Quiz Discussion

\(\frac{{{{\left( {a - b} \right)}^2} - {{\left( {a + b} \right)}^2}}}{{ - 4a}}{ \text{ = }}\frac{x}{y}\)     On simplifying the given equations, which of the following equations will be obtained ?

• 1] xy = b
• 2] bx = y
• 3] ab = x
• 4] yb = x
• 5] ay = x

If \(\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1\)     and \(\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0\)     where a, b, c, p, q, r are non-zero real numbers, then \(\frac{{{p^2}}}{{{a^2}}} + \frac{{{q^2}}}{{{b^2}}} + \frac{{{r^2}}}{{{c^2}}}\)    is equal to = ?

• 1] 0
• 2] 1
• 3] 3
• 4] 9

(36.14)^2 – (21.28)^2 =?

• 1]

  850

• 2]

  860

• 3]

  865

• 4]

  853

The simplification of \(\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right)\)yields the result = ?

• 1] 121796
• 2] 121866
• 3] 121956
• 4] 121966

\({ \text{If }}\left( {{n^r} - tn + \frac{1}{4}} \right)\)     be a perfect square, then the values of t are = ?

• 1] ± 2
• 2] 1, 2
• 3] 2, 3
• 4] ± 1

If \(\root 3 \of {{3^n}} { \text{ = 27,}}\)  then the value of n is = ?

• 1] 9
• 2] 6
• 3] 1
• 4] 3

\(4\frac{4}{5} \div 6\frac{2}{5} = ?\)

• 1]

  3/4

• 2]

  5/7

• 3]

  5/8

• 4]

  7/11

• 5]

  None of these

If x = a + m, y = b + m, z = c + m, then the value of \(\frac{{{x^2} + {y^2} + {z^2} - yz - zx - xy}}{{{a^2} + {b^2} + {c^2} - ab - bc - ca}}\)       is = ?

• 1]

  1

• 2]

  \(\frac{{x + y + z}}{{a + b + c}}\)

• 3]

  \(\frac{{a + b + c}}{{x + y + z}}\)

• 4]

  Not possible to find

If x + y + z = 0, then x3 + y3 + z3 + 3xyz is equal to = ?

• 1] 0
• 2] 6xyz
• 3] 12xyz
• 4] xyz

Number of digits in the square root of 62478078 is = ?

• 1] 4
• 2] 5
• 3] 6
• 4] 3