Description : If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th
Last Answer : Let p(x) = a5 -4a2x3 +2x + 2a +3 Since, x + 2a is a factor of p(x), then put p(-2a) = 0 (-2a)5 – 4a2 (-2a)3 + 2(-2a) + 2a + 3 = 0 ⇒ -32a5 + 32a5 -4a + 2a+ 3 = 0 ⇒ -2a + 3 = 0 2a =3 a = 3/2. Hence, the value of a is 3/2.
Description : If (x^4 – 2x^2y^2 + y^2)^(a –1) = (x – y)^2a (x + y) ^–2, then the value of a is -Maths 9th
Last Answer : answer:
Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th
Last Answer : The value of a
Description : The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th
Last Answer : Given, point (2,3) lies on the line. So, the point (2, 3) is the solution of 3x - (a -1) y = 2a - 1 On putting x = 2 and y = 3 in given solution. ∴ 3 2 - (a-1) 3 = 2a - 1 ⇒ 6 - 3a + 3 = 2a - 1 ⇒ - 3a ... 2 2) 3 = 3b ⇒ 10 - 9 = 3b ⇒ 1 = 3b ⇒ 1 / 3 = b Hence, the value of b is 1 / 3.
Description : If a + b + c = 0, then what is the value of a^4 + b^4 + c^4 – 2a^2b^2 – 2b^2c^2 – 2c^2a^2 ? -Maths 9th
Description : If (x+1) is a factor of ax(cube) + x(square) - 2x + 4a - 9,find the value of a. -Maths 9th
Last Answer : solution :-
Description : Find the value of k if (x-2)is a factor of polynomial p(x) = 2x(cube) - 6x(square) + 5x + k. -Maths 9th
Last Answer : Solution :-
Description : If(x)/((b-c)(b+c-2a))=(y)/((c-a)(c+a-2b))=(z)((a-b)(a+b-2c)), what is the value of x + y + z ? -Maths 9th
Description : Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th
Last Answer : Solution of this question
Description : If tan x = b/a , then what is the value of a cos 2x + b sin 2x? -Maths 9th
Description : If sin^4x + sin^2x = 1 then what is 1 are the value of cot^4 x + cot^2 x? -Maths 9th
Description : If 2x^2 – 7xy + 3y^2 = 0, then the value of x : y is -Maths 9th
Description : If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th
Last Answer : Given that the following polynomials leave the same remainder when divided by (x - 4) : We are to find the value of a. Remainder theorem: When (x - b) divides a polynomial p(x), then the remainder is p(b). So, from (i) and (ii), we get Thus, the required value of a is 1.
Description : If the HCF of (x^2 + x – 12) and (2x^2 – kx – 9) is (x – k), then what is the value of k ? -Maths 9th
Description : If x^3 + 5x^2 + 10k leaves remainder – 2x when divided by x^2 + 2, then what is the value of k ? -Maths 9th
Last Answer : x3+5x2+10k =(x2+2)(x+5)+10k−2x−10 ⇒10k−2x−10=−2x ⇒10k−10=0 or k=1.
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
Description : If a = log12m and b = log18m, then (a-2b)/(b-2a) equals -Maths 9th
Last Answer : (a) log32\(rac{a-2b}{b-2a}\) = \(rac{ ext{log}_{12}\,m-\,2 ext{log}_{18}\,m}{ ext{log}_{18}\,m-\,2 ext{log}_{12}\,m}\)
Description : The adjacent sides of a parallelogram are 2a and a. If the angle between them is 60°, then one of the diagonals of the parallelogram is -Maths 9th
Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th
Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x
Description : The smallest integral value of a such that `|x+a-3|+|x-2a|=|2x-a-3|` is true `AA x in R` is
Last Answer : The smallest integral value of a such that `|x+a-3|+|x-2a|=|2x-a-3|` is true `AA x in R` is A. `0` B. `1` C. `2 D. `3`
Description : If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th
Last Answer : (a) Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation. ⇒ 2 (2) + 3 (0) = k ⇒ k = 4 Hence, the value of k is 4.
