Simplification - SSC

Find the value of the following expression:

$\frac{4{\displaystyle \frac{1}{3}}+3{\displaystyle \frac{1}{3}}\times 1{\displaystyle \frac{4}{5}}÷3{\displaystyle \frac{3}{4}}\times \left(6{\displaystyle \frac{1}{4}}\right) \mathrm{of} 1{\displaystyle \frac{1}{15}}}{{\displaystyle \frac{2}{3}}÷{\displaystyle \frac{5}{6}}\times {\displaystyle \frac{2}{3}}}$​​​​​​​

• A.

  $28\frac{1}{8}$

• B.

  $\frac{1}{8}$

• C.

  $289\frac{3}{8}$

• D.

  $12\frac{1}{2}$

• View Answer

Find the value of the following expression:

$\frac{{(7.03)}^3-0.0027}{{(7.03)}^2+2.109+{(0.3)}^2}$

• A.

  7.06

• B.

  7

• C.

  7.33

• D.

  6.73

• View Answer

Select the correct combination of mathematical signs to replace the * signs and to balance the given equation.
42*19*4*69*81*9*58

• A.

  +, ×,−,+,÷,=

• B.

  ÷,−,×,=,×,+

• C.

  −,−,=,×,÷,−

• D.

  ×,−,=,+,×,−

• View Answer

Select the correct combination of mathematical signs to replace the * signs and to balance the given  equation.
40*2*15*30*5

• A.

  ×,−,=,+

• B.

  ×,=,−,−

• C.

  ÷,=,+,−

• D.

  ÷,+,=,+

• View Answer

Simplify the folowing expression.

$\left(\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\right)$ + $\left(\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\right)$ + (6 × 6 × 6) + 3$\left(\frac{1}{2}+\frac{3}{2}\right)$ $\left(\frac{1}{2}+6\right)$ $\left(6+\frac{3}{2}\right)$​​​​​​​

• A.

  521

• B.

  64

• C.

  512

• D.

  256

• View Answer

Find the value of ‘a’ using the concept of BODMAS.

42 ÷ 2 + a × 3 - 22 = 8

• A.

  4

• B.

  6

• C.

  5

• D.

  3

• View Answer

Simplify (5 × 5 × 5 × 5 × 5)⁵ × (5 × 5 × 5)⁵ ÷ 5 = (125)^?​​​​​​​.

• A.

  15

• B.

  21

• C.

  13

• D.

  14

• View Answer

Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?

(132 ÷ 12) + (6 × 11) + 18 - (64 ÷ 16) × 8 = 70

• A.

  11 and 8

• B.

  12 and 6

• C.

  8 and 6

• D.

  12 and 11

• View Answer

If 2z = x + y, then the value of $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ is:

• A.

  0

• B.

  1

• C.

  2

• D.

  5

• View Answer

If P varies directly as Q, and P = 227 when Q = 232, find P when Q = 116.

• A.

  120.5

• B.

  113.5

• C.

  132

• D.

  118

• View Answer

If x - y = 25 and xy = 78, then what is the value of x² + y²?

• A.

  625

• B.

  781

• C.

  103

• D.

  756

• View Answer

Simplify the following expression.

4 ÷ [ 2 + 2 ÷ {2 + 2 ÷ (2 + $\frac{2}{3}$)}]

• A.

  $\frac{11}{15}$

• B.

  $-\frac{11}{15}$

• C.

  $\frac{22}{15}$

• D.

  $-\frac{22}{15}$

• View Answer

If (ab + bc + ca) = 0, then what is the value of ($\frac{1}{a^2-bc}$ + $\frac{1}{b^2-ca}$ + $\frac{1}{c^2-ab}$)?

• A.

  2

• B.

  0

• C.

  1

• D.

  a + b + c

• View Answer

Which of the following options is NOT divisible by 18?

• A.

  571032

• B.

  732546

• C.

  245798

• D.

  459018

• View Answer

What should be subtracted from 246837 to make it divisible by 13 ?

• A.

  5

• B.

  6

• C.

  3

• D.

  4

• View Answer

The fourth proportional to 14,21,28 is:

• A.

  46

• B.

  40

• C.

  42

• D.

  44

• View Answer

If x = $\sqrt{10}$ + $\sqrt{11},$ y = $\sqrt{10}$ - $\sqrt{11},$ then value of 7x² - 50xy + 7y² =

• A.

  344

• B.

  704

• C.

  1360

• D.

  386

• View Answer

If 9 × 4 of 3 ÷ 2 - 5 × Q + 2 × 3 = 10, then find the value of Q.

• A.

  10

• B.

  0.2

• C.

  0.1

• D.

  5

• View Answer

The expression x⁴ - 8x² + m will be a perfect square when the value of m is:

• A.

  2

• B.

  16

• C.

  8

• D.

  4

• View Answer

If a + b = $\sqrt{7}$ and a - b = $\sqrt{5}$, then find the value of 8ab (a² + b²) - (a - b)²

• A.

  19

• B.

  23

• C.

  27

• D.

  21

• View Answer

96 ÷ 48 × $\frac{29}{2}$ + 5² - (1 + 2 + 3 + 4) = ?

• A.

  64

• B.

  44

• C.

  34

• D.

  54

• View Answer

If x + y = 13, then (x - 8)³ + (y - 5)³ is:

• A.

  2197

• B.

  0

• C.

  169

• D.

  13

• View Answer

Simplify:

$\frac{{\displaystyle \frac{27}{14}}÷{\displaystyle \frac{24}{7}} \mathrm{of} {\displaystyle \frac{63}{28}}-{\displaystyle \frac{9}{4}}}{{\displaystyle \frac{35}{8}}÷{\displaystyle \frac{15}{4}} \mathrm{of} {\displaystyle \frac{7}{48}}+{\displaystyle \frac{5}{16}}}$ ÷ $\frac{196}{95}$

• A.

  $-\frac{40}{357}$

• B.

  $\frac{40}{343}$

• C.

  $-\frac{40}{343}$

• D.

  $-\frac{40}{243}$

• View Answer

If (a - 1) 2 + (b + 2) 2 + (c - 1) 2 = 0 , then the value of a² + b² + c² is:

• A.

  6

• B.

  0

• C.

  2

• D.

  1

• View Answer

The value of $\frac{{(a-b)}^3+{(b-c)}^3+{(c-a)}^3}{{(a^2-b^2)}^3+{(b^2-c^2)}^3+{(c^2-a^2)}^3}$ is equal to:

• A.

  ab + bc + ca

• B.

  0

• C.

  1

• D.

  $\frac{1}{(a+b)(b+c)(c+a)}$

• View Answer