Quantitative Aptitude Objective Type Questions - 6

1. Five students viz, P, Q, R, S and T are independently trying to solve a problem in mathematics. The probabilities that they will be able to solve the problem are 3/5, 1/3, 5/6, 1/2 and 5/8 respectively. What is the probability that the problem will be solved?
[A]5.2%
[B]0.83%
[C]25.5%
[D]99.17%


2. A bin in a hardware store, contains 150 bolts and 250 nuts. One-fifth of the bolts and three-fifth of the nuts are defective. One item is picked randomly from the bin. What is the probability that the item is either a defective item or it is a nut?
[A]45%
[B]37.5%
[C]7.5%
[D]75%


3. Two persons, A and B, committed a crime together. The police has arrested both of them for the purpose of interrogation. A tells truth 4 out of 5 times, while B tells truth 3 out of 4 times. The police will be interrogating them separately. What is the probability that they will give contradictory statements during the course of interrogation?
[A]80%
[B]75%
[C]15%
[D]35%


4. An NGO has been studying the literacy level among the male and female adults, in a certain village. 6 out of every 10 adults in the village are males. It is observed that 5 out of every 10 adult males, are illiterate and, 8 out of every 10 adult females are illiterates. If an adult is randomly selected and found to be illiterate then, what is the probability that the adult is a female?
[A]32%
[B]25.8%
[C]68%
[D]51.6%


5. In an arithmetical progression (A.P) j times the jth term is equal to k times the kth term. The first term is a and common difference is d. What is the (j + k)th term of the A.P.?
[A]0
[B](j + k) d
[C](j + k –1) d
[D]a


6. In an arithmetical progression (A.P.) the first term is 8 and the last term is 48. The sum of all the terms in the A.P. is 308. What is the common difference of the A.P.?
[A]10
[B]6
[C]4
[D]2


7. Three numbers are in arithmetical progression. The sum of the three numbers is 36 and the sum of their squares is 560. Which of the following statements are correct?
I. The first number is 6 or 10.
II. The first number is 4 or 20.
III. The first number is 6.
IV. The second number is 12.
V. The second number is 2 or 6.
VI. The second number is 6 or 10.
VII. The third number is 6 or 2.
VIII. The third number is 6.
IX. The third number is 20 or 4.
[A](I) and (VI)
[B](V) and (VII)
[C](II) and (VIII)
[D](II), (IV) and (IX)


8. Three numbers are in geometrical progression such that their sum is 21 and their product is 216. Which of the following statements are correct?
I. The first number is 6.
II. The first number is 6 or 12.
III. The first number is 3 or 12.
IV. The second number is 12.
V. The second number is 3.
VI. The second number is 3 or 12.
VII. The second number is 6.
VIII. The third number is 6.
IX. The third number is 3 or 6.
X. The third number is 12 or 3.
[A](I), (IV) and (VIII)
[B](II), (IV) and (IX)
[C](II), (V) and (VIII)
[D](III), (VII) and (X)


9. The sum of the first four terms of a geometrical progression (G.P.) is 60 and the sum of the first six terms of the same G.P. is 252. The common ratio is 2. What is the tenth term of the G.P. from the beginning?
[A]64
[B]256
[C]1024
[D]2048


10. The linear programming formulation of a problem is given below:
Maximize Z = 80 P + 60 Q
Subject to the constraints:
2 P + Q <= 80
P + Q <= 60
P <= 30
Q <= 50
P, Q >= 0
Solve the above problem graphically and find out which of the following statements are correct? (In the ordered pairs given below the value of P appears first and the value of Q appears next).
I. The feasible region is bounded by the points (0,0), (0,60), (30,30) and (30,0).
II. The feasible region is bounded by the points (0,0), (0,80), (30,20) and (30,0).
III. The feasible region is bounded by the points (40,0), (30,20), (30,30) and (60,0).
IV. The feasible region is bounded by the points (0,0), (20,40), (30,20) and (30,0).
V. The feasible region is bounded by the points (0,0), (0,50), (10,50), (20,40), (30,20) and (30,0).
VI. The optimal combination is P = 40 and Q = 20.
VII. The optimal combination is P = 40 and Q = 0.
VIII. The optimal combination is P = 60 and Q = 0.
IX. The optimal combination is P = 30 and Q = 20.
X. The optimal combination is P = 20 and Q = 40.
XI. The optimal value of Z is 3200.
XII. The optimal value of Z is 4400.
XIII. The optimal value of Z is 4800.
XIV. The optimal value of Z is 2400.
XV. The optimal value of Z is 4000.
[A](I), (VIII), and (XI)
[B](II), (IX) and (XIV)
[C](III), (VII) and (XII)
[D](V), (X) and (XV)


11. The variance of a set of data is 9 and the arithmetic mean is 5. What is the coefficient of variation?
[A]6%
[B]60%
[C]80%
[D]150%


12. What are the possible number of permutations of 5 different things taking 2 things at a time?
[A]10
[B]20
[C]30
[D]40


13. The variance of a set of data is 3. If every item is doubled then, what will be the variance of the resulting data set?
[A]40972
[B]40970
[C]3
[D]12


14. The probability of failure in a Bernoulli experiment is 0.60. The experiment is repeated 25 times. The mean of the binomial distribution of the number of successes is
[A]10
[B]15
[C]20
[D]25


15. The slope and the intercept on y-axis for a simple regression line are 3 and 5 respectively. If the independent variable has a value of 10, then the estimated value of the dependent variable is
[A]3
[B]5
[C]20
[D]35