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MCQ Objective Sample Model Tests for INDIA

Questions are taken from previous papers of competitive exams and will deliver a fair idea for entrance exams

UPSC CDS POLICE OBJECTIVE TEST MCQ FULLY SOLVED

Questions 1 and 2: A truck travelled from town A to town B over several days. During the first day, it covered I/p ofthe total distance, where p is a natural
number. During the second day, it travelled l/q of the remaining distance, where q.is a natural number.During the third day, it travelled I/P of the distance remaining after the second day. and during the fourth day, l/q of the distance remaining after third day. By the end of the fourth day the truck had travelled 3/4 of the distance between A and B.
1. The value of p+q is
A. 4
B. 5
C. 6
D. 7
E. 8
Ans.D

2. lf the total distance is 100 kilometers, the minimum distance that can be covered on day I is - kilometres.
A. 25
B. 30
C. 33
D. 35
E. 40
Ans.A

3. For how many integers n, EG is the square of an integer'?
A. 0
B. l l
C. 2
D. 3
E. 4
Ans.C

Questions 4 am! 5:lt is possible to arrange eight ofthe nine numbers 2,LA,5;7,l0, l l ,12, I3 in the vacant squares of the 3 by 4 array shown below so that the
arithmetic average ofthe numbers in each row and column is the same integer.
4. The arithmetic average is :
A. 6
B. 7
C. 8
D. 9
E. 12
Ans.C

5. Which one of the nine numbers must be Left out when completing the array?
A. 4
B. S
C. 7
D. 10
E. 11
Ans.D

6. ABC is a triangle with∟CAB = l5º and ∟ ABC = 30 º. If M is the midpoint of AB then ∟ ACM;
A. 15 º
B. 30 º
C. 45 º
D. 60 º
E. None of the above
Ans.C

Questions 7 and 8: Let ‘f’ be a function defined on the set of integers. Assume that °l" satisfies the following properties:
1. f(0) is not equal to 0
2. f(l) = 3; and
3. f`(x)f (y) ='f(x + y) + f(x - y) for all integers x and y.

7. f(3) =
A. 7
B. 18
C. l23
D. 322
E. None of the above
Ans.B

8. f(7) =
A, l23
B. 322
C. 843
D. ll26
E. None of the above
Ans.C

9. Let p be any positive integer and 2x+p=2y, p+y=x and x+y=z. For what value of p would x+y+z attain its maximum value?
A, 0
B. l
C. 2
D. 3
E. None of the above
Ans.A


10. Eight cities A. B, C, D, E. F, G and H are connected with one-way roads R1 ,R2, R3, R4. R5 and R6 in the following manner:

R1 leads from A to C via B;
R2 leads from C to D and then via B to F;
R3 leads from D to A and then via E to H
R4 leads from F to B via G;
R5 leads from G to D; and
R6 leads from F to H
The minimum number of road segments that have to be blocked in order to make all trathc from B to D impossible is
A. 5
B. 4
C. 3
D. 2
E. 1
Ans.D

11. We define a function fon the integers f(x) = x/10 if x is divisible by 10. and f(x) = x + 1 if x is not divisible by I0. 1f A0 = 1994 and An+1 = f(An) , What •
is the smallest n such that An = 27
A. 9
B. 18
C. 128
D. 1993
E. An never equals 2
Ans.A

12. lf the polynomial x‘ + px + q has three distinct roots,then which of the following, is a possible value of p?
A. -1
B. 0
C. l
D. 2
E. 3
Ans.A

13. n a certain factory. each day the expected number of accidents is related to the number of overtime hours by linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported, and on another day there were 400 overtime hours logged and 5 accidents. What are the expected numbers of accidents when no overtime hours are logged?
A. 2
B. 3
C. 4
D. 5 '
E, None of the above
Ans.B

14. ABCD is a rectangle. The points Pt and Q lie on AD and AB respectively. lf the triangles —PAQ, QBC and PCD all have the same areas and BQ = 2 then AQ =
A. 1 + √5
B. 1 - √5
D. √7
E. Not uniquely determined.
Ans.A

15. A brokerage house offers 3 stock portfolios. Portfolio 1 consists of2 blocks of common stock and 1 municipal bond. Portfolio ll consists ot"4 blocks of common stock. 2 municipal bonds and 3 blocks of preferred stock. Portfolio lll consists of2 blocks of common stock, 2 municipal bond and 3 blocks of preferred stock. A customer Wants 12 blocks of common stock, 6 municipal bonds and 6 preferred
stocks. How many portfolio lll should be offered?
A. l `
B. 2
C, 3
D. 4
E. None of the above
Ans.E

