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General Test - 25

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General Test - 25
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  • Question 1
    4 / -1

    Three taps \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) together can fill an empty cistern in 5 minutes. The tap \(\mathrm{A}\) alone can fill it in 10 minutes and the tap \(\mathrm{B}\) alone in 20 minutes. How long will the tap \(\mathrm{C}\) alone take to fill it?

    Solution

    Let the time in which \(\mathrm{C}\) alone takes to fill be \(\mathrm{c}\) mins.

    Given, taps A, B and C together can fill an empty cistern in 5 minutes.

    Also tap A alone can fill it in 10 minutes and the tap B alone in 20 minutes.

    \(\therefore\) In \(1 \mathrm{~min}\),

    \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) fill part of cistern \(=\frac{1}{5}\)

    A alone fills part of cistern \(=\frac{1}{10}\)

    \(B\) alone fills part of cistern \(=\frac{1}{20}\)

    \(\mathrm{C}\) alone fills part of cistern \(=\frac{1}{c}\)

    \(\Rightarrow \frac{1}{c}+\frac{1}{10}+\frac{1}{20}=\frac{1}{5}\)

    \(\Rightarrow \frac{1}{c}=\frac{1}{5}-\frac{3}{20}\)

    \(\Rightarrow \frac{1}{c}=\frac{1}{20}\)

    \(\Rightarrow c=20 \mathrm{~min}\)

  • Question 2
    4 / -1

    \(A\) can-do work in 21 days and \(B\) in 28 days. If they work on it together for 3 days, then the fraction of the work that left is:

    Solution

    Given,

    \(A\) can-do work in 21 days.

    \(B\) can do the same work in 28 days.

    LCM of 21 and \(28=84\) (Total units of work)

    So, \(A\) does \(\frac{84}{21}=4\) units per day and \(B\) does \(\frac{84}{28}=3\) units per day.

    Therefore, in 3 days, they can do \(3 \times(4+3)=21\) units.

    So, the work done is \(\frac{21}{84}=\frac{1}{4}\)

    Therefore, the remaining work is \(\frac{3}{4}\).

  • Question 3
    4 / -1
    A rectangle with length \(14 \mathrm{cm}\) and width \(3 \mathrm{cm}\) is rotated along its length by \(150^{\circ} .\) What is the volume of the shape thus generated? (Use \(\pi=\frac{22}{7})\)
    Solution

    If rotated \(360^{\circ}\), It will become cylinder.By rotating along its length by \(150^{\circ}\),

    Radius \(=\) width \(=3 \mathrm{~cm}\);Height \(=\) length \(=14 \mathrm{~cm}\)

    Volume \(=\pi r^{2} \mathrm{~h} \times \frac{150 }{ 360}\)

    \(= \frac{22 }{ 7} \times 3^{2} \times 14 \times \frac{150 }{ 360 }= 165 \mathrm{~cm}^{3}\)

  • Question 4
    4 / -1

    A metallic cylindrical pipe has outer radius of \(3 \;cm\) and an inner radius of \(2 \;cm\). If the length of the pipe is \(70\; cm\), then the volume of metal in the pipe, in \(cm ^3\), is:

    Solution

    The inner volume of the pipe \(=\pi \times 2 \times 2 \times 70=280 \pi\)

    The outer volume of the pipe\(=\pi R^2 h\)

    The outer volume of the pipe\(=\pi× 3 ×3 × 70\) \(=630 \pi\)

    The volume of the metal in the pipe

    \(=\) Outer Volume \(-\) Inner Volume\(=630 \pi-280 \pi\)\(=350 \pi\)

  • Question 5
    4 / -1

    Three different positions of the same dice are shown. Select the option that will be opposite to the face having ‘@’.

    Solution

    Adjacent elements of @ are &, #, %, ©

    Adjacent elements can never be on the opposite surface of a particular element.

    The only element left is O.

    So, O will be opposite to the face having @.

    Therefore, “O” is the correct answer.

  • Question 6
    4 / -1

    Directions For Questions

    Directions: Read the instructions carefully and answer the question below.

    A, B, C, D, E, F, G, and H are the eight male members sitting around a circular table. Four of them are facing the inward direction and four are facing the outward direction. These eight people are married to eight girls namely L, M, N, O, P, Q, R, and S but not necessarily in the same order. No three consecutive people are facing the same direction.

    Only one person is sitting between B and the husband of L. Both the immediate neighbours of D are facing the same direction. Either R or P is the wife of D. The husband of Q is facing the outward direction and he is sitting to the immediate right of D. B is sitting third to the right of the person who is the husband of R and they are facing the same direction. The husband of P and the husband of Q are facing the same direction. The wife of D is sitting third to the left of F. Neither O nor P is the wife of B. G is sitting third to the right of C. The husband of L is sitting third to the left of E. Only one person is sitting between F and the husband of M and they are facing the same direction. The husband of S is sitting third to the right of H. A is an immediate neighbour of the husband of M. C is sitting third to the right of the husband of M and they are facing different directions.

