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SSC CGL level Question Set 57, Algebra 13

Hard Algebra Questions SSC CGL Set 57

Hard algebra questions for SSC CGL with answers

Solve 10 various types of hard algebra questions of SSC CGL Set 57 in 12 mins. Verify from answers. Learn to solve the questions quickly from solutions.

The questions are of various types that would need key pattern identification, graphical algebraic solution, properties of sum of inverses, least value of sum of reciprocals, inequality algebra and more.

Answers and link to the quick conceptual solutions are at the end.

10 hard algebra questions for SSC CGL Set 57 - answering time 12 mins

Problem 1.

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

  1. $1$
  2. $0$
  3. $a+b+c$
  4. $3$

Problem 2.

The graph of the linear equations $3x+4y=24$ is a straight line intersecting x-axis and y-axis at the points $A$ and $B$ respectively. $P (2, 0)$ and $Q \left(0, \displaystyle\frac{3}{2}\right)$ are two points on the sides OA and OB respectively of $\triangle OAB$, where O is the origin of the co-ordinate system. If $AB=10$ cm, PQ will be equal to,

  1. 2.5 cm
  2. 20 cm
  3. 5 cm
  4. 40 cm

Problem 3.

If $x^4+\displaystyle\frac{1}{x^4}=119$, then the positive value of $x^3-\displaystyle\frac{1}{x^3}$ is,

  1. 27
  2. 36
  3. 49
  4. 25

Problem 4.

If $a$, $b$, $c$ are positive real numbers and $a+b+c=1$, then the least value of $\displaystyle\frac{1}{a}+\displaystyle\frac{1}{b}+\displaystyle\frac{1}{c}$ is,

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

Problem 5.

If $\displaystyle\frac{x-a^2}{b+c} +\displaystyle\frac{x-b^2}{c+a} +\displaystyle\frac{x-c^2}{a+b}=4(a+b+c)$, with $a$ $b$, and $c$ positive real variables, value of $x$ is,

  1. $a^2+b^2+c^2$
  2. $ab +bc +ca$
  3. $a^2+b^2+c^2 - ab - bc - ca$
  4. $(a+b+c)^2$

Problem 6.

Number of solutions in the two equations, $4x-y=2$ and $2y-8x+4=0$ is,

  1. zero
  2. two
  3. one
  4. infinitely too many

Problem 7.

Let $a=\sqrt{6}-\sqrt{5}$, $b=\sqrt{5}-2$ and $c=2-\sqrt{3}$. Then the relation between $a$, $b$ and $c$ is,

  1. $b \lt c \lt a$
  2. $b \lt a \lt c$
  3. $a \lt b \lt c$
  4. $a \lt c \lt b$

Problem 8.

For real $x$, the maximum value of $3x^2+\displaystyle\frac{4}{x^2}$ is,

  1. $2\sqrt{3}$
  2. $3\sqrt{2}$
  3. $4\sqrt{3}$
  4. none of the above

Problem 9.

If $(3x-2y):(2x+3y)=5:6$ then one of the values of $\left(\displaystyle\frac{\sqrt[3]{x}+\sqrt[3]{y}}{\sqrt[3]{x}-\sqrt[3]{y}}\right)^2$ is,

  1. $25$
  2. $5$
  3. $\displaystyle\frac{1}{5}$
  4. $\displaystyle\frac{1}{2}$

Problem 10.

If $\displaystyle\frac{x^{24}+1}{x^{12}}=7$, then the value of $\displaystyle\frac{x^{72}+1}{x^{36}}$ is,

  1. 433
  2. 322
  3. 432
  4. 343

Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 57 on Algebra where you will get detailed explanations on easiest path to the solutions.

Answers to the Hard algebra question for SSC CGL Set 57

Problem 1. Answer: Option b: 0.

Problem 2. Answer: Option a : 2.5 cm.

Problem 3. Answer: Option b: 36.

Problem 4. Answer: Option c: 9.

Problem 5. Answer: Option d: $(a+b+c)^2$.

Problem 6. Answer: Option d : infinitely too many.

Problem 7. Answer: Option c: $a \lt b \lt c$.

Problem 8. Answer: Option d: none of the above.

Problem 9. Answer:Option a: 25.

Problem 10. Answer: Option b: 322.

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Suresolv Algebra Reading and Practice Guide for SSC CHSL, SSC CGL, SSC CGL Tier II and Other Competitive exams.

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