Description : If the roots ff the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are equal, then prove that either a = 0 or a3 + b3 + c3 = 3abc -Maths 10th
Last Answer : (c2 – ab) x2 + 2(bc - a2 ) x+ (b2 – ac) = 0 Comparing with Ax2 + Bx + C = 0 A = (c2 – ab), B = 2(bc - a2 ) and C = b2 – ac According to the question, B2 - 4AC = 0 Put the values in the above equation we get 4a(a3 + b3 + c3 -3abc) = 0 hence, a = 0 or a3 + b3 + c3 = 3ab
Description : If a+b+c= 5 and ab+bc+ca =10, then prove that a3 +b3 +c3 – 3abc = -25. -Maths 9th
Last Answer : Prove that a3 +b3 +c3 – 3abc = -25
Description : If a + b + c = 9 and ab + bc + ca = 23, then a3 + b3 + c3 – 3 abc = (a) 108 (b) 207 (c) 669 (d) 729 -Maths 9th
Last Answer : a+b+c=9 and a2+b2+c2=35 Using formula, (a+b+c)2=a2+b2+c2+2(ab+bc+ca) 92=35+2(ab+bc+ca) 2(ab+bc+ca)=81−35=46 (ab+bc+ca)=23 using formula, (a3+b3+c3)−3abc=(a2+b2+c2−ab−bc−ca)(a+b+c) a3+b3+c3−3abc=(35−23)×9=9×12=108
Description : If a + b + c =0, then a3+b3 + c3 is equal to -Maths 9th
Last Answer : (d) Now, a3+b3 + c3 = (a+ b + c) (a2 + b2 + c2 – ab – be – ca) + 3abc [using identity, a3+b3 + c3 – 3 abc = (a + b + c)(a2+b2+c2 –ab–bc-ca)] = 0 + 3abc [∴ a + b + c = 0] a3+b3 + c3 = 3abc.
Description : Prove that (a +b +c)3 -a3 -b3 – c3 =3(a +b)(b +c)(c +a). -Maths 9th
Last Answer : Solution to (a +b +c) 3 -a 3 -b 3 – c 3 =3(a +b)(b +c)(c +a)
Description : In right triangle ABC, right angled at C, if tan A = 1, then the value of 2 sin A cos A is (a) 0 (b) 1 (c) – 1 (d) 2
Last Answer : (b) 1
Description : If a – b = 4 and ab = 21, find the value of a3-b3. -Maths 9th
Last Answer : Given, a−b=4,ab=21 Then, ⇒(a−b)3=a3−3a2b+3ab2−b3=a3−3ab(a−b)−b3 ⇒43=a3−b3−3(21)(4) ⇒64+252=a3−b3 ∴a3−b3=316
Description : If a + b = 10 and ab = 21, find the value of a3 + b3. -Maths 9th
Last Answer : Given, a+b=10,ab=21 then, ⇒(a+b)3=a3+3ab(a+b)+b3 ⇒(10)3=a3+b3+3(21)(10) ⇒1000−630=a3+b3 ∴a3+b3=370
Description : In a spreadsheet software, the formula =A1 +$2 was entered in cell A3 and then copied into cell B3. What is the formula copied into B3? -Technology
Last Answer : Need Answer
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
Last Answer : answer:
Description : In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is: a 12/7 b 24/7 c 20/7 d 7/24
Last Answer : b 24/7
Description : D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then, length of DE (in cm) is (a) 2.5 (b) 3 (c) 5 (d) 6
Last Answer : (b) 3
Description : A (5,-1) , B (-3,-2) and C (-1,8) are the vertices of ∆ ABC . The median from A meets BC at D ,then the coordinates of the point D are: (a) (-4,6) (b) (2,7/2) (c) (1,-3/2) (d) (-2,3)
Last Answer : (d) (-2,3)
Description : If G is the centroid of `Delta ABC`, then the area of `Delta BGC` is `"_______________"` times the area of quadrilateral ABCG.
Last Answer : If G is the centroid of `Delta ABC`, then the area of `Delta BGC` is `"_______________"` times the area of quadrilateral ABCG.
Description : There are two congruent triangles each with area 198 cm^2. Triangle DEF is placed over triangle ABC in such a way that the centroid of -Maths 9th
Description : If α and 1/α are the zeroes of the polynomial ax2 + bx + c, then value of c is (a) 0(b) a (c) -a (d) 1
Last Answer : (a) 0
Description : If the distance between the points (4, p) and (1, 0) is 5units , then the value of p is: (a) 4 only (b) 0 (c) – 4 only (d) 4, - 4
Last Answer : (d) 4, - 4
Description : If Log2 x - 5 Log x + 6 = 0, then what would the value(s) of x be?
Last Answer : Answer: x = e2 or e3.
Description : If a+b+c=5 and ab+bc+ca=10 find the value of a^3+b^3+c^3-3abc -Maths 9th
Last Answer : We know , a³ + b³ + c³ -3abc = (a + b + c )(a² + b² + c² -ab -bc-ca) now , a + b + c = 5 ab + bc + ca = 10 (a + b + c)² = a² + b² + c² +2(ab + bc+ca) (5)² -2 10 = a² + b² + c² a² + b² + c² = ... )(a² + b² + c² -ab- bc-ca) =( 5)( 5 - 10) = 5 (-5) = -25 Hope this will help u..... by :- RAXTAR.....