    ...view full instructions

    Who is sitting second to the left of the husband of Q?

    Solution

    1) B is sitting third to the right of the person who is the husband of R and they are facing the same direction.

    (As it is a circular arrangement, we can randomly place the husband of R on any seat and then we can place B according to the direction the husband of R is facing.)

    2) Both the immediate neighbours of D are facing the same direction.

    (Implies, the immediate neighbours of D are facing a different direction than D.)

    3) The husband of Q is facing the outward direction and he is sitting to the immediate right of D.

    (Implies, D must be facing the inward direction. It also means that the other immediate neighbour of D must also be facing the outward direction and B is facing the inward direction.)

    4) Either R or P is the wife of D.

    5) The husband of P and the husband of Q are facing the same direction.

    (Implies, the husband of P is also facing the outward direction. It means that R is the wife of D.)

    6) Only one person is sitting between B and the husband of L.

    (Implies, the husband of L is sitting second to the right of B because the husband of Q is sitting second to the left of B.)

    7) The wife of D is sitting third to the left of F.

    (It is only possible if F is the husband of L and F is facing the outward direction.)

    8) Only one person is sitting between F and the husband of M and they are facing the same direction.

    (Implies, the husband of M is sitting second to the left of F because B is facing the inward direction.)

    9) C is sitting third to the right of the husband of M and they are facing different directions.

    (Implies, C is sitting between F and B. Also, C is facing the inward direction because the husband of M is facing the outward direction.)

    10) The husband of L is sitting third to the left of E.

    (Implies, E is sitting to the immediate left of B and E is facing the outward direction as it is the only possibility. Also, now that we have identified the four people who are facing the outward direction, we can say that all the other people are facing the inward direction.)

    11) A is an immediate neighbour of the husband of M.

    (Implies, A is sitting to the immediate left of F.)

    12) G is sitting third to the right of C.

    (Implies, G is the husband of M. Now, that only H is left to be placed, we can safely say that H is sitting to the immediate right of D.)

    13) The husband of S is sitting third to the right of H.

    (Implies, A is the husband of S.)

    14) Neither O nor P is the wife of B.

    (Implies, N is the wife of B as it is the only option left. Also, O and P are the wives of C and E but not necessarily in the same order.)

    Clearly, B is sitting second to the left of H who is the husband of Q.

  • Question 7
    4 / -1

    Directions For Questions

    Directions: Study the following information carefully and answer the question that follow:

    Fifteen persons from A to O are sitting in three rows namely Row-1, Row-2 and Row-3 facing north. Five persons are sitting in each row and seats of all rows are such that each seat is exactly behind or in front of another seat of a neighbouring row. Row-1 is to the north of Row-2 and Row-2 is to the north of Row-3.

    It is given that Engineers are sitting in row-1, Doctors are sitting in row-2 and Teachers are sitting in row-3.

    Further, it is given that:

    1. The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    2. Two persons are sitting between A and F but neither of them is doctorand F is sitting third to the left of A.

    3. N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    4. E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    5. G is sitting exactly behind A but not exactly in front of L.

    6. I is sitting exactly behind O.

    7. K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    8. C is sitting immediate to the right of H.

    9. D is not an engineer and not sitting at any of the ends.

    10. M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11. G is sitting at one of the ends but not in front of L.

    ...view full instructions

    Select the odd one out.

    Solution

    1) Two persons are sitting between A and F but neither of them is doctor and F is sitting third to the left of A.

    2) N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    3) E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    So, cases 2a and 2b are rejected. We have the following cases now:

    4) The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    5) I is sitting exactly behind O.

    6) K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    7) G is sitting exactly behind A but not exactly in front of L.

    So, cases 1a and 2a are rejected.

    8) C is sitting immediate to the right of H.

    9) D is not an engineer and not sitting at any of the ends.

    10) M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11) G is sitting at one of the ends but not in front of L.

    So, case 1b is rejected.

    Unlike in other options, in B-L-F, both B and F are from the same row.

    So, the correct answer is B-L-F.

  • Question 8
    4 / -1

    Directions For Questions

    Directions: Study the following information carefully and answer the question that follow:

    Fifteen persons from A to O are sitting in three rows namely Row-1, Row-2 and Row-3 facing north. Five persons are sitting in each row and seats of all rows are such that each seat is exactly behind or in front of another seat of a neighbouring row. Row-1 is to the north of Row-2 and Row-2 is to the north of Row-3.

    It is given that Engineers are sitting in row-1, Doctors are sitting in row-2 and Teachers are sitting in row-3.

    Further, it is given that:

    1. The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    2. Two persons are sitting between A and F but neither of them is doctorand F is sitting third to the left of A.