Description : if (1.-2) is a solution of the equation 2x-y=p,then find the value of p. -Maths 9th
Last Answer : x = 1 y = -2 2x-y = p Therefore, p = 2(1)-(-2) = 2 + 2 = 4
Last Answer : 2x-y=p put x-1,y=-2 =2(1)-(-2)=p p=4
Description : Show that 2x+1 is a factor of polynomial 2x(cube) - 11x(square) - 4x + 1. -Maths 9th
Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th
Last Answer : The given linear equation is 2x + cy= 8. …(i) Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y. Put y = x in Eq. (i), we get
Description : Find the value of x, if(6/5)to the power x ,(5/6) to the power 2x = 125/216. -Maths 9th
Description : If 4 to the power 2x-1 - 16 to the power x-1 = 348,Find the value of x. -Maths 9th
Description : Find the value of f(x) = 2x(square) + 7x + 3 at x= -2. -Maths 9th
Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y as its solution? -Maths 9th
Description : Find the value of the polynomial p(x) = x^3-3x^2-2x+6 at x = underroot 2 -Maths 9th
Last Answer : In this chapter, we shall proceed with recalling some of the constructions already learnt in the earlier classes and deal with some more. Here in this section, we will construct some of these ... be done? 2. Always explain the construction. Write the sequence of steps that are actually taken.
Description : For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th
Description : Let R be a relation on the set N, defined by {(x, y) : 2x – y = 10} then R is -Maths 9th
Last Answer : (a) ReflexiveGiven, {(\(x\), y) : 2\(x\) – y = 10} Reflexive, \(x\) R \(x\) = 2\(x\) – \(x\) = 10 ⇒ \(x\) = 10 ⇒ y = 10 ∴ Point (10, 10) ∈ N ⇒ R is reflexive.
Description : If the expression (px^3 + x^2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ? -Maths 9th
Last Answer : Let f(x)=px3+x2−2x−q Since f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0. Therefore, p+1−2−q=0, i.e., p−q=1; and −p+1+2−q=0, i.e., p+q=3 Thus p=2 and q=1
Description : If x + y + z = 0, then x^2/(2x^2+yz)+y^2/(2y^2+zx)+z^2/(2z^2+xy) = -Maths 9th
Description : simplify (2a + b)3 + (2a - b)3 -Maths 9th
Last Answer : (2a + b)3 + (2a - b)3 = (8a3 + 12a2b + 3ab2 + b3 ) + (8a3 - 12a2b + 3ab2 - b3) = 16a3 + 6ab2
Description : For any two real number a b and , we defined aRb if and only if sin^2a + cos^2b = 1. The relation R is -Maths 9th
Last Answer : (d) an equivalence relationGiven, a R b ⇒ sin2a + cos2b = 1 Reflexive: a R a ⇒ sin2 a + cos2 a = 1 ∀ a ∈ R (True) Symmetric: a R b ⇒ sin2 a + cos2 b = 1 ⇒ 1 - cos2 a + 1 - sin2 b = 1 ⇒ sin2 b + ... + cos2 b + sin2 b + cos2 c = 2 ⇒ sin2 a + cos2 c = 1 ⇒ a R c (True)∴ R is an equivalence relation.
Description : (2a)/(a+b)+(2b)/(b+c) + (2c)/(c+a) + ((b-c)(c-a)(a-b))/((b+c)(c+a)(a+b))equals -Maths 9th
Description : Find the following products: (i) (3x + 2y + 2z) (9x2 + 4y2 + 4z2 – 6xy – 4yz – 6zx) (ii) (4x -3y + 2z) (16x2 + 9y2+ 4z2 + 12xy + 6yz – 8zx) (iii) (2a – 3b – 2c) (4a2 + 9b2 + 4c2 + 6ab – 6bc + 4ca) (iv) (3x -4y + 5z) (9x2 + 16y2 + 25z2 + 12xy- 15zx + 20yz) -Maths 9th
Description : Find the value of k if the line on 2x + y = k passes through the point (3,5). -Maths 9th
Description : If the point (2k – 3, k + 2) lies on the graph of the equation 2x + 3y +15 = 0, find the value of k. -Maths 9th
Description : If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 21y3. -Maths 9th
Last Answer : 2x +3y = 13-----(1) xy =6-----(2) 8x³ +27y³ = (2x)³ +(3y)³ = (2x+3y)³ - 3*2x*3y(2x+3y) [using (a+b)³ = a³+b³+3ab(a+b)] = (13)³- 18 * 6 *13 [ using (1) and (2)] = 2197 - 1404 =793
Description : if 2x + 3y = 8 and xy = 2, find the value of 4X2 + 9y2. -Maths 9th
Last Answer : Given 2x+3y=8 and xy=2, formula, (a+b)2=a2+b2+2ab ∴(2x+3y)2=4x2+9y2+2(2x)(3y) (2x+3y)2=4x2+9y2+12xy 82=4x2+9y2+12(2) ∴4x2+9y2=64−24=40
Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th
Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.