Lakshya Education MCQs

Question: If $$a + \frac{1}{b} = 1$$   and $$b + \frac{1}{c} = 1{\text{,}}$$   then $$c + \frac{1}{a}$$   is equal to = ?
Options:

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Question 1. The simplified value of $${\left[ {{{\left( {0.111} \right)}^3} + {{\left( {0.222} \right)}^3} - {{\left( {0.333} \right)}^3} + {{\left( {0.333} \right)}^2}\left( {0.222} \right)} \right]^3} = ?$$
  1.    0.999
  2.    0
  3.    0.888
  4.    0.111
Answer: Option B
Question 2. If $$\frac{a}{{b + c}}{\text{ = }}\frac{b}{{c + a}}$$   = $$\frac{c}{{a + b}}{\text{ = k,}}$$    then find the value of k is
  1.    -$$ \frac{1}{2}$$
  2.    1
  3.    -1
  4.    $$\frac{1}{2}$$
Answer: Option D
Question 3. If $$\frac{x}{{\left( {2x + y + z} \right)}}$$   = $$\frac{y}{{\left( {x + 2y + z} \right)}}$$   = $$\frac{z}{{\left( {x + y + 2z} \right)}}   = a{\text{,}}$$     then find a, If x + y + z ≠ 0
  1.    $$\frac{1}{3}$$
  2.    $$\frac{1}{4}$$
  3.    $$\frac{1}{2}$$
  4.    $$\frac{1}{8}$$
Answer: Option B
Question 4. $$\frac{2}{{2 + \frac{2}{{3 + \frac{2}{{3 + \frac{2}{3}}}}} \times 0.39}}$$     is simplified to = ?
  1.    $$\frac{1}{3}$$
  2.    2
  3.    6
  4.    None of these
Answer: Option D
Question 5. $$\sqrt {{{\left( {0.798} \right)}^2} + 0.404 \times 0.798 + {{\left( {0.202} \right)}^2}} $$       $$ + 1$$ $$ = ?$$
Answer: Option D
Question 6. If $$\frac{m}{n}{\text{ = }}\frac{4}{3}$$   and $$\frac{r}{t}{\text{ = }}\frac{9}{{14}}{\text{,}}$$   then the value of $$\frac{{3mr - nt}}{{4nt - 7mr}}{\text{ is}} = {\text{?}}$$
  1.    $$ - {\text{5}}\frac{1}{2}$$
  2.    $$ - \frac{{11}}{{14}}$$
  3.    $$ - 1\frac{1}{4}$$
  4.    $$\frac{{11}}{{14}}$$
Answer: Option B

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