Description : If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is (a) 4 (b) 2 (c) 1 (d) 3
Last Answer : (b) 2
Description : ABCD is a parallelogram with diagonal AC If a line XZ is drawn such that XZ ∥ AB, then BX/XC = ? (a) (AY/AC) (b) DZ/AZ (c) AZ/ZD (d) AC/AY Answer: (c) AZ/ZD 13. In the given figure, value of x (in cm) is (a) 5cm (b) 3.6 cm (c) 3.2 cm (d) 10 cm
Last Answer : (a) 5cm
Description : If ̳α ‘ and ̳β ‘ are the zeroes of a quadratic polynomial x 2 − 5x + b and α − β = 1, then the value of ̳b‘ is (a) – 5 (b) 6 (c) 5 (d) – 6
Last Answer : (b) 6
Description : If α , β are the zeroes of f(x) = px 2 – 2x + 3p and α + β = αβ then the value of p is: (a) 1/3 (b) -2/3 (c) 2/3 (d) -1/3
Last Answer : (c) 2/3
Description : If one zero of the quadratic polynomial x 2 + 3x + k is 2, then the value of k is (a) 10 (b) –10 (c) 5 (d) –5
Last Answer : (b) –10
Description : The point (-1,2) divides the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4, then the value of x2 + y2 is : (a) 27 (b) 28 (c) 29 (d) 30
Last Answer : (c) 29
Description : If A(5,2), B(2,-2) and C(-2,t) are the vertices of a right angled triangle with ∠B = 900 , then the value of t is: (a) -1 (b) 1 (c) -2 (d) 2
Description : If (x, y) is a solution of the following pair of linear equations in two variables, then the value of expression (√ is: x + 2y = 4 and 3x - y = 5 (a) 2 (b) 3 (c) 4 (d) √2
Last Answer : (a) 2
Description : In the given figure, if AB = 14 cm, BD = 10 cm and DC = 8 cm, then the value of tan B is a) 4/3 b) 14/3 c) 11/3 d) 9/12
Last Answer : a) 4/3
Description : Given that sin A=1/2 and cos B=1/√2 then the value of (A + B) is: (a)30 (b)45 (c)75 (d)60
Last Answer : (c)75
Description : If x=y=2z and xyz=256 then what is the value of x? (a)12 (b)8 (c)16 (d)6
Last Answer : (b)8
Description : Value of p(3) + p(1) =a) 0 b) 1 c) 2 d) 3
Last Answer : c) 2
Description : What value/s can x take in the expression k(x – 10) (x + 10) = 0 where k is any real number. (a) 100, -100 (b) Infinitely many (c) Depends on value of k (d) 10, -10
Last Answer : (d) 10, -10
Description : The value of x and y which satisfy the equations : √ e) x=1,y=0 f) x=0,y=0 g) x=1,y=1 h) x=0,y=1
Last Answer : f) x=0,y=0
Description : The value of m obtained on solving equations : 2n + m =2n – m = √ a) 1/4 b) 0 c) 1/2 d) 3/4
Last Answer : b) 0
Description : The value of x and y which satisfy the equations : √ a) x=1,y=0 b) x=0,y=0 c) x=1,y=1 d) x=0,y=1
Last Answer : b) x=0,y=0
Description : Assertion (A) : The value of k for which the system of linear equations kx+2y+1=0 and 6x+4y-5=0 has a unique solution is 3. Reason (R):The system of linear equations a1x + b1y + c1= 0 and a2x + ... not the correct explanation of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect.
Last Answer : (d) R is correct; A is incorrect.
Description : The value(s) of 'k' for which the following pair of linear equations will represent a pair of intersecting lines graphically is/are: 3x - 4y + 7 = 0 kx - 8y = 5 (a) k = 6 (b) k ≠ 6(c) any real number (d) any real number except 6
Last Answer : (d) any real number except 6
Description : The value of 2 tan 2 45°+ cos 2 30° − sin 2 60° is (a) 0 (b) 1 (c) -2 (d) 2
Last Answer : (d) 2
Description : The value of sin 60° cos 30° + sin 30° cos 60° is: a 0 b 1 c 2 d 4
Last Answer : b 1
Description : If α, β are the zeroes of the polynomial x2 – 16, then αβ(α + β) is (a) 0 (b) 4 (c) -4 (d) 16
Description : The points (-2,-1),(a,0),(4,b),(1,2) are the vertices of a parallelogram taken in order , then the values of a and b are: (a) a = 1,b = 3 (b) a = 3 , b = 1 (c) a = 1 , b = 1 (d) a = 0 , b = 4
Last Answer : (a) a = 1,b = 3
Description : If cos 2α = 1⁄2 ,then α is a 15 0 b 30 0 c 60 0 d 0 0
Last Answer : b 30 0
Description : 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
Description : If (0, 0) and (2, 0) are the two vertices of a triangle whose centroid is (1, 1), then the area of the triangle is: -Maths 9th
Last Answer : (b) \(\bigg(rac{2\sqrt{13}+20\sqrt2}{\sqrt{13}+\sqrt{17}+5\sqrt2},rac{8\sqrt{13}-6\sqrt{17}}{\sqrt{13}+\sqrt{17}+5\sqrt2}\bigg)\)Let A(x1, y1), B(x2, y2), C(x3, y3) be the vertices of ΔABC the ... +6)^2}\) = \(\sqrt{4+196}\) = \(\sqrt{200}=10\sqrt{2}\)∴ Co-ordinates of incentre of Δ ABC are
Description : What is the value of .03 *.50?
Last Answer : If you multiply .03 and .5 you get .015 Come on these are easy!
Description : Value of polynomial when x = -1 is: a) 12 b) 13 c) 14 d) -12
Last Answer : a) 12