Difficult Algebra Questions with Answers for SSC CGL Set 14

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SSC CGL level Question Set 58, Algebra 14

SSC CGL difficult algebra questions with answers set 14

Difficult algebra questions with answers for SSC CGL

10 difficult algebra questions with answers in SSC CGL Algebra Question set 14 to be answered in 12 minutes. Take the test and verify from answers.

For best results take the timed test, score your efforts from answers and learn to solve the questions in 12 minutes from solutions.

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10 difficult algebra questions for SSC CGL Set 14 - time to solve 12 mins

Problem 1.

If $x=5-\sqrt{21}$, then the value of $\displaystyle\frac{\sqrt{x}}{\sqrt{32-2x}-\sqrt{21}}$ is,

  1. $\displaystyle\frac{1}{\sqrt{2}}\left(\sqrt{3}-\sqrt{7}\right)$
  2. $\displaystyle\frac{1}{\sqrt{2}}\left(\sqrt{7}+\sqrt{3}\right)$
  3. $\displaystyle\frac{1}{\sqrt{2}}\left(\sqrt{7}-\sqrt{3}\right)$
  4. $\displaystyle\frac{1}{\sqrt{2}}\left(7-\sqrt{3}\right)$

Problem 2.

If $a+b+c+d=4$, then find the value of $\displaystyle\frac{1}{(1-a)(1-b)(1-c)}+\displaystyle\frac{1}{(1-b)(1-c)(1-d)}+$

$\hspace{30mm}\displaystyle\frac{1}{(1-c)(1-d)(1-a)}+\displaystyle\frac{1}{(1-d)(1-a)(1-b)}$ is,

  1. 1
  2. 4
  3. 5
  4. 0

Problem 3.

If $a(2+\sqrt{3})=b(2-\sqrt{3})=1$, then the positive value of $\displaystyle\frac{1}{a^2+1}+\displaystyle\frac{1}{b^2+1}$ is,

  1. $1$
  2. $4$
  3. $9$
  4. $-5$

Problem 4.

If $\displaystyle\frac{x}{xa+yb+zc}=\displaystyle\frac{y}{ya+zb+xc}=\displaystyle\frac{z}{za+xb+yc}$, and $x+y+z \neq 0$ then each ratio can be expressed as,

  1. $\displaystyle\frac{1}{a+b-c}$
  2. $\displaystyle\frac{1}{a+b+c}$
  3. $\displaystyle\frac{1}{a-b-c}$
  4. $\displaystyle\frac{1}{a-b+c}$

Problem 5.

If $3(a^2+b^2+c^2)=(a+b+c)^2$, then the relation between $a$, $b$ and $c$ is,

  1. $a=b=c$
  2. $a \neq b=c$
  3. $a=b \neq c$
  4. $a \neq b \neq c$

Problem 6.

If $x=\sqrt{5} + \sqrt{3}$ and $y=\sqrt{5} - \sqrt{3}$, then the value of $(x^4-y^4)$ is,

  1. $16$
  2. $544$
  3. $64\sqrt{15}$
  4. $32\sqrt{15}$

Problem 7.

Let $p=\displaystyle\frac{5}{18}$, then $27p^3-\displaystyle\frac{1}{216} - \displaystyle\frac{9}{2}p^2 + \displaystyle\frac{1}{4}p$ is equal to,

  1. $\displaystyle\frac{4}{27}$
  2. $\displaystyle\frac{10}{27}$
  3. $\displaystyle\frac{5}{27}$
  4. $\displaystyle\frac{8}{27}$

Problem 8.

For real $x+y+z=6$, then the value of $(x-1)^3+(y-2)^3+(z-3)^3$ is,

  1. $3xyz$
  2. $3(x-1)(y-2)(z-3)$
  3. $2(x-1)(y-2)(z-3)$
  4. $(x-1)(y-2)(z-3)$

Problem 9.

If $x+\displaystyle\frac{1}{x}=\sqrt{3}$, then the value of $x^{30}+x^{24}+x^{18}+x^{12}+x^6+1$ is,

  1. $1$
  2. $\sqrt{3}$
  3. $-\sqrt{3}$
  4. $0$

Problem 10.

If $\displaystyle\frac{p}{a}+\displaystyle\frac{q}{b}+\displaystyle\frac{r}{c}=1$, and $\displaystyle\frac{a}{p}+\displaystyle\frac{b}{q}+\displaystyle\frac{c}{r}=0$ where $a$, $b$, $c$ and $p$, $q$, $r$ are non-zero, the value of $\displaystyle\frac{p^2}{a^2}+\displaystyle\frac{q^2}{b^2}+\displaystyle\frac{r^2}{c^2}$ is,

  1. $1$
  2. $-1$
  3. $2$
  4. $0$

Answers to the 10 difficult algebra questions for SSC CGL Set 14

Problem 1. Answer: Option c: $\displaystyle\frac{1}{\sqrt{2}}\left(\sqrt{7}-\sqrt{3}\right)$.

Problem 2. Answer: Option d : 0.

Problem 3. Answer: Option a: 1.

Problem 4. Answer: Option b: $\displaystyle\frac{1}{a+b+c}$.

Problem 5. Answer: Option a: $a=b=c$.

Problem 6. Answer: Option c : $64\sqrt{15}$.

Problem 7. Answer: Option d: $\displaystyle\frac{8}{27}$.

Problem 8. Answer: Option b: $3(x-1)(y-2)(z-3)$.

Problem 9. Answer: Option d: 0.

Problem 10. Answer: Option a: 1.


Solutions to the problems

Learn how to solve the questions quickly and easily from the paired solution set at,

SSC CGL level Solution Set 58 on Algebra.


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