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Question : In the figure, chords XY = $x$ cm and PQ = 10 cm intersect each other at point L. Find the length of XY (in cm).
Option 1: 22
Option 2: 21
Option 3: 20
Option 4: 23
Correct Answer: 20
Solution : For two chords, PQ and XY intersect each other externally at L, QL × PL = YL × XL ⇒ $6 × (10+6) = 4 × (x+4)$ ⇒ $x+4=24$ $\therefore x=20$ Hence, the correct answer is 20 cm.
Question : If $x+ \frac{1}{x} =\sqrt{13}$, then $\frac{3x}{{x}^{2} -1}$ equals to:
Option 1: $\sqrt[3]{13}$
Option 2: $\frac{\sqrt{13}}{3}$
Option 3: 1
Option 4: 3
Correct Answer: 1
Solution : Given: $⇒x+ \frac{1}{x} =\sqrt{13}$ By squaring both sides, $⇒({x}+ \frac{1}{x})^{2} =(\sqrt{13})^{2}$ $⇒{x}^{2}+ \frac{1}{x^{2}}+2×x×\frac{1}{x} =13$ $⇒{x}^{2}+ \frac{1}{x^{2}}=13-2 =11$ ---(1) Also, $({x}- \frac{1}{x})^{2} ={x}^{2}+ \frac{1}{x^{2}}-2×x×\frac{1}{x}$ By using the value of equation (1), we get, $⇒({x}- \frac{1}{x})^{2} = 11 - 2=9$ $⇒({x}- \frac{1}{x}) = \sqrt{9}=3$ Multiplying by $x$
Question : Comprehension:
Read the following passage and answer the questions.
On a cold, wintry Christmas day in 1998, the ice and snow were beating down upon the windows of the vehicles as we travelled to an obscure orphanage in Bosnia and Herzegovina. We battled unstable hills blanketed with two feet of snow. The narrow road forced us to drive perilously close to the edge. This would be my first Christmas away from home and family. I could imagine my wife and my two little daughters opening their gifts on Christmas day. Today, I was going to learn for the first time how it would be to spend Christmas day with other children.
Enemy activity had devastated the villages. I had heard stories and seen pictures of this particular village where we were headed. What I did not know was that it would be a camp full of destitute families and children. As we entered the village, the children lined the roads on both sides and cheered. They ran to us in excitement as we climbed out of our vehicles. Within moments, I saw my soldiers passing out sweets and chocolates and talking with the children. The adults, who were not sure if we could be trusted, kept their distance. But soon, they too were won over by my men. The soldiers unloaded 87 boxes of toys, clothes, shoes, school supplies, and candy. We were soon surrounded by the people of the village, who shook our hands and smiled shyly in thanks for our gifts and our presence.
After the two hour visit, as we rose to leave, the camp leader said to us, "Please come again, even if you have nothing to give. We enjoyed having you here." We had loved every moment we had been there. This year, we truly learned the Christmas spirit of loving and giving!
Question:
Initially the adults were not as friendly as the children because:
Option 1: they were not interested in gifts
Option 2: they were missing their families
Option 3: they did not trust the soldiers
Option 4: they did not want to celebrate Christmas
Correct Answer: they did not trust the soldiers
Solution : The correct choice is the third option.
Explanation: Initially, the adults in the village were not as friendly as the children because of uncertainty and perhaps a lack of trust. The text says, "The adults who were not sure if
Question : What are the characteristics of isotopes?
Option 1: Same neutron and same proton
Option 2: Same atomic number and different mass number
Option 3: Same atomic number and same mass number
Option 4: Same neutron and different proton
Correct Answer: Same atomic number and different mass number
Solution : The correct answer is the Same atomic number and different mass number.
Elements having the same number of protons and electrons but varying neutron counts are called isotopes. In other words, the isotopes have different numbers of nucleons.
Question : Directions: In the following question, select the related word from the given alternatives. School : Teacher :: Court : ?
Option 1: Lawyer
Option 2: Play
Option 3: Tennis
Option 4: Justice
Correct Answer: Lawyer
Solution : Given: School : Teacher :: Court : ?
A teacher is someone who is employed at a school to educate students. Similarly, a lawyer is someone who works in a court.
Hence, the first option is correct.
Question : Select the option that expresses the given sentence in passive voice. No one immediately owned responsibility for the bomb attack.
Option 1: Responsibility for the bomb attack has not been owned by anyone immediately.
Option 2: Responsibility for the bomb attack was not owned by anyone immediately.
Option 3: Responsibility for the bomb attack was not owned by no one immediately.
Option 4: Responsibility for the bomb attack is not owned by anyone immediately.
Correct Answer: Responsibility for the bomb attack was not owned by anyone immediately.
Solution : The correct choice is the second option.
The passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence
Question : Water is used in a hot water bag because:
Option 1: it is easily available
Option 2: it has high specific gravity
Option 3: it has high specific heat
Option 4: it is a liquid substance
Correct Answer: it has high specific heat
Solution : The correct option is it has a high specific heat.
Water is used in a hot water bag because it has a high specific heat capacity, which allows it to absorb and maintain a substantial quantity of heat energy while
Question : Select the option that can be used as a one-word substitute for the given group of words.
Burial ground consisting of graves.
Option 1: Courtyard
Option 2: Cemetery
Option 3: Sanctuary
Option 4: Auditorium
Correct Answer: Cemetery
Solution : The correct one-word substitute is the second option.
Explanation: Cemetery is the correct choice. It refers to a place where the deceased is buried, consisting of graves and often tombstones or markers.
The meanings of the other options are as follows:
Courtyard: A courtyard is
Question : Rearrange the parts of the sentence in the correct order.
The study led P. collaborators from Bristol, Cambridge, and Germany Q. by scientists at the University of Bath and including R. used fossils and analysed genetic differences between S. modern snakes to reconstruct snake evolution
Option 1: QPRS
Option 2: PRQS
Option 3: SPQR
Option 4: QSRP
Correct Answer: QPRS
Solution : The correct choice is the first option.
In this case, the subject is "the study," and the verb is "used". To form a coherent sentence, it's crucial to place these elements in the appropriate order. The other parts of the sentence provide additional information
Question : Identify the segment that contains a grammatical error. The people living in coastal areas were evacuated by time.
Option 1: were evacuated
Option 2: living in coastal areas
Option 3: by time
Option 4: The people
Correct Answer: by time
Solution : The error lies in the third option.
"By time" implies that evacuation was done according to a schedule or deadline, which may not be the intended meaning. "In time" indicates that the evacuation was done with enough time to spare before a particular
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