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Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: UVX
Option 2: BCD
Option 3: HIJ
Option 4: PQR
Correct Answer: UVX
Solution : Let's check the options –
First option: UVX; U + 1 = V; V + 2 = X Second option: BCD; B + 1 = C; C + 1 = D Third option: HIJ; H + 1 = I; I + 1 = J Fourth
Question : Rs.11,500 has to be divided between X, Y, and Z such that X gets $\frac{4}{5}$th of what Y gets and Y gets $\frac{2}{3}$rd of what Z gets. How much more does Z get over X (in Rs.)?
Option 1: 7200
Option 2: 1800
Option 3: 1170
Option 4: 2450
Correct Answer: 2450
Solution : Given: Rs.11,500 has to be divided between X, Y, and Z such X gets $\frac{4}{5}$th of what Y gets and Y gets $\frac{2}{3}$rd of what Z gets. Let Z get Rs. $p$. From the question, Y will get $\frac{2p}{3}$ and X will obtain $\frac{2p}{3}×\frac{4}{5}=\frac{8p}{15}$ Also,
Question : Directions: Among five objects P, Q, R, S, and T, Q is twice as heavy as P. S is twice as heavy as Q. R is half as heavy as T. T is equally as heavy as Q. Which is the heaviest among all five objects?
Option 1: Q
Option 2: S
Option 3: T
Option 4: R
Correct Answer: S
Solution : Given: (I) Among five objects P, Q, R, S, and T, Q is twice as heavy as P. Q = 2P (II) S is twice as heavy as Q. S = 2 × 2P = 4P (III) R is half as heavy as T. R
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. ACCUSED : UCCASDE :: FACTORY : TCAFOYR :: DYNAMIC : ?
Option 1: YNMICAD
Option 2: DNYMACI
Option 3: ANYDMCI
Option 4: DANYMIC
Correct Answer: ANYDMCI
Solution : Given: ACCUSED : UCCASDE :: FACTORY : TCAFOYR :: DYNAMIC : ?
Here, the letters of the given words are being shuffled following a certain pattern as shown below – ACCUSED : UCCASDE→
FACTORY : TCAFOYR→
Similarly, follow the same pattern for DYNAMIC→
So, ANYDMCI
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each blank.
Let us take a brief look at the planet (1)______ which we live. As the earth hurtles through space at a (2)______ of 70, 000 miles per hour, it spins, as we all know, on its axis, (3)______ causes it to be flattened at the poles. Thus, if you (4)______ to stand at the North or South Pole, you would be 13 miles nearer the centre of the earth (5)______ if you stood on the Equator. Question
Select the most appropriate option to fill in the blank no. 5.
Option 1: than
Option 2: from
Option 3: where
Option 4: when
Correct Answer: than
Solution : The first option is the correct answer.
The sentence is making a comparison between two situations: standing at the North or South Pole and standing on the Equator. When making comparisons in English, we often use the word "than" to introduce the second part of
Question : The monthly income of a person was INR 12,000 and his monthly expenditure was INR 8,000. Next year, his income increased by 10% and his expenditure by 8%. Find the percentage increase in his savings.
Option 1: 10%
Option 2: 14%
Option 3: 12%
Option 4: 15%
Correct Answer: 14%
Solution : Given: Monthly Income = INR 12000 Monthly Expenditure = INR 8000 Increase in income = 10% Increase in expenditure = 8% Solution: Savings before increase = 12000 – 8000 = INR 4000 Increase in income = 12000 + $\frac{10}{100}$ × 12000 = INR 13200 Increase
Question : If $p=\frac{5}{18}$, then $27p^{3}–\frac{1}{216}–\frac{9}{2}p^{2}+\frac{1}{4}p$ is equal to:
Option 1: $\frac{4}{27}$
Option 2: $\frac{5}{27}$
Option 3: $\frac{8}{27}$
Option 4: $\frac{10}{27}$
Correct Answer: $\frac{8}{27}$
Solution : Given: $p=\frac{5}{18}$ So, $27p^{3}–\frac{1}{216}–\frac{9}{2}p^{2}+\frac{1}{4}p$ Putting the value of $p=\frac{5}{18}$ in the expression, = $27×(\frac{5}{18})^{3}–\frac{1}{216}–\frac{9}{2}×(\frac{5}{18})^{2}+\frac{1}{4}×\frac{5}{18}$ = $27×(\frac{125}{18×18×18})–\frac{1}{216}–\frac{9}{2}×(\frac{25}{18×18})+\frac{1}{4}×\frac{5}{18}$ = $\frac{125}{216}–\frac{1}{216}–\frac{25}{72}+\frac{5}{72}$ = $\frac{124}{216}–\frac{20}{72}$ = $\frac{124–60}{216}$ = $\frac{64}{216}$ = $\frac{8}{27}$ Hence, the correct answer is $\frac{8}{27}$.
Question : The expression $\frac{\cos ^4 \theta-\sin ^4 \theta+2 \sin ^2 \theta+3}{(\operatorname{cosec} \theta+\cot \theta+1)(\operatorname{cosec} \theta-\cot \theta+1)-2}, 0^{\circ}<\theta<90^{\circ}$, is equal to:
Option 1: $\frac{1}{2} \sin \theta$
Option 2: $2 \sin \theta$
Option 3: $\sec \theta$
Option 4: $2\operatorname{cosec} \theta$
Correct Answer: $2 \sin \theta$
Solution : $\frac{\cos ^4 \theta-\sin ^4 \theta+2 \sin ^2 \theta+3}{(\operatorname{cosec} \theta+\cot \theta+1)(\operatorname{cosec} \theta-\cot \theta+1)-2}, 0^{\circ}<\theta<90^{\circ}$ $=\frac{(cos^2\theta)^2-(\sin^2\theta)^2+2 \sin ^2 \theta+3}{(\operatorname{cosec} \theta+1+\cot \theta)(\operatorname{cosec} \theta+1-\cot \theta)-2}$ $=\frac{(cos^2+\sin^2\theta)(cos^2-\sin^2\theta)+2 \sin ^2 \theta+3}{[(\operatorname{cosec} \theta+1)^2-\cot^2 \theta]-2}$ $=\frac{cos^2+\sin^2\theta +3}{[\operatorname{cosec^2} \theta+1+2\operatorname{cosec \theta}-\cot^2 \theta]-2}$ $=\frac{4}{2+2\operatorname{cosec} \theta-2}$ $=\frac{4}{2\operatorname{cosec} \theta}$ $=2 \sin \theta$ Hence, the correct answer
Question : Directions: In the following question, select the odd letter pair from the given alternatives.
Option 1: CD
Option 2: PR
Option 3: ST
Option 4: WX
Correct Answer: PR
Solution : Let's check the options – First option: CD; C + 1 = D Second option: PR; P + 2 = R Third option: ST; S + 1 = T Fourth option: WX; W + 1 = X
So, the second option is different from the
Question : P and Q can do a piece of work in 24 days, while R and S can do the same work in 8 days. In how many days P, Q, R, and S do it together?
Option 1: 10 days
Option 2: 6 days
Option 3: 7 days
Option 4: 5 days
Correct Answer: 6 days
Solution : P and Q in 1 day can do $\frac{1}{24}$ part R and S in 1 day can do $\frac{1}{8}$ part So, P, Q, R, and S together in 1 day can do ($\frac{1}{24}$ + $\frac{1}{8}$) = $\frac{1}{6}$ part of work. Hence, the correct answer
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