1. The cost price of 10 articles is equal to the selling price of 9 articles. find the profit percent.
a. 101/9 %
b. 100/9 %
c. 102/9 %
d. 103/9 %
Ans: 100/9 %
Let Cost Price be x and selling price be y
Then given that cost price of 10 articles is equal to the selling price of 9 articles
That means 10x=9y
Y= 10x/9
Profit percent = (( selling price – cost price )/cost price ) * 100 = 100/9 %
2. The ratio of radii of two right circular cylinders is 6:7 and their heights are in the ratio 5:9. The ratio of their respective curved surface areas is
a. 14:15
b. 17:19
c. 23:29
d. 10:21
Ans: 10 : 21
Curved surface area of a cylinder = 2 * Pi * r * h
Ratio = (6/7) * (5/9) = 10:21
3. In how many ways can the 7 letters A,B,C,D,E,F and G be arranged so that C and E never together.
a. 5040
b. 6480
c. 3600
d. 1440
Ans: 3600
C and E never together = Total arrangements – C and E together
Total arrangements are 7!
C and E together = pack c and e into one unit + 5 other alphabets = 6! 2! ( 2! Is two arrange c and e
internally)
C and E never together = Total arrangements – C and E together = 7! – 6! 2! = 3600
4. How many numbers are there in all from 4000 to 4999 (both 4000 and 4999 included) having at least one of their digits repeated?
a. 356
b. 216
c. 496
d. 504
Ans: 496
Atleast one of their digits repeated = Total numbers – None of the digits repeated
Total numbers from 4000 to 4999 = 1000
None of the digits repeated = _ _ _ _5
There are total 4 places
1st place is filled with 4 only. So only one choice
2nd place is filled with any 9 digits except 4 as we have used 4 in 1st place. So 9 choices
Similarly 3rd place is filled with any 8 digits. So we have 8 choices
4th place is filled with any 7 digits. So we have 7 choices.
So total arrangements = 1 * 9 * 8 * 7 = 504
Ans= 1000 – 504 = 496
5. if 1/2x +1/4x+1/8x=14 Then the value of x is:
a. 8
b. 12
c. 4
d. 16
Ans: x = 16
8. Find the value of h[f(1,2,3), g(2,1,-2), h(1,-1,-1)].
a. 0.5
b. none
c. 1
d. 0
Ans(D)
9. A trapezium with an area of 5100 cm2 has a perpendicular distance between the two parallel sides of 60m . if one of the parallel sides be 40m. find the length of the other side.
a. 130 m
b. 110 m
c. 120 m
d. 145 m6
Ans: 130 m
Area of a trapezium = (1/2) (a+b) h
10. Find the simple interest on Rs. 306.25 from March 3rd to July 27th( In the same year ) at 3.75 percent.
a. Rs. 4.57
b. Rs. 4.59
c. Rs. 4.53
d. Rs 4.58
Ans: 4.59
from March 3rd to July 27th( In the same year) = 146 days
(306.25 * 146 * 3.75 )/ ( 365 * 100) = 4.59
11. Dhruv and Naksh drive at the speeds of 36 Kmph and 54 kmph respectively. If Naksh takes 3 hours
lesser than what Dhruv takes for the same distance. Then distance is :
a. 324 km b. 524 km
c. 320 km
d. 420 km
Ans: 324 km
Let Dhruv takes t hours then Naksh takes t-3 hours
Because distance is same in both cases
So 36 * t = 54 (t-3)
t=9
ans: 36 * 9 = 324 km
12. The radius of wheel of axis's car is 50 cm. What is the distance that the car would cover in 14
revolutions?
a. 11 m
b. 22 m
c. 33 m
d. 44 m
Ans: 44 m
Distance covered in one revolution is equal to wheel surface area = 2 * Pi * r
Distance covered in 14 revolutions = 14 ( 2 * (22/7) * 50) = 44000 cm= 44 m
13. P can do a piece of work in 5 days of 8 hours each and Q can do in 4 days of 6 hours each. How long will they take do it working 5 hours a day?
a. 2 days
b. 3 days
c. 4 days
d. 5 days
Ans: 3 days
P can do in 5* 8 hours= 40 hours
Q can do in = 24 hours
Working together in one hour = (1/40) + (1/24) = 1/15
Total work can be finished in 15 hours
They 5 hours a day so total number of days = 15/5 = 3 days7
14. Libra had three diamonds weighing equal. One of the diamond fell and broke into 4 equal pieces weighing 20 gm each. what was the total weight of the three diamonds?
a. 200 gm
b. 280 gm
c. 320 gm
d. 240 gm
Ans: 20 * 4 * 3 = 240 gm
16. if the antecedent and consequent of a ratio are increased by 5 and 6 respectively then the ratio is 5:6.
find the original ratio.
a. 5:6
b. 1:2
c. 2:3
d. 3:4
Ans: (a) let’s say original ratio is x:y
(x+5)/(y+6) = 5/6
Then x/y = 5/6
17. Rohit and Rahul start from the same point and move away from each other at right angle. After 4 hours they are 80 km apart. if the speed of Rohit is 4 kmph more than Rahul. what is the speed of Rohit?
a. 16 kmph
b. 20 kmph
c. 12 kmph
d. none
Ans: x is the speed of rahul then (x+4) will be rohit speed
802 = (4x)2 + ((x+4)4)2
X=12
Rohit speed = 12 + 4 = 16kmph
18. Abhimanyu and supreet can together finish a work in 50 days. They worked together for 35 days and
then supreet left. After another 21 days, Abhimanyu finished the remaining work. In how many days
Abhimanyu alone can finish the work?
a. 70 days
b. 75 days
c. 80 days
d. 60 days
Ans: 35 days worked together + 21 days abhimayu worked = finished the work
35(1/50) + 21(x) = 1
X=70 days
19. if two fair dice are thrown simultaneously. then what is the probability that sum of the numbers appearing on the top faces of the dice is less than 4?
a. 6/14
b. none
c. 1/12
d. 3/18
Ans: possible cases are (1,1) (1,2) and (2,1) = 3
3/36 = 1/12
21. 3 individuals john wright, greg chappell and gary kristen are in the race for the appointment of new
coach of team india. The probabilities of their appointment are 0.5, 0.3 and 0.2 respectively. If john
wright is appointed then probability of ganguly appointed as a captain will be 0.7 and corresponding
probability if greg chappell or gary kristen is appointed are 0.6 and 0.5 respectively. find the overall
probability that ganguly will appointed as a captain.
a. 0.63
b. 0.35
c. 0.18
d. 0.89
Ans: 0.63
22. A man spends Rs 660 on tables and chairs. the price of each table is Rs. 150 and the price of each
chair is Rs. 20. If he buys the maximum number of tables, what is the ratio of chairs to tables purchased?
a. 2: 5
b. 3:5
c. 2:3
d. 3:4
4 tables + 3 chairs =660
Chairs to tables ratio is 3:4
23. two packets are available for sale.
packet a: peanuts 100 gms for Rs 48 only
packet b: peanuts 150 gms for Rs 72 only
which is a better buy?
a. both have the same value
b. packet b
c. data insufficient
d. packet a
Ans: a. both have the same value
Packet-a : 1 gm cost = 48/100
Packet-b : 1 gm cost = 72/150
24. Find the surface area of a piece of metal which is in the form of a parallelogram whose base is 10 cm and height is 6.4 cm
a. 64 cm2
b. 65 cm2
c. 45 cm2
d. 56 cm2
Ans: a
25. Sridevi is younger than Rajeev by 4 years. if their ages are in the ratio of 7:9. how old is Sridevi?
Ans: if Sridevi is x then Rajeev will be (x+4)
x/(x+4) = 7/9
x=149
26. A sum of Rs. 900 amounts to Rs. 950 in 3 years at simple interest. If the interest rate is increased
by 4%, it would amount to how much?
27. two trains for Palwal leave Kanpur at 10a.m and 10:30 am and travel at speeds of 60 kmph and
75 kmph respectively. After how many kilometers from Kanpur will the two trains be together?
Ans: 150 km
28. (x + 1/x) = 6 the value of ( x5 + 1/x5 ) = ?
Ans: 6726
29. In how many ways can 44 people be divided into 22 couples?
Ans: Short cut how many ways n people be divided into n/2 couples
(n!)/{(2!)n/2 (n/2)!} so ans is b. (44!)/{(2!)22 (22!)}
30. Find the remainder when ( x3 + 4 x2 + 6 x - 2 ) is divided (x+5)
Ans: -57
31. a solid cylinder has total surface area of 462 cm2 . If total surface area of the cylinder is thrice of its
curved surface area. then the volume of the cylinder is:
a. 539 cm3
b. 545 cm3
c. 531 cm3
d. 562 cm3
Ans:539
32. In which year was there lowest wheat import?
a. 1973
b. 1974
c. 1975
d. 1982
Ans: a
33. What is the ratio of number of years which have imports above the average imports to those which
have imports below the average imports?
a. 5:3
b. 2: 6
c. 3: 8
d. none
Ans: d
34. The increase in imports in 1982 was what percent of the imports in 1981?
a. 25%
b. 5%
c. 125%
d. 80%
Ans: a
35. The section of a solid right circular cone by a plane containing vertex and perpendicular to base is
an equilateral triangle of side 10 cm. find the volume of the cone?
a. 221.73 cm3 b.223.73 cm3 c.228.73 cm3 d.226.61 cm3
36. A sum of Rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months, the total
amount of Rs 500 is recieved. find the rate of interest.
a. 2% b. 4% c. 1% d. 3%
Ans: 4%
37.Consider the following two curves in the X-Y plane
y=(x3+x2+5)
y=(x2+x+5)
Which of the following statements is true for -2<= x <=2?
a. The two curves do not intersect.
b. The two curves intersect thrice.
c. The two curves intersect twice.
d. The two curves intersect once.
Ans: b
38. Give a model for maximizing the profit in a company or minimizing the loss in a conflict with
optimization techniques. where quantity f(x) is referred to as the objective function while the vector
‘x’ consists of decision variables.
A. None of the mentioned options.
B. x* =arg min f(x) C. x* =arg max f(x)
D. x* =an-1+an arg
min f(x)n
39. A positive integer is selected at random and is divided by 7,what is the probability that the remainder is 1?
A. 3/7 B. 4/7 C. 1/7 D. 2/7
Ans: 1/7
40. A mixture of 40 litres of salt and water contains 70%of salt. How much water must be added to
decrease the salt percentage to 40%?
A. 40 litres B. 30 litres C. 20 litres D.2 litres
Ans: x=30
Ques 41 : Choose the correct answer.
If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively,
then the sum of the reciprocals of the numbers is equal to:
Option 1 : 55/601
Option 2 : 601/55
Option 3 : 11/120
Option 4 : 120/11
Correct Answer :11/120
Ques 42 : Choose the correct answer.
Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water
respectively. What biggest measure can measure all the different quantities exactly ?
Option 1 : 1 litre
Option 2 : 7 litre
Option 3 : 31 litre
Option 4 : 41 litre
Correct Answer :31 Liters
Ques 43 : Choose the correct answer.
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
Option 1 : 4
Option 2 : 10
Option 3 : 15
Option 4 : 16
Correct Answer : 16
Ques 44 : Choose the correct answer.
Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45
minutes respectively. All the devices beeped together at 12 noon. They will again beep together at:
Option 1 : 12 midnight
Option 2 : 3 a.m.
Option 3 : 6 a.m.
Option 4 : 9 a.m.12
Correct Answer : 9am
Ques 45 : Choose the correct answer.
The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:
Option 1 : 47
Option 2 : 60
Option 3 : 72
Option 4 : None of these
Correct Answer : None Of These
Ques 46 : Choose the correct answer.
What least value must be assigned to * so that the number 63576*2 is divisible by 8?
Option 1 : 1
Option 2 : 2
Option 3 : 3
Option 4 : 4
Correct Answer :3
Ques 47 : Choose the correct answer.
Which of the following numbers is exactly divisible by 24 ?
Option 1 : 35718
Option 2 : 63810
Option 3 : 537804
Option 4 : 3125736
Correct Answer :3125736
Ques 48 : Choose the correct answer.
The number nearest to 15207, which is divisible by 467, is:
Option 1 : 14342
Option 2 : 15211
Option 3 : 14944
Option 4 : 15411
Option 5 : None of these
Correct Answer :1541113
Ques 49 : Choose the correct answer.
The smallest number, which is a perfect square and contains 7936 as a factor is:
Option 1 : 251664
Option 2 : 231564
Option 3 : 246016
Option 4 : 346016
Option 5 : None of these
Correct Answer :246016
Ques 50 : Choose the correct answer.
In a division problem, the divisor is twenty times the quotient and five times the remainder. If the remainder is 16, the number will be:
Option 1 : 3360
Option 2 : 336
Option 3 : 1616
Option 4 : 20516
Option 5 : None of these
Correct Answer :336
Ques 51 : Choose the correct answer.
The L.C.M. of two numbers is 4800 and their G.C.M. is 160. If one of the numbers is 480, then the other number is:
Option 1 : 1600
Option 2 : 1800
Option 3 : 2200
Option 4 : 2600
Option 5 : None of these
Ques 52 : Choose the correct answer.
The L.C.M. of two numbers is 140. If their ratio is 2:5, then the numbers are:
Option 1 : 28,70
Option 2 : 28,7
Option 3 : 8,70
Option 4 : 8,40
Option 5 : None of these
Ques 53 : Choose the correct answer.
If a number is exactly divisible by 85, then what will be the remainder when the same number is divided by 17?
Option 1 : 3
Option 2 : 1
Option 3 : 4
Option 4 : 0
Ques 54 : Choose the correct answer.
The least perfect square number which is exactly divisible by 3, 4, 7, 10 and 12 is:
Option 1 : 8100
Option 2 : 17600
Option 3 : 44100
Option 4 : None of these
Ques 55 : Choose the correct answer.
(xn+yn) is divisible by (x-y):
Option 1 : for all values of n
Option 2 : only for even values of n
Option 3 : only for odd values of n
Option 4 : for no values of n
Ques 56 : Choose the correct answer.
The greatest number that will divide 63, 138 and 228 so as to leave the same remainder in each case:
Option 1 : 15
Option 2 : 20
Option 3 : 35
Option 4 : 40
Ques 57: Choose the correct answer.
Find the largest number, smaller than the smallest four-digit number, which when divided by 4,5,6 and 7
leaves a remainder 2 in each case.
Option 1 : 422
Option 2 : 842
Option 3 : 12723
Option 4 : None of these
Ques 58 : Choose the correct answer.
What is the highest power of 5 that divides 90 x 80 x 70 x 60 x 50 x 40 x 30 x 20 x 10?
Option 1 : 10
Option 2 : 12
Option 3 : 14
Option 4 : None of these
Ques 59 : Choose the correct answer.
If a and b are natural numbers and a-b is divisible by 3, then a3-b3 is divisible by:
Option 1 : 3 but not by 9
Option 2 : 9
Option 3 : 6
Option 4 : 27
Ques 60 : Choose the correct answer.
What is the greatest positive power of 5 that divides 30! exactly?
Option 1 : 5
Option 2 : 6
Option 3 : 7
Option 4 : 8
Ques 61: Choose the correct answer.
In how many ways can the number 6084 be written as a product of two different factors ?
Option 1 : 27
Option 2 : 26
Option 3 : 13
Option 4 : 14
Ques 62: Choose the correct answer.
What is the smallest four-digit number which when divided by 6, leaves a remainder of 5 and when divided by 5 leaves a remainder of 3?
Option 1 : 1043
Option 2 : 1073
Option 3 : 1103
Option 4 : None of these
Ques 63: Choose the correct answer.
P is an integer. P>883. If P-7 is a multiple of 11, then the largest number that will always divide (P+4) (P+15) is:
Option 1 : 11
Option 2 : 121
Option 3 : 242
Option 4 : None of these
Ques 64: Choose the correct answer.
Let C be a positive integer such that C + 7 is divisible by 5. The smallest positive integer n (>2) such that C +
n2 is divisible by 5 is:
Option 1 : 4
Option 2 : 5
Option 3 : 3
Option 4 : Does not exist
Ques 65: Choose the correct answer.
Four bells begin to toll together and then each one at intervals of 6 s, 7 s, 8 s and 9 s respectively. The number of times they will toll together in the next 2 hr is:
Option 1 : 14 times
Option 2 : 15 times
Option 3 : 13 times
Option 4 : 11 times
Ques 66: Choose the correct answer.
The product of two numbers is 16200. If their LCM is 216, find their HCF.
Option 1 : 75
Option 2 : 70
Option 3 : 80
Option 4 : Data inconsistent
Ques 67: Choose the correct answer.
There are four prime numbers written in ascending order of magnitude. The product of first three is 385 and that of last three is 1001. Find the first number.
Option 1 : 5
Option 2 : 7
Option 3 : 11
Option 4 : 17
Ques 68: Choose the correct answer.
M and N are two distinct natural numbers. HCF and LCM of M and N are K and L respectively. A is also a natural number, which of the following relations is not possible?
Option 1 : K*L=A
Option 2 : K*A=L
Option 3 : L*A=K
Option 4 : None of these
Ques 69: Choose the correct answer.
On dividing a number by 999, the quotient is 366 and the remainder is 103.The number is:
Option 1 : 364724
Option 2 : 365387
Option 3 : 365737
Option 4 : 366757
Ques 70: Choose the correct answer.
The difference between two numbers is 1365. When the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15. The smaller number is:
Option 1 : 240
Option 2 : 270
Option 3 : 295
Option 4 : 360
Ques 71: Choose the correct answer.
The ratio of two numbers is 3:4 and their HCF is 4.Their LCM is:
Option 1 : 12
Option 2 : 16
Option 3 : 24
Option 4 : 48
Ques 72: Choose the correct answer.
A rectangular courtyard 3.78 meters long and 5.25 meters wide is to be paved exactly with square tiles, all of the same sizes. What is the largest size of the tile which could be used for the purpose?
Option 1 : 14 cm
Option 2 : 21 cm
Option 3 : 42 cm
Option 4 : None of these
Ques 73: Choose the correct answer.
The least perfect square which is divisible by 3, 4, 5, 6, 8 is:
Option 1 : 900
Option 2 : 1200
Option 3 : 2500
Option 4 : 3600
Ques 74: Choose the correct answer.
What will be obtained if 8 is subtracted from the HCF of 168, 189, and 231?
Option 1 : 15
Option 2 : 10
Option 3 : 21
Option 4: None of these
Ques 75: Choose the correct answer.
The largest four digit number which is a multiple of 8, 10,12 and 15 is:
Option 1 : 120
Option 2 : 9600
Option 3 : 9840
Option 4 : 9960
Ques 76: Choose the correct answer.
If logx (0.1) = -1/3, then the value of x is:
Option 1 : 10
Option 2 : 100
Option 3 : 1000
Option 4 : 1/1000
Ques 77: Choose the correct answer.
If ax = by, then:
Option 1 : log(a/b) = x/y
Option 2 : log(a) / log(b) = x/y
Option 3 : log(a) / log(b) = y/x
Option 4 : None of these
Ques 78: Choose the correct answer.
If log8 x + log8 (1/6) = 1/3 then the value of x is:
Option 1 : 12
Option 2 : 16
Option 3 : 18
Option 4 : 24
Ques 79: Choose the correct answer.
If log x + log y = log (x + y), then:
Option 1 : x = y
Option 2 : xy=1
Option 3 : y = (x-1)/x
Option 4 : y = x/(x-1)
Ques 80: Choose the correct answer.
If log10 7 = a, then log10(1/70) is equal to:
Option 1 : -(1 + a)
Option 2 : (1 + a)-1
Option 3 : a/10
Option 4 : 1/10a
Ques 81: Choose the correct answer.
If log{(a+b)/3} = 0.5(log a + log b), then the correct relation between a and b is:
Option 1 : a2+b2 = 7ab
Option 2 : a2-b2 = 7ab
Option 3 : (a+b)2 = 2
Option 4 : (a+b)/3 = (1/2)(a+b)
Option 5 : None of these
Ques 82: Choose the correct answer.
