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Question : The given expression is equal to: $(\cot B-\tan B)\sin B\cos B$:
Option 1: $1-2 \sec ^2 B$
Option 2: $1-2 \cos ^2 {B}$
Option 3: $2 \cos ^2 {B}-1$
Option 4: $2 \sec ^2 {B}-1$
Correct Answer: $2 \cos ^2 {B}-1$
Solution : $(\cot B-\tan B)\sin B\cos B$ = $(\frac{\cos B}{\sin B}-\frac{\sin B}{\cos B})\sin B\cos B$ = $(\frac{\cos^2 B - \sin^2 B}{\sin B\cos B})\sin B\cos B$ = $\cos^2 B - \sin^2 B$ = $\cos^2 B - (1- \cos^2 B)$ = $2\cos^2 B - 1$ Hence,
Question : Directions: Ajay, Priti, Rakesh, Mehak, Saloni, and Yogesh are sitting in a row facing north. Saloni and Yogesh are sitting in the centre. Ajay and Priti are at the ends. Rakesh is sitting to the immediate left of Ajay. Who is sitting to the immediate right of Priti?
Option 1: Yogesh
Option 2: Saloni
Option 3: Mehak
Option 4: Rakesh
Correct Answer: Mehak
Solution : Given: (I) Ajay, Priti, Rakesh, Mehak, Saloni, and Yogesh are sitting in a row facing north. North facing row; Left end;_, _, _, _, _; Right end (II) Saloni and Yogesh are sitting in the centre. _, _, Saloni, Yogesh, _, _ (III) Ajay and
Question : A line of length 1.5 metres was mistakenly measured as 1.55 metres. What is the percentage error in the measurement?
Option 1: $0.05$%
Option 2: $3\frac{7}{31}$%
Option 3: $3\frac{1}{3}$%
Option 4: $0.5$%
Correct Answer: $3\frac{1}{3}$%
Solution : Given: A line of length 1.5 metres was measured as 1.55 metres by mistake. Wrong Number = 1.55 metres Actual Number = 1.5 metres Error percentage = $\frac{\text{Wrong number – Actual number}}{\text{Actual number}}$ × 100 = $\frac{1.55-1.5}{1.5}$ × 100 = $\frac{0.05}{1.5}$ × 100 = $\frac{5}{1.5}$%
Question : J1 can do a piece of work alone in 10 days, J2 can do the same work alone in 12 days, while J3 can do it alone in 15 days. They work together and complete the work, and receive a total of INR 2,250 for doing the work. What is the difference in the shares of J1 and J3?
Option 1: INR 450
Option 2: INR 400
Option 3: INR 300
Option 4: INR 350
Correct Answer: INR 300
Solution : LCM of 10. 12 and 15 is 60 Total work = 60 Efficiency of J1 = $\frac{60}{10}=6$ Efficiency of J2 = $\frac{60}{12}=5$ Efficiency of J3 = $\frac{60}{15}=4$ The ratio of their efficiencies = 6 : 5 : 4 Amount received =
Question : Which temple is the epicentre for the Rath Yatra in Odisha?
Option 1: Lingaraja Temple
Option 2: Konark Temple
Option 3: Mukteshwar Temple
Option 4: Jagannath Puri Temple
Correct Answer: Jagannath Puri Temple
Solution : The correct answer is Jagannath Puri Temple.
Celebrated annually during the bright half of the lunar month of Ashadha, the Ratha Yatra of Puri, also known as the Ratha Jatra, is regarded as the oldest and largest Hindu chariot event. The three
Question : Directions: One/two statement(s) is/are given followed by two conclusions, I and II. You have to consider the statement(s) to be true, even if it/they seem(s) to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statement(s). Statements: Some shoes are white. All white are blue. Conclusions: I. All shoes are blue. II. Some shoes are blue.
Option 1: Only I follows
Option 2: Only II follows
Option 3: Both I and II follow
Option 4: Neither I nor II follows
Correct Answer: Only II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion I: All shoes are blue – From the Venn diagram, it is evident that the circles representing shoes and blue overlap each other and
Question : What is the value of $111\frac{1}{2} + 111\frac{1}{6} + 111\frac{1}{12} + 111\frac{1}{20} + 111\frac{1}{30}?$
Option 1: $111\frac{1}6$
Option 2: $111\frac{5}6$
Option 3: $555\frac{5}6$
Option 4: $555\frac{1}6$
Correct Answer: $555\frac{5}6$
Solution : $111 \frac{1}{2} + 111 \frac{1}{6} + 111\frac{1}{12}+111 \frac{1}{20} + 111\frac{1}{30}$ = $5\times 111+( \frac{1}{2} + \frac{1}{6} + \frac{1}{12}+\frac{1}{20} + \frac{1}{30})$ = $555+( \frac{1}{1\times 2} + \frac{1}{2\times 3} + \frac{1}{3\times 4}+\frac{1}{4\times 5} + \frac{1}{5\times 6})$ = $555+(\frac{1}{1}-\frac{1}{2} + \frac{1}{2} -\frac{1}{3}+ \frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5} + \frac{1}{5}-\frac{1}{6})$ = $555 +(\frac{1}1-\frac{1}6)$
Question : Directions: In this question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
Lata Mangeshkar was ___ with a natural talent for music.
Option 1: Given
Option 2: found
Option 3: endowed
Option 4: entrusted
Correct Answer: endowed
Solution : The correct word to fill in the blank is the third option.
This means to be naturally gifted or possessed of a particular quality or talent. In the context of the sentence, it conveys the idea that Lata Mangeshkar had an inherent, natural talent for
Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows the given statements. Statements: I. Some boys are human. II. All humans are hard. Conclusions: I. Some hard are not a boy. II. Some humans are not boys. III. No hard is human.
Option 1: Both conclusions I and III follow
Option 2: Both conclusions II and III follow
Option 3: Only conclusion I follows
Option 4: Neither conclusion follows
Correct Answer: Neither conclusion follows
Let's analyse the conclusions – Conclusion (I): Some hard are not boy – It is a possibility that the circle representing hard is not completely overlapped by the circle representing
Question : Tribal leader Birsa was associated with which tribe?
Option 1: Munda
Option 2: Bhil
Option 3: Gond
Option 4: Bhutia
Correct Answer: Munda
Solution : The correct option is Munda.
Tribal leader Birsa Munda emerged as a tribal leader from Bihar and Jharkhand belt. He belonged to the Munda tribe. He encouraged his people to follow their religion and culture. The birth anniversary of Birsa Munda is celebrated as
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