Algebra questions for SSC CGL Tier 2 Set 1 with answers
Algebra questions for SSC CGL Tier 2 Set 1 contains 10 chosen algebra questions to solve in 12 mins. It's not easy, but you may learn how from solutions.
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Answers and link to the solutions are at the end.
10 algebra questions for SSC CGL Tier 2 Set 1 - answering time 12 mins
Q1. Find the maximum value of the expression $(p^2 +7p+13)^{-1}$.
- $\displaystyle\frac{5}{7}$
- $\displaystyle\frac{4}{3}$
- $20$
- $\displaystyle\frac{3}{7}$
Q2. If $n=7+3\sqrt{5}$, then the value of $\left(\sqrt{n} + \displaystyle\frac{1}{\sqrt{n}}\right)$ is,
- $\displaystyle\frac{5}{7}$
- $\displaystyle\frac{7}{12}$
- $\displaystyle\frac{9+\sqrt{5}}{2\sqrt{2}}$
- $\displaystyle\frac{\sqrt{5}}{2\sqrt{2}}$
Q3. If $x=20$, $y=19$, the value of $\displaystyle\frac{x^2+y^2+xy}{x^3-y^3}$ is,
- $35$
- $1$
- $324$
- $365$
Q4. If $p + \displaystyle\frac{2p}{3} + \displaystyle\frac{p}{2} +\displaystyle\frac{p}{7}=97$, then the value of $p$ is,
- 46
- 44
- 40
- 42
Q5. If $p=1+\sqrt{2}+\sqrt{3}$, then $\left(p+\displaystyle\frac{1}{p-1}\right)$ is,
- $1 +2\sqrt{3}$
- $2\sqrt{3}-1$
- $2+\sqrt{3}$
- $3+\sqrt{2}$
Q6. If $(x+y) : (y+z) : (z+x) = 6 : 7 : 8$ and $x+y+z=14$, then value of $z$ is,
- 6
- 14
- 8
- 7
Q7. If $x=\displaystyle\frac{\sqrt{2}+1}{\sqrt{2}-1}$ and $xy=1$ find the value of $\displaystyle\frac{2x^2+3xy+2y^2}{2x^2-3xy+2y^2}$.
- $\displaystyle\frac{71}{65}$
- $\displaystyle\frac{7}{12}$
- $\displaystyle\frac{65}{71}$
- $\displaystyle\frac{72}{7}$
Q8. If $x=\displaystyle\frac{a+b}{1-ab}$ and $y=\displaystyle\frac{a-b}{1+ab}$ then the value of $\displaystyle\frac{x+y}{1-xy}$ is,
- $\displaystyle\frac{a}{1+b^2}$
- $\displaystyle\frac{2a}{1+b}$
- $\displaystyle\frac{2a}{1-a^2}$
- $\displaystyle\frac{2a}{1+a^2}$
Q9. If $x+\displaystyle\frac{1}{x}=-2$, then the value of $x^{2n+1}+\displaystyle\frac{1}{x^{2n+1}}$ where $n$ is a positive integer is,
- $0$
- $2$
- $-5$
- $-2$
Q10. If $x=5^{n-1} +5^{-n-1}$ where $n$ is real, the minimum value of $x$ is,
- $10$
- $\displaystyle\frac{5}{2}$
- $2$
- $\displaystyle\frac{2}{5}$
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SSC CGL Tier II level Solution set 1 Algebra 1.
Answers to the algebra questions for SSC CGL Tier 2
Problem 1. Answer: Option b: $\displaystyle\frac{4}{3}$.
Problem 2. Answer: Option c : $\displaystyle\frac{9+\sqrt{5}}{2\sqrt{2}}$.
Problem 3. Answer: Option b: 1.
Problem 4. Answer: Option d: 42.
Problem 5. Answer: Option a: $1+2\sqrt{3}$.
Problem 6. Answer: Option a : 6.
Problem 7. Answer: Option a: $\displaystyle\frac{71}{65}$.
Problem 8. Answer: Option c: $\displaystyle\frac{2a}{1-a^2}$.
Problem 9. Answer: Option d: -2.
Problem 10. Answer: Option d: $\displaystyle\frac{2}{5}$.
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