    3. N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    4. E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    5. G is sitting exactly behind A but not exactly in front of L.

    6. I is sitting exactly behind O.

    7. K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    8. C is sitting immediate to the right of H.

    9. D is not an engineer and not sitting at any of the ends.

    10. M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11. G is sitting at one of the ends but not in front of L.

    ...view full instructions

    How many persons are sitting between N and B?

    Solution

    1) Two persons are sitting between A and F but neither of them is doctor and F is sitting third to the left of A.

    2) N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    3) E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    So, cases 2a and 2b are rejected. We have the following cases now:

    4) The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    5) I is sitting exactly behind O.

    6) K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    7) G is sitting exactly behind A but not exactly in front of L.

    So, cases 1a and 2a are rejected.

    8) C is sitting immediate to the right of H.

    9) D is not an engineer and not sitting at any of the ends.

    10) M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11) G is sitting at one of the ends but not in front of L.

    So, case 1b is rejected.

    F and O are sitting between N and B.

    So, the correct answer is Two.

  • Question 9
    4 / -1

    Directions For Questions

    Directions: Study the following information carefully and answer the question that follow:

    Fifteen persons from A to O are sitting in three rows namely Row-1, Row-2 and Row-3 facing north. Five persons are sitting in each row and seats of all rows are such that each seat is exactly behind or in front of another seat of a neighbouring row. Row-1 is to the north of Row-2 and Row-2 is to the north of Row-3.

    It is given that Engineers are sitting in row-1, Doctors are sitting in row-2 and Teachers are sitting in row-3.

    Further, it is given that:

    1. The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    2. Two persons are sitting between A and F but neither of them is doctorand F is sitting third to the left of A.

    3. N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    4. E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    5. G is sitting exactly behind A but not exactly in front of L.

    6. I is sitting exactly behind O.

    7. K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    8. C is sitting immediate to the right of H.

    9. D is not an engineer and not sitting at any of the ends.

    10. M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11. G is sitting at one of the ends but not in front of L.

    ...view full instructions

    Select the pair of teachers among the following.

    Solution

    1) Two persons are sitting between A and F but neither of them is doctor and F is sitting third to the left of A.

    2) N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    3) E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    So, cases 2a and 2b are rejected. We have the following cases now:

    4) The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    5) I is sitting exactly behind O.

    6) K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    7) G is sitting exactly behind A but not exactly in front of L.

    So, cases 1a and 2a are rejected.

    8) C is sitting immediate to the right of H.

    9) D is not an engineer and not sitting at any of the ends.

    10) M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11) G is sitting at one of the ends but not in front of L.

    So, case 1b is rejected.

    K, L, H, C and E are the teachers in the given arrangement.

    So, the answer is K-C-H.

  • Question 10
    4 / -1

    Directions For Questions

    Directions: Study the following information carefully and answer the question that follow:

    Fifteen persons from A to O are sitting in three rows namely Row-1, Row-2 and Row-3 facing north. Five persons are sitting in each row and seats of all rows are such that each seat is exactly behind or in front of another seat of a neighbouring row. Row-1 is to the north of Row-2 and Row-2 is to the north of Row-3.

    It is given that Engineers are sitting in row-1, Doctors are sitting in row-2 and Teachers are sitting in row-3.

    Further, it is given that:

    1. The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    2. Two persons are sitting between A and F but neither of them is doctorand F is sitting third to the left of A.

    3. N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    4. E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    5. G is sitting exactly behind A but not exactly in front of L.

    6. I is sitting exactly behind O.

    7. K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    8. C is sitting immediate to the right of H.

    9. D is not an engineer and not sitting at any of the ends.

    10. M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11. G is sitting at one of the ends but not in front of L.

    ...view full instructions

    Which doctor among the following is sitting at one of the ends of the row?

    Solution

    1) Two persons are sitting between A and F but neither of them is doctor and F is sitting third to the left of A.

    2) N and A are sitting in the same row but N is sitting at one of the ends and J is sitting exactly behind or in front of him.

    3) E is a teacher and two persons are sitting between him and L but neither E nor L is sitting exactly behind J.

    So, cases 2a and 2b are rejected. We have the following cases now:

    4) The number of persons sitting between N and O is the same as the number of persons sitting between E and H.

    5) I is sitting exactly behind O.

    6) K is neither an engineer nor sitting in the same row as I but he is sitting at one of the ends.

    7) G is sitting exactly behind A but not exactly in front of L.

    So, cases 1a and 2a are rejected.

    8) C is sitting immediate to the right of H.

    9) D is not an engineer and not sitting at any of the ends.

    10) M is sitting in the same row as G is sitting but they are not neighbours of each other.

    11) G is sitting at one of the ends but not in front of L.

    So, case 1b is rejected.

    J and G are sitting at the ends of the row of Doctors.

    So, the correct answer is J.

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