th

Description : If m parallel lines in a plane are intersected by a family of n parallel lines, find the number of parallelograms formed? -Maths 9th

Last Answer : answer: