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What is the largest number which divides both

2³⁵ -1 and 2⁹¹ -1?

1. 34

2. 90

3. 127

4. 129

What is the largest power of 10 that divides

tbe product 29 x 28 x 27 x . . . 2 x 1 ?

1. 4

2. 5

3. 6

4. 7

What is the remainder when 65⁹⁹ is divided by 11 ?

1. 0

2. 5

3. 9

4. 10

If the roots of the equation x² — bx + c = 6 differ by 5, then which one of the following is correct?

1. b^{2 =} 4c + 5 

2. c^{2 =} 4b - 5 

3. b²⁺c^{2 =} 5 

4. b^{2 -} c^{2 =} 5 

In a party of 160 persons, 75 persons take tea, 60 persons take coffee and 50 persons take milk 15 of them take both tea and coffee, but no one taking milk takes tea. If each person in the party takea at least one drink, then what is the number of persona taking milk only ?

1. 50

2. 40

3. 30

4. 20

6. A, B, C, D and E enter into a business. They invest money in the ratio 2 : 3 : 4 : 5 : 6. However, the time invested by them is in the ratio 6 : 6 : 4 : 3 : 2. If the profit distributed is directly proportional to time and money invested, then who receives the highest amount of profit ?

1. C

2. Both B and D

3. Both C and D

4. All get equal profit

1. Only One

2. Only two

3. All three

4. None

A can do a certain work at twice the speed of B. Purther, B can do the same work at 1 5 times the speed of C. All of them together can finish the work in 12 days. In how many days can C alone finish the work ?

1. 36 days

2. 45 days

3. 60 days

4. 66 days

The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number ?

1. 1

2. 2

3. 3

4. 4

The time taken by a train to cross a man travelling in another train is 10 seconds, when the other train is travelling in the opposite direction. However, it takes 20 seconds, if both the trains are travelling in the same direction. The length of the first train is 200 m and that of the second train is 150 m. What is the speed of the first train ?

1. 60 km/hr

2. 56 km/hr

3. 54 km/hr

4. 52 km/hr

If a, b, c, d, e and f satisfy

2a = 3b = 6c = 9d = 12e = 18f, then what is the value of (a + b)/(c + d + e + f) ?

1. 4/7

2. 2

3. 5/2

4. 9/2

If a,  b, c are  non-zero  real  numbers  such  that a + b + c = 0, then what are the roots of the equation ax² + bx + c = 0 ?

1. 2, 1 + (c/a)
    

2. 1, a/c

3. 1, c/a

4. 2, (c/a) - 1

Twelve percent of bananas bought by a fruit vendor got lost during transportation. On selling the remaining bananas, the vendor’s overall profit turned out to be 4%. If the vendor had not lost any bananas and had sold them at the price of the remaining bananas, what would have been his profit percentage ?

1. 8 1/9%

2. 9 1/11%

3. 18 2/11%

4. None of these

If  the  positive  square  root  of (5+3 √2 ) (5-3 √2 ) is α, then what is the positive square root of 8 + 2α ?

1. 2 + √3

2. 3 - √2

3. √7 - 1

4. √7 + 1

When every even power of every odd integer (greater than 1) is divided by 8, what is the remainder ?

1. 3

2. 2

3. 1

4. The remainder is not necessarily 1.

Which of the statements given above ie/are correct ?

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither 1 nor 2

It is given that 5 does not divide n — 1, n and n + 1, where n is a positive integer. Which one of the following is correct ?

1. 5 divides (n² + l)

    

2. 5 divides (n² — l)
    

3. 5 divides (n² + n)
    

4. 5 divides (n² - n)

What is the largest 5-digit number, which leaves remainder 7, when divided  by 18 as well as by 11 ?

1. 99981

2. 99988

3. 99997

4. 99999

In a business dealing, A owes B Rs. 20,000 payable  after   5  years,  whereas  B  owes  A  Rs. 12,000 payable  after  4  years.  They  want to settle it now at the rate of 5&  simple interest. Who gives how much money in this settlement ?

1. Both are at par
    

    

2. B gives Rs. 6,000 to A
    

3. A gives Rs. 6,000 to B
    

4. A gives Rs. 4,000 to B

Average marks in Mathematics of Section A comprising 30 students is 65 and that of Section B comprising 35 students is 70. What are the average marks (approximately) of both the sections if it was detected later that an entry of 47 marks was wrongly made as 74 ?

1. 67 28
    

    

2. 67-58
    

3. 68 11
    

4. 68-63

1. 2207

2. 2247

3. 2317

4. 2337

1. 1 only

2. 2 only

3. Both 1 and 2

    

4. Neither 1 nor 2

Consider a 6-digit number of the form XYXYXY. The number is divisible by :

1. 3 and 7 only
    

    

2. 7 and 13 only
    

3. 3, 13 and 37 only
    

4. 3, 7, 13 and 37

1. a

2. b

3. c

4. d

1. 2

2. 4

3. 8

4. 16

Let m and n be natural numbers. What is the minimum value of (m + n) such that 33m + 22n ia divisible by 121?

1. 3

2. 4

3. 5

4. 10

The product of two numbers is 2160 and their HCF is 12. If tbe sum of the squares of the squares of the two numbers is 4896, tben what is tbe mean of the two numbers ?

1. 24

2. 36

3. 48

4. 96

The age of Q exceeds the age of P by 3 years. The age of R is twice the age of P and the age of Q is twice the age of S. Further, the age difference of R and S is 30 years. What is the Sum of the ages of P and Q ?

1. 35 years

2. 38 years

3. 39 years

4. 45 years

If a, b aod c are tbe sides of a triangle ABC, then √a + √b - √c is always :

1. Negative
    

2. Positive
    

    

3. Non-negative
    

4. Non-positive

There are four bells which ring at on interval of 15 minutes, 25 minutes, 35 minutes and 45 minutes respectively. If all of them ring at 9 A.M., how many more times will they ring together in the next 72 hours. 

1. 0

2. 1

3. 2

4. 3

1. One
    

2. Two
    

3. Three

4. Four

The number 97³⁰- 14³⁰ is divisible by :

1. 37 but not 83

2. 83 but not 37

3. Both 37 and 83

4. Neither 37 nor 83

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither 1 nor2

1. a

2. b

3. c

4. d

1. 1

2. 2

3. 4

4. 6

A, B aod C can complete a work in x, 1.5x and 2x days zespectîvely.If they complete the work together, in what ratio should they be paid?

1. 2 : 3 : 4

2. 6 : 4 : 3

3. 3 : 2 : 1

4. 4: 3 : 2

1. 1 and 2 only

2. 2 and 3 only

3. 1 and 3 only

4. 1, 2  and 3

What is the last digit of the sum S = 9²⁷ + 27⁹ ?

1. 3

2. 6

3. 7

4. 9

1. a

2. b

3. c

4. d

The speed of a  boat in still water is 15 km/hr. If it can travel 42 km downstream and 28 km upstream in the same time, then what is the speed of the stream ?

1. 2.5 km/hr

    

2. 3 km/hr

3. 4.5 km/hr

4. 6 km/hr

1. Rs.842

2. Rs.756

3. Rs.641

4. Rs.542

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither 1 nor 2

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither l nor 2

For what values of m, is mx² + mx + 8x + 9 a perfect square ?

1. 1,4

2. 4,9

3. 9,16

4. 4,16

1. a

2. b

3. c

4. d

1. 1 and 2 only

2. 2 and 3 only

3. 1 and 3 only

4. 1, 2 and 3

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

What is the minimum value of 6 - 4 sin θ

0 ≤ θ ≤  π/2? 

1. 1

2. 2

3. 4

4. 6

1. 1

2. 2

3. 3

4. 6

1. 2

2. 3

3. 4

4. 5

1. -1

2. 0

3. 1

4. 2

1. a

2. b

3. c

4. d

If 2 cos²  θ + sin θ -2 = 0, 0 < θ ≤ π/2, then what is the value of θ ?

1. π/6

2. π/4

3. π/3

4. π/2

A woman is standing on the deck of a shipi which is h (in metres) above water level. She observes the angle of elevation of the top of a tower as 60° and the angle of depression of the base of the tower as 30°. What is the height of the tower ?

1. 2h

2. 3h

3. 4h

4. 5h

Let ABC be a right-angled triangle with sidea 5 cm, 12 cm and 13 cm. If p is the length of the perpendicular drawn from vertex A on the hypotenuse BC, then what is the value of 13p?

1. 24

2. 48

3. 60

4. 90

OABC is a rhombua whoae three vertices lie on a circle with centre at O. If the area of the rhombus is 32?3 aquare cm, then what ia the radius of the circle ?

1. 4 cm

2. 6 cm

3. 8 cm

4. 16 cm

The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which one of the following is

1. 16 <p <18

2. 14 <p <16

3. 12 <p <14

4. 10 <p <12

A solid cube is cut into two cuboids of equal volume. What is the ratio of total surface area of the given cube to that of one of the cuboids ?

1. 2 : 1

2. 3 : 2

3. 4 : 3

4. 5 : 3

The length of a diagonal of a cuboid is 11 cm. The surface area is 240 square cm. What is the sum of its length breadth aod height ?

1. 16 cm

2. 17 cm

3. 18 cm

4. 19 cm

What is the area of the circle (approximately) inscribed in a triangle with side lengths 12 cm, 16 cm and 20 cm ?

1. 48 square cm

2. 50 square cm

3. 52 square cm

4. 54 square cm

Two times the total surface area of a solid right circular cylinder is three times ito curved surface area. If h is the height and r is the radius of the base of the cylinder, then which one of the following is correct ?

1. h = r

2. h = 2r

3. 2h = 3r

4. 3h = 4r

A   floor   of   a   big   hall    has   dimensions 30 m 60 cm and 23 m 40 cm. It is to be paved with square tiles of same size. What is the minimum number of tiles required ?

1. 30

2. 36

3. 169

4. 221

How long will a man take to walk around the boundary of a square field of area 25 hectares at the rate of 5 km/hr ?

1. 36 minutes

2. 30 minutes

3. 24 minutes

4. 18 minutes

1. a

2. b

3. c

4. d

If the length of a rectangle is increased by 66 2/3% then bar what percent should the width of the rectangle be decreased in order to maintain the same area ?

1. 50%

2. 45%

3. 40%

4. 35%

What is the maximum area that can be covered by three non-intersecting circles drawn inside a rectangle of sides 8 cm and 12 cm ?

1. 16π square cm

2. 18π square cm

3. 20π square cm

4. 24π square cm

1. a

2. b

3. c

4. d

A solid iron ball is melted and 64 smaller solid balls of equal aize are made uaing the entire volume of iron. What is the ratio of the surface area of the larger ball to the aum of the surface areas of all the smaller balls ?

1. 0.25

2. 0.50

3. 0.75

4. 1

A triangle ABC has been divided into four smaller triazzgles P, Q, It, S wbose peztzoeteza aze 16 cm, 12 cm, 4 cm aod 12 cmo respectively. P, R and S contain the vertices A, B and C respectively. What is the perimeter of the triangle ABC ?

1. 18 cm

2. 20 cm

3. 22 cm

4. 24 cm

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.
2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

2. Choose this option if the Question can be answered by either Statement alone.

3. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.

4. Choose this option if the Question cannot be answered even by using both Statements together.

1. 60

2. 72

3. 75

4. 80

Class               0 - 30     30 - 60       60 - 90    90 - 120

Frequency          4             5                7              4

If the median (P) and mode (Q) satisfy the relation 7 (Q - P) = 9R, then what is the value of R ?

1. 6

2. 5

3. 3

4. 1

Class               40 - 50     50 - 60       60 - 70    70 - 80

Frequency          4             3                1              2

What is the mean of the distribution ?

1. 51

2. 52

3. 54

4. 56

Class               40 - 50     50 - 60       60 - 70    70 - 80

Frequency          4             3                1              2

If M is the median then what ia the value of 3M ?

1. 53 1/3

2. 60

3. 160

4. 180

The  plinth  of  a   houae  has  an  area  of 200 square metres. It is rectangular in sdape and  its  length  and  breadth  are in the ratio 2 : 1. The owner of the house extends the terracé by 1 at on each side. What is the percentage of area that has increased in the terrace relative to the plinth ?

1. 40%

2. 32%

3. 20%

4. 15.5%

1. 6776 cubic cm

2. 6248 cubic cm

3. 5896 cubic cm

4. 5680 cubic cm

The. volume  of a  cuboid  is  3600 cubic cm. The   areas   of   two   adjacent    faces    are 225 square cm and 144 square cm. What is the area of the other adjacent face ?

1. 400 square cm

2. 360 aquaré cm

3. 320 aquare cm

4. 300 square cm

The perimeter and the area of a right-angled triangle are 36 cm and 54 aquare cm respectively. What is the length of the hypotenuse ?

1. 12 cm

2. 14 cm

3. 15 cm

4. 16 cm

1. 10

2. 11

3. 12

4. 13

The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. What is the area of the sector ?

1. 15.6 square cm

2. 15 square cm

3. 14.4 square em

4. 14.1 square cm

Question:

What is the length of QC ?

1. 4.4 cm

2. 4.2 cm

3. 3.6 cm

4. 3.2 cm

Question:

If < ABD = θ, then what is sin θ equal to ?

1. 0.4

2. 0.5

3. 0.6

4. 0.8

Question:

1. 5 cm

2. 4.8 cm

3. 4.4 cm

4. 4 cm

Question:

What is the area of the circle ?

1. 100π square cm

    

2. 96π square cm

3. 50π square cm

4. 48π square cm

Question:

1. a

2. b

3. c

4. d

Question:

1. a

2. b

3. c

4. d

Question:

1. a

2. b

3. c

4. d

Question:

1. a

2. b

3. c

4. d

Question:

What is the relation between x and y ?

1. x = y

2. 2x = 3y

3. x = 3y

4. 3x = 4y

Question:

If y = 15, then what is < ACB equal to ?

1. 30°

2. 40°

3. 45°

4. 60°