SSC CGL 201911)ab(a - b) + bc(b - c) + ca(c - a) is equal to :
(b - a)(b - c)(c - a)
ab(a - b) + bc(b - c) + ca(c - a) = -2; From option D, (b - a) (b - c) (c - a) = (1) (-1) (2) = -2
SSC CGL 201912)Given that \((5x-3)^3+(2x+5)^3\)\(+27(4-3x)^3=\)\(9(3-5x)\)\((2x+5)\)\((3x-4)\), then the value of (2x + 1) is:
15
SSC CGL 201913)If \(5\sqrt5x^3+2\sqrt2y^3=\)\((Ax+\sqrt2y)\)\( (Bx^2+2y^2+Cxy)\), then the value of \((A^2+B^2-C^2)\) is :
20
SSC CGL 201914)The value of \({2\sqrt{10}\over\sqrt{5}+\sqrt{2}-\sqrt{7} }\)\(-{\sqrt{\sqrt{5}-2\over\sqrt{5}+2}}\)\(-{3\over\sqrt{7}-2}\) is :
\(\sqrt2\)
Rationalize and solve the equation
SSC CGL 201915)If \({3(x^2+1)-7x\over3x}=6\), \(x\neq0\), then the value of \(\sqrt x+{1\over\sqrt x}\) is :
\(\sqrt{31\over3}\)
SSC CGL 201916)a, b and c are three fractions such that a < b < c. If c is divided by a, the result is \(9\over2\), which exceeds b by \(23\over6\). The sum of a, b and c is \(19\over12\). What is the value of (2a + b - c)?
\(1\over4\)
SSC CGL 201917)Let \(x=\sqrt [6]{27}-\sqrt{6\frac{3}{4}}\) and \(y={\sqrt {45}+\sqrt{605}+\sqrt{245}\over\sqrt {80} +\sqrt{125}}\), then the value of \((x^2+y^2)\) is :
\(223\over36\)
SSC CGL 201918)If (5x + 2y) : (10x + 3y) = 5 : 9, then \((2x^2+3y^2):\) \((4x^2+9y^2) = \space ?\)
31 : 87
⇒ (5x + 2y)/(10x + 3y) = 5/9
⇒ 45x + 18y = 50x + 15y
⇒ x : y = 3 : 5
Let x = 3 and y = 5
Now, (2x2 + 3y2) : (4x2 + 9y2)
⇒ (2 × 9 + 3 × 25) : (4 × 9 + 9 × 25)
⇒ 93 : 261
SSC CGL 201919)If \(x+y+z=6\), \(xyz=-10\) and \(x^2+y^2+z^2=30\), then what is the value of \((x^3+y^3+z^3)\)?
132
SSC CGL 201920)If \(x+{1\over16x}=3\), then the value of \((16x^3+{1\over256x^3})\) is :
423