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Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.
Option 1: $3$
Option 2: $4$
Option 3: $1$
Option 4: $\frac{1}{2}$
Correct Answer: $3$
Solution : Given: $a+b+c=0$ According to the question, $a^3+b^3+c^3=3abc$ Dividing both sides by $abc$, we get $\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=\frac{3abc}{abc}$ ⇒ $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=3$ Hence, the correct answer is 3.
Question : If $\cos A=\frac{15}{17}, 0 \leq A \leq 90^{\circ}$, then the value of $\cot(90° - A)$ is:
Option 1: $\frac{8}{15}$
Option 2: $\frac{2 \sqrt{2}}{15}$
Option 3: $\frac{\sqrt{2}}{15}$
Option 4: $\frac{7}{15}$
Correct Answer: $\frac{8}{15}$
Solution : Given: $\cos A=\frac{15}{17}$ $\sec A=\frac{1}{\cos A}=\frac{17}{15}$ $\cot(90^\circ - A)=\tan A=\sqrt{\sec^2 A-1}$ $=\sqrt{(\frac{17}{15}^2)-1}$ $=\sqrt{\frac{289}{225}-1}$ $=\sqrt{\frac{289-225}{225}}$ $=\sqrt{\frac{64}{225}}$ $=\frac{8}{15}$ Hence, the correct answer is $\frac{8}{15}$.
Question : Which among the following has written the book ‘The Pregnancy Bible’?
Option 1: Vidya Balan
Option 2: Shilpa Shetty
Option 3: Rani Mukherji
Option 4: Kareena Kapoor
Correct Answer: Kareena Kapoor
Solution : The correct answer is Kareena Kapoor.
The Pregnancy Bible is a book written by Kareena Kapoor. It is a comprehensive guide to pregnancy, covering everything from conception to birth.
The book is approved by the Federation of Obstetric and Gynaecological Societies of India (FOGSI),
Question : Directions: Study the bar diagram and answer the question. Total number of boys and girls in five different departments of a college.
The percentage of the boys from the Biology department compared to the total number of boys from all the departments together is:
Option 1: $33\frac{1}{2}\%$
Option 2: $50\%$
Option 3: $33\frac{1}{3}\%$
Option 4: $30\%$
Correct Answer: $33\frac{1}{3}\%$
Solution : From the given graph, The total number of boys from all the departments = 60 + 220 + 100 + 160 + 120 = 660 The number of boys in the Biology Department = 220 The required percentage = $\frac{\text{The number of boys in the
Question : Directions: In a certain code language, EDITOR is coded as CBGQLO. What is the code for FOLDER in that code language?
Option 1: DMJABO
Option 2: BMJBCR
Option 3: DMJACO
Option 4: DMJABR
Correct Answer: DMJABO
Solution : Given: EDITOR is coded as CBGQLO.
Subtract 2 from the place value of the first three letters and subtract 3 from the place value of the last three letters of EDITOR to obtain the required code – E – 2 = C; D – 2
Question : The following histogram shows the weekly wages of workers at a factory. How many workers get wages of more than Rs.200?
Option 1: 95
Option 2: 85
Option 3: 70
Option 4: 80
Correct Answer: 85
Solution : According to the question: Number of workers getting wages of more than Rs. 200 = 20 + 50 + 15 = 85 Hence, the correct answer is 85.
Question : Directions: Words given on the left side of (::) are related to each other by some Logic/Rule/Relation. Select the missing word/word pair on the right side of (::) from the given alternatives based on the same Logic/Rule/Relation. Sword : Warrior :: ?
Option 1: Mason : Plumbline
Option 2: Scalpel : Sculptor
Option 3: Axe : Woodcutter
Option 4: Tailor : Needle
Correct Answer: Axe : Woodcutter
Solution : Given: Sword : Warrior (Sword is used by a Warrior who fights in a war).
Let's check the options – First option: Mason : Plumbline; Plumbline is a tool used by Mason but the words are written in the reverse order. Second option:
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Music can improve mood, decrease pain and anxiety, and facilitate opportunities for emotional expression. Research (1)______ that music can benefit our physical and mental health in numerous ways. Music can (2)______ the brain’s production of the hormone dopamine. This increased dopamine production helps (3)________ feelings of anxiety and depression. Music is processed directly by the amygdala, which is the part of the brain (4)________ in mood and emotions. By reducing stress levels and providing a strong competing stimulus to the pain (5) ________ that enter the brain, music therapy can assist in pain management.
Question:
Select the most appropriate option to fill in the blank 5.
Option 1: deter
Option 2: signals
Option 3: deform
Option 4: substance
Correct Answer: signals
Solution : The correct choice is the second option.
In the context of the sentence, the phrase "stimuli to the pain" suggests that there are signals related to pain entering the brain. The correct word to describe these signals is signals. The sentence implies that music
Question : Directions: Read the following pie chart carefully to answer the question. Distribution of sales of Hindi and English newspapers in five localities (A, B, C, D, and E).
English newspaper:
Hindi newspaper: What is the ratio of the average number of sales of English newspapers in localities B and D together to the average sale of Hindi newspapers in all the localities?
Option 1: 25 : 32
Option 2: 40 : 33
Option 3: 33 : 40
Option 4: 43 : 33
Correct Answer: 25 : 32
Solution : The average sales of English newspapers in localities B and D = $\frac{2000+3000}{2}$ = $\frac{5000}{2}$ = 2500 The average sale of Hindi newspapers in all the localities = $\frac{4000+2500+3600+2400+3500}{5}$ = $\frac{16000}{5}$ = 3200 The ratio of the average sales of English newspapers in
Question : A and B together can complete a piece of work in 18 days, B and C in 24 days, and A and C in 36 days. In how many days, will all of them together complete the work?
Option 1: 16 days
Option 2: 15 days
Option 3: 12 days
Option 4: 10 days
Correct Answer: 16 days
Solution : 1 day work of A and B = $\frac{1}{18}$ ---------(1) 1 day work of B and C = $\frac{1}{24}$ ---------(2) 1 day work of A and C = $\frac{1}{36}$ ---------(3) Adding equations (1), (2) and (3), we get: ⇒ 2 × (A + B
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