2/15, 18/29, 7/18, 10/87.

A. 7/18 < 2/15 < 18/29 < 10/87

B. 10/87 < 7/18 < 2/15 < 18/29

C. 10/87 < 2/15 < 7/18 < 18/29

D. 18/29 < 10/87 < 2/15 < 7/18

The terms in the required order are 10/87, 2/15, 7/18, 18/29.

To arrange the terms from lowest to greatest, we will have to convert them into like terms.

So, we will find the LCM of the numbers' denominators.

The common and smallest multiple of 15, 29, 18, and 87=2×3×3×5×29

=2610

The terms will change as follows-

2×174/15×174=348/2610

18×90/29×90=1620/2610

7×145/18×145=1015/2610

10×30/87×30=300/2610

We will now compare the numerators of these numbers and arrange them accordingly.

The arrangement becomes: 300/2610, 348/2610, 1015/2610, 1620/2610

= 10/87, 2/15, 7/18, 18/29

Therefore, the terms in the required order are 10/87, 2/15, 7/18, 18/29.

Option C.

A. 2⁶ * 3⁵ * 7

B. 2⁶ * 3⁵ * 5 * 7

C. 2⁶ * 3⁵ * 5

D. 2⁶ * 3⁵

A. -5

B. -2

C. -4

D. -3

Formula:
log_b(x) = y, if b^y = x

Input:
x = 1/4096 = 8^-4
b = 8

y = log₈ (1/4096)
= log₈ 8^-4
= -4 log₈ 8 = -4 x 1
log₈ 4096 = -4

Option C

A. -2

B. 2

C. -1

D. 1

We all know that the GCD of two polynomials means that it is a common factor of both the polynomials.

Here we are given: GCD = x+1

this means that (x+1) is a factor of both the polynomials.

i.e.  x = -1 is a zero of both the polynomial.

This implies on putting x=-1 in polynomial equation x² - px – 4

we have polynomial equation will be = zero.

x² - px - 4 = 0 at x = -1

1 - (-1)p - 4 = 0

1 + p - 4 = 0

p = 3

similarly, on putting x = -1 in the second polynomial and equating it equal to zero, we will have p = 3

A. 15

B. 10

C. 8

D. 16

The given ratio is 4 : 8 : 5

Let the number of 1 rupee coin is 4x, number of 2-rupee coin is 8x and number of 5-rupee coin is 5x

Number of coins = 4x + 8x + 5x = 17x

Total amount = 1 * 4x + 2*8x + 5*5x = 90 (given)

45x = 90

X = 2

So, the number of 5-rupee coins is 5x = 5*2 = 10

Option B.

Given that LCM and HCF of two numbers are 234 and 13 respectively here we need to find smallest factor of the product of 2 numbers

As we know that the product of LCM and HCF of two numbers is equals to product of the two numbers 

then the product of 2 numbers = LCM × HCF = 234 × 13 = 3042

here the smallest factor of 3042 = 2

option A.

A.34%

B.4%

C.12%

D.22%

22 litres of a mixture that contains 25% of orange essence and the remaining quantity is water.

Therefore, orange essence in 22 litres of a mixture = 25% of 22 = 5.5 ltres

3litres of water is added to the mixture

Therefore, total mixture = 22 + 3 = 25 litres

The percentage of orange essence now in the mixture = (  5.5/25 )* 100 = 22%

Option D

A.Rs.15,800

B.Rs.14,500

C.Rs.13,800

D.Rs.12,500

new SP=18400-10% of 18400=16560
Let CP=x
then x + 20% of x=16560
x=13800
therefore actual cost=13800

Option C

A.50

B.40

C.35

D.60

Let Sony's mother's age be 'x'.

Now the conditions given for both of their ages related to their mom is

1/5(x-15) + 3/5(x-10) = 31

x-15 + 3x-30 = 1554

x-45 = 155

4x = 200

x = 50

So, Mother's age = 50.

Option A

A.12 √7

B.7 √14

C.7 √12

D.14 √7

A.316

B.315

C.320

D.300

Let in the mixture of x litres, quantity of alcohol= (2/100) *x=x/50 litres.

When 10 litres of alcohol are added

Quantity of mixture= (x+10) litres and 

Quantity of alcohol=10+ x/50 litres.

So % of alcohol in new mixture= (10 + x/50)/(x+10) = 5/100

x= 950/3= 316.66 ~ 316 litres

A.10

B.12

C.15

D.16

Total work = no. of men * efficiency of men * no. of days * no. of hours a day

Let efficiency of men be = X, women = x + 33.33% of x = 4X/3

Total work = 20*x * 10 * 8 = 1600X units

In the case of women

Equating total work

1600 x = no. of women * 4x/3 * 10 * 6

No. of women = 20

A.6:5

B.9:5

C.3:2

D.5:1

Distance covered by car = 1.5 * 30 = 45km

Distance covered by cycle = 1 * 25 = 25 km

Ratio of distance = 45: 25 = 9: 5

A. ⁶P₃  ways

B. ⁶C₃  ways

C. ³C₁, ³C₁, ³C₁, ³C₁, ³C₁.

D. (³C₁)⁶

No. of ways to select answer for the 1^st question = 3c1 out of (yes, no or none one answer should be selected)

Similarly, every question has 3 options

No. of ways of answering = 3c1 * 3c1 * 3c1 *3c1*3c1 *3c1 = (3c1)⁶

A.  3 m

B.  20 m

C.  6 m

D.  0..6 m

Given that we are working with different units we need to do some conversions.

v=300000000m/s

t=20nanoseconds = 20 *10 ⁻⁹ seconds

Distance travelled by the beam = V * T

=3×10 ⁸ × 20 *10 ⁻⁹

=6m

A.23.59 tons

B.7.56 tons

C.6.89 tons

D.6.41 tons

A.20

B.22

C.24

D.28

A.484

B.485

C.441

D.525

Difference of times = 10:45:12 - 8:54:57 = 9:104:72 - 8:54:57 = 1:50 :15 = 3600 + 3000 + 15 = 6615 seconds.

Now tremors are felt at the intervals of 15 seconds.  

Total = 6615/15 = 441

Option C

A.0.4

B.0.2

C.0.25

D.0.15

Solution:

Let us find the price of one flower

The cost of twelve flowers = Rs. 96

The cost of one flower = 96/12

 ∴ The cost of one flower = Rs. 8

Let us calculate the profit

The selling cost of each flower = Rs. 10

∴ Profit on each flower selling = Rs. 10 - Rs. 8 = Rs. 2

 Let us determine the profit percentage

Profit Percentage = (2/8) *100 = 25%

Option C

A.3,000 m

B.5,400 m

C.6,000 m

D.10,800 m

Speed of the Train= 250 kmph

 Speed of the cycle = 10kmph

The train overtakes the cyclist who travels in 45 secs with a speed of 10 kmph

Now Relative speed= 250-10 = 240 kmph

Finding the length of the train

Then the Relative speed of the cyclist and the train = 240

The length of the train = (240*5*45)/18 = 3000 m

Option A