If log x = log 3 + 2 log 2- (3/4) log 16. The value of x is:
Option 1 : 1/2
Option 2 : 1
Option 3 : 3/2
Option 4 : 2
Option 5 : None of these
Ques 83: Choose the correct answer.
If log x =(1/2) log y = (1/5) log z, the value of x4y3z-2 is:
Option 1 : 0
Option 2 : 1
Option 3 : 2
Option 4 : 3
Option 5 : None of these
Ques 84: Choose the correct answer.
If log10000 x = -1/4, then x is given by:
Option 1 : 1/100
Option 2 : 1/10
Option 3 : 1/20
Option 4 : none of these
Ques 85: Choose the correct answer.
The value of 3-1/2 log3(9) is:
Option 1 : 3
Option 2 : 1/3
Option 3 : 2/3
Option 4 : none of these
Ques 86: Choose the correct answer.
loge xy - loge |x| equals to:
Option 1 : loge x
Option 2 : loge |x|
Option 3 : - loge x
Option 4 : none of these
Ques 87: Choose the correct answer.
The value of (loga n) / (logab n) is given by:
Option 1 : 1 + loga b
Option 2 : 1 + logb a
Option 3 : loga b
Option 4 : logb a
Ques 88: Choose the correct answer.
If (a4 - 2a2b2 + b4)x-1 = (a-b)2x (a+b)-2, then x equals to:
Option 1 : (a - b) / (a + b)
Option 2 : log (a2 - b2)
Option 3 : log (a + b) / log (a - b)
Option 4 : log (a - b) /log (a + b)
Ques 89: Choose the correct answer.
If a, b, and c are in geometric progression then loga n, logb n and logc n are in:
Option 1 : AP
Option 2 : GP
Option 3 : HP
Option 4 : None of these
Ques 90: Choose the correct answer.
What is the value of antilog10100?
Option 1 : 2
Option 2 : 10100
Option 3 : 100
Option 4 : 10
Ques 91: Choose the correct answer.
If antilog x 5 = 30, what can you infer about x?
Option 1 : x is a number between 1 and 2
Option 2 : x is 305
Option 3 : x is a number between 2 and 3
Option 4 : None of these
Ques 92: Choose the correct answer.
Every time x is increased by a given constant number, y doubles and z becomes three times. How will log(y) and log(z) behave as x is increased by the same constant number?
Option 1 : Both will grow linearly with different slopes
Option 2 : Both will grow linearly with same slopes
Option 3 : y will grow linearly, while z will not
Option 4 : z will grow linearly, while y will not
Ques 93: Choose the correct answer.
x triples every second. How will log2x change every second?
Option 1 : It will double every second
Option 2 : It will triple every second
Option 3 : It increases by a constant amount every second.
Option 4 : None of these
Ques 94: Choose the correct answer.
f(x) grows exponentially with x, how will f(log(x)) grow?
Option 1 : Exponentially
Option 2 : Linearly
Option 3 : Quadratically
Option 4 : None of these
Ques 95: Choose the correct answer.
What is the value of log512 8?
Option 1 : 3
Option 2 : 1/3
Option 3 : -3
Option 4 : -1/3
Ques 96: Choose the correct answer.
What is the value of log7 (1/49)?
Option 1 : 2
Option 2 : 1/2
Option 3 : -1/2
Option 4 : -2
Ques 97: Choose the correct answer.
Given that log64 x = 2/6, what is the value of x?
Option 1 : 2
Option 2 : 4
Option 3 : 6
Option 4 : 8
Ques 98: Choose the correct answer.
If 7x = 85, what is the value of x?
Option 1 : log785
Option 2 : log857
Option 3 : log107
Option 4 : log1085
Ques 99: Choose the correct answer.
If log102 = 0.3010, what is the number of digits in 264
Option 1 : 19
Option 2 : 20
Option 3 : 18
Option 4 : None of these
Ques 100: Choose the correct answer.
What is log110?
Option 1 : 1
Option 2 : 10
Option 3 : 0
Option 4 : Tends to infinity