16. Triangle ABC has vertices A(0, O) B (0. 6) and C(9, 0), The points P and Q lie on side.AC such that AP I PQ = QC. Similarly. the points R and S lie on side AB such that AR = RS = SB, lf the line segments PB and RC intersect at X. then the slope or" the line AX is
A. 2/3
B. -2/3
C. 3/2
D. -3/2
E. None ofthe above.
Ans.A

17. ln a rainy season. Jamshedpur experienced some rain for thirteen days. A morning rain was always followed by a clear evening. An evening rain was always preceded by a clear morning, A total of 9mornings and 12 evenings were clear. How many rainless days did Jamshedpur have in the period?
A. 7
B. 6
C. 5
D. 4
E. 3
Ans.E

18. a. b. c. cl and e be non—negative real numbers such that a + b + c + d + e ; l0. Let X be the maximum of the numbers a + b. b + c. 0+ d and d + e.The _ least possible value of X lies in the "interval
A. [O. 2]
B. 2,3]
C. [3.4]
D. [4. 5]
E. [5. l0]
Ans.A

Questions 19 to 21: Substitute different digits (0, °1,2, 9) for different letters in the problem below. so that the corresponding addition is correct and it results in the maximum possible value of MONEY.
P A Y
M E
R E A L
M O N E Y

19. The letter Y should be
A. 0
B. 2
C. 3
D. 7
E. None of these
Ans.D

20. There are nine letters and ten digits. The digit that remains unutilized is:
A. 4
B. 3
C. 2
D. 1
E. None of the above.
Ans.A

21. The resulting value of‘ MONEY` is
A. 10364
B. 10563
C. 10978
D. 19627
E. None of the above.
Ans.D

22. Consider the system of linear equations
2x+3y+4z= 16
4x +4y + 52 = 26
ax + by + cz = r
For r = 5 and a = I then the system of linear equation will have infinite number of solutions ifc Z
A. 3/2
B. 1
C. 1/2
D. 0
E. None of the above.
Ans.C

23. A management institute has six senior professors and four junior professors. Three professors are selected at random for a Government project. The probability that at least one of the junior professors would get selected is:
A. 5/6
B. 2/3
C. 1/5
D. 1/6
E. None of the above.
Ans.D

Questions 24 to 27: Seven integers A, B, C, D,E, F and G are to be arranger! in an increasing order such that
i. First four numbers are in arithmetic progression.
ii. Last four numbers are in geometric progression.
There exists one number between E and G.
iv. There exist no numbers between A and B.
v. D is the smallest number and E is the greatest.
vi. A/D = G/C = F/A is greater than 1
vii. E = 960


24. E/A =
A. 2
B. 3 .
C. 4
D. 5
E. None of the above
Ans.E

25. D =
A. 30
B. 25
C. 22
D. 20
E. None of the above
Ans.A

26. The common difference in the A.P. is
A. 20
B. 22
C. 25 •
D, 30
E. None of the above
Ans.D

27. The position and value ofA is
A. Sth highest and 100
B. 4th highest and 100
C. 4th highest and 110
D. 3rd highest and 180
E. None ofthe above
Ans.E

Questions 28to 31 are followed by two statements labelled as (1) and (2). You have to decide y" these statements are sumcienl to conclusively » answer the question. Choose
A. lf- Statement (1) alone is sufficient to answer the question.
B. lf Statement (2) alone is sufficient to answer the question
C. lfStatement (1) and Statement (2) together are sufficient but neither of the two alone is sufficient to answer the question
D. Ifeither Statement (1 ) or ‘Statement (2) alone i is sufficient to answer the question. _
E. Both Statement (1) and Statement (2) are insufficient to answer the question.

28. What is the maximum value of a/b'?
1, a, a + b and a +2b are three sides ofa triangle.
2. a and b both are positive.
Ans.A

29. ABC is a triangle with angle B=90°. Whatis the length of the side AC?
1. D is the midpoint of BC and E is the midpoint of AB.
2. AD=7andCE=5
Ans.C

30. Five integers A, B, C, D and E are arranged in such a waythat there are two integers between B and C and
B is not the greatest. There exists one integer be and E and D is smaller than E. A is not
smallest integer. Which one is the smallest?
1. E is the greatest
2. There exists no integer between Band E.
Ans.E

31. For which value of non-negative “a` will the sys ierri x² - y² = 0, (x - a )² + y² = 1 have exactly three teal solutions?
A,. -√2
B. 1
C. √2
D. 2
E. No such ‘a’ exists.
Ans.B

32. Let { An} be a unique sequence of positive integers satisfying the following properties: A1 = 1, A2=2, A4 = l2,
and An + l . An-1 = An + 1 for n = 2, 3, 4, ..., Then, A 7, is
A. 60
B. 120
C. 149
D. 169
E. 187
Ans.D

33. ABC is a triangle with angle BAC = 60º. . A point P lies on one-third of the way from B to C. and AP bisects LBAC. LAPC =
A. 30 º
B. 45 º
C. 60 º
D. 90 º
E. 120 º
Ans.A


Directions (quesdtion 34 –40) Each group of questions in this section besed on a set of conditions. In answering some of the questions it may be useful to draw a rough diagram. Choose response which most accurately amd completely answers the each question and blaken the corresponding space on each on your answer sheet
(Questions 34 to 40) Seven film buffs gangadhar Indra lalatakshaya, mahashwar
Rudra,vyomkesha, and Yogi - attend n showing of classic jilms. Three films nre shown: one each rlireetetl Irv Guru Dutt, Sntvajit Ray, and] Ritwik G/mink. Each of the buffs sees exactly one of the three films. The films are shown only once, one
film at a time. T he following restrictions apply :
Exactly twice as many of the film buffs see the Satyajit Ray film as see the Guru Dutt film. Gangadhar and Rudra do not see the same film as each other. lndra and l\/laheshwar do not see the same film as each other. Vyomkesha and Yogi see the same film as each other. Lalatakshaya sees the Satyajit Ray film.Gangadhar secs either the Guru Dutt film or the Ritwik(il1a1af\ film.

34, Which one ofthe following could be an accurate matching of film buffs to films?
A. Gangadhar: the Satyajit Ray film; lndra: the Ritwik Ghatak film; Maheshwar: the Satyajit Ray nlm
B. Gangadhar; the Ritwik Ghatak film; Indra: the Guru Dutt film; Vyomkesha: the Guru Dutt film
C. Indra: the Satyajit Ray film; Rudra: the Ritwik Ghatak film; Vyomkesha: the Guru Dutt film
D. Maheshwar: the Ritwik Ghatak film; Rudra: the Ritwik Ghatak film; Vyomkesha: the Ritwik
Ghatak film
E. l\/laheshvsar; the Satyajit Ray film; Rudra: the Satyaj it Ray film; Yogi: the Satyajit Ray film
Ans.D

35. Each ofthe following must be false EXCEPT:
A. Rudra is the only film buffto see the Guru Dutt film.
B. Rudra is the only film buff to see the Satyajit Ray Elm.
C. Yogi is the only film buff to see the Ritwik Ghatak film.
D. Exactly two film buffs see the Ritwik Ghatak film.
E. Exactly three film buffs see the Satyajit Ray film. .
Ans.A

36. Which one of the following could be a complete and accurate list of the film buffs who DO NOT see the Satyaj it Ray film?
A. Gangadhar. Maheshwar
B. Gangadhar, Rudra
C. Gangadhar, Indra, Ruclra.
D. Gangadhar, l\/laheshwar. Yogi
E. Gangadhar, Vyomkesha, Yogi
Ans.E

37. lf exactly one film bu ff sees the Ritwik Ghatak film, then which one ofthe following must be true?
A. Vyomkesha sees the Satyajit Ray film.
B. Gangadhar sees thc Guru Dutt film.
C. l\/laheshwar see the Guru Duft film.
D. Indra sees the Guru Dutt film.
E. Rudra sees the Satyajit Ray film. '
Ans.A

38. If Vyomkesha and Gadhadhar see the same film,then which one ofthe following could be true'?
A. Gangadhar sees the Guru Dutt film.
B. Indra sees the Satyaj it Ray film.
C. Rudra sees the Ritwik Ghatak film.
D. Vyomkesha sees the Satyaj it Ray film.
E. Yogi sees the Guru Dutt film
Ans.B

40. Each ofthe following could be a complete and accurate list of the film buffs who see the Guru Dutt film EXCEPT:
A. Gangadhar, Indra
B. Gangadhar, Maheshwar
C. Indra, Rudra
D. Maheshwar, Rudra
E. Vyomkesha, Yogi

Ans.E