Andhra University, Visakhapatnam
Hello aspirant,
Andhra University is one of the oldest universities of India and is well known for its quality education. I would have suggested for you to go ahead with your admission procedures but because it is an online course, I am a bit skeptical about it. A company or
Question : If $x+y+z=1, \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1,$ and $xyz=-1$, then $x^3+y^3+z^3 $ is equal to:
Option 1: –1
Option 2: 1
Option 3: –2
Option 4: 2
Correct Answer: 1
Solution : Given: $x+y+z=1,\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1$, $xyz=-1$ Consider, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1$ ⇒ $xy+yz+zx=xyz=-1$ Now, $x+y+z=1$ ⇒ $(x+y+z)^2=1^2$ ⇒ $x^2+y^2+z^2+2(xy+yz+zx)=1$ ⇒ $x^2+y^2+z^2+2(-1)=1$ ⇒ $x^2+y^2+z^2=3$ We know, $x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-(xy+yz+zx)$ So, putting all the values, we get, ⇒ $x^3+y^3+z^3-3×(-1)=1×[3-(-1)]$ ⇒ $x^3+y^3+z^3=4-3$ $\therefore x^3+y^3+z^3=1$ Hence, the correct answer is 1.
Question : Direction: Find out the number of all those people who can speak Tamil and Telugu.
Option 1: 3
Option 2: 59
Option 3: 21
Option 4: 112
Correct Answer: 21
Solution : The people who can speak Tamil and Telugu is represented by the region common to the circles representing Tamil and Telugu. The required region is shaded in the venn diagram below –
So, the number of all those people who can speak Tamil and Telugu
Question : Select the most appropriate option that can substitute the underlined words in the given sentence. She has gone to the stationery store to buy a scissor.
Option 1: buying a pair of scissors
Option 2: buy a scissors
Option 3: buy a pair of scissors
Option 4: buy a pair of scissor
Correct Answer: buy a pair of scissors
Solution : The correct choice is the third option.
Explanation: The sentence needs "a pair of scissors" because "scissors" is a plural noun. "Pair" is used to indicate two connected objects functioning together. The sentence means she's purchasing a tool with
Question : Direction: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
0.15, 0.3, ? , 1.2, 2.4
Option 1: 0.6
Option 2: 0.9
Option 3: 0.06
Option 4: 4.8
Correct Answer: 0.6
Solution : Given –
The pattern follow for the series is –
0.15 × 2 = 0.3; 0.3 × 2 = 0.6; 0.6 × 2 = 1.2; 1.2 × 2 = 2.4
The series is 0.15, 0.3, 0.6,
Question : What is the number of common tangents that can be drawn to two circles that touch each other externally?
Option 1: 2
Option 2: 4
Option 3: 3
Option 4: 1
Correct Answer: 3
Solution : Only three tangents can be drawn passing through two external touching circles. Hence, the correct answer is 3.
Question : Every year, Halloween is celebrated on_______.
Option 1: 24th November
Option 2: 25th November
Option 3: 1st October
Option 4: 31st October
Correct Answer: 31st October
Solution : The correct answer is 31st October.
Every year, Halloween is celebrated on 31st October. It is a festival in various countries, especially in the United States, where people engage in activities like trick-or-treating, costume parties, and decorating homes with spooky themes. The day
Question : A and B work together to complete the rest of the job in 7 days. However, $\frac{37}{100}$ of the job was already done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work?
Option 1: 20
Option 2: 25
Option 3: 30
Option 4: 10
Correct Answer: 20
Solution : Let the total work done be $100$ units. Remaining work = $100 - \frac{37}{100}×100$ = $100-37$ = $63$ units 5 × efficiency of A = 4 × efficiency of B $\frac{\text{Efficiency of A}}{\text{Efficiency of B}}$ = $\frac{4}{5}$ Efficiency of A = $4x$ Efficiency of B
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