Mathematics Mock Test - 6 - CDS MCQ

Let us assume that the number with which Anita has to perform the multiplication is 'x'.

Instead of finding 35x, she calculated 53x.

The difference = 53x - 35x = 18x = 540

Therefore, x = 540/18 = 30

So, the new product = 30 x 53 = 1590.

Let the 4 digit no. be xyzw.
According to given conditions we have x + y = z + w, x + w = z, y + w = 2x + 2z.
With help of these equations, we deduce that y = 2w, z = 5x.
Now the minimum value x can take is 1 so z = 5 and the no. is 1854, which satisfies all the conditions. Hence option A.

• Different possibilities for the number of pencils = 12 or 13.
• Since it cannot be divided into his 4 brothers and sisters, it has to be 13.
• The number of erasers should be less than the number of pencils and greater than or equal to 11. So the number of erasers can be 11 or 12.
• If the number of erasers is 12, then the number of pens = 38 - 13 - 12 = 13, which is not possible as the number of pens should be more than the number of pencils.
• So the number of erasers = 11 and therefore the number of pens = 14 

Seema saved Rs. 900 in the first 3 months. She must saved Rs. (11400 – 900) = Rs. 10500 in the subsequent months.
The sequence will be of the form: 350 + 400 +……….. n terms = 10500

Solving, we get n = 15
The savings of Rs. 10500 is done in 15 months. Seema saved Rs. 11400 in 15+3 = 18 months.
Hence, option A is the correct answer.

Let ‘x’ be the strength of group G. Based on the information, 0.65x constitutes of literate people {the rest 0.35x = illiterate}
Of this 0.65x , 75% are old people =(0.75)0.65x old literates.
The total number of old people in group G is 0.72x  {72% of the total}.
Thus, the total number of old people who are illiterate = 0.72x - 0.4875x = 0.2325x.
This is 
≈ 66& of the total number of illiterates.
Hence, Option C is the correct answer.

19 * 38 – 958 + 364 = 128

In order to find the average age of the family before Ram was born, we need to know the age of the youngest member of the family. 
Since, we do not know the age of the youngest member, we can not calculate the total age of the family before Ram was born.
Hence, we can not calculate the answer with the given conditions.

Thus, D is the right choice.

Let initial average be x.
Then the initial total is 20x and the New average will be (x – 4),

The new total will be:
20(x – 4) = 20x – 80.

The reduction of 80 is created by the replacement. Hence, the new student has 80 marks less than the student he replaces. Hence, he must have scored 10 marks.

Short Cut:
The replacement has the effect of reducing the average marks for each of the 20 students by 4. Hence, the replacement must be 20 X 4 = 80 marks below the original.

Hence, answer = 10 marks. 

Work done will be directly proportional to number of men and days.
So according to the question:

• [(p)(p + 2)] / [(p + 4)(p - 1)] = 1/1 
• p² + 2p /  p² + 4p - p - 4 = 1
• p² + 2p =  p² + 3p - 4
• -p = -4
• p = 4

To find the speed of the train, we first need to find the speed of the steamer and the speed of the horse transit. The total distance traveled is 120 km + 450 km + 60 km = 630 km, and the total time taken for the journey is 13.5 hours. Therefore, the average speed of the journey is 630 km / 13.5 hours = 46.67 km/hr.

Since the speed of the train is three times that of the horse-transit and 1.5 times that of the steamer, we can write the following equations:

t = 3h t = 1.5s

where t is the speed of the train, h is the speed of the horse transit, and s is the speed of the steamer. Solving these equations, we find that the speed of the horse transit is 23.01 km/hr and the speed of the train is 69.03 km/hr.

Therefore, the speed of the train is 69.03 km/hr. The correct answer is B

• X’s five day work = 5/20 = 1/4. Remaining work = 1 – 1/4 = 3/4.
• This work was done by Y in 15 days. Y does 3/4th of the work in 15 days, he will finish the work in 15 × 4/3 = 20 days.  
• X & Y together would take 1/20 + 1/20 = 2/20 = 1/10 i.e. 10 days to complete the work.

So Option C is correct

x² + 5x - 3x - 15 = 0
⇒ x(x + 5) - 3(x + 5) = 0
⇒ (x - 3)(x + 5) = 0
⇒ x = 3 or x = -5.

The Correct option is A: 3

Let the roots of the equation 2a and 3a respectively.
Sum of Roots: 2a + 3a = 5a = -(- 5/2) = 5/2 
⇒ a = 1/2
Product of the roots: 6a² = b/2 
⇒ b = 12a² = 3
Hence, the values are: a = 1/2, b = 3.

y = 38 => x = 1

y = 36 => x = 2

…

…

y = 14 => x = 13

y = 12 => x = 14 => Cases from here are not valid as x > y.

Hence, there are 13 solutions.

y² + 3y - 18 ≥ 0

⇒ y² + 6y - 3y - 180

⇒ y(y + 6) -3(y + 6) ≥ 0

⇒ (y - 3)(y + 6) ≥ 0

⇒ y ≥ 3andy ≤ - 6

Let BC be the height of the tower and DC be the height of the student.
In rt. ΔABC,
AB = BC cot 45° = 100 m

In rt. ΔABD, AB = BD cot 60° = (BC + CD) cot 60° = (10 + CD) * (1 / √3)
∵ AB = 100 m
⇒ (10 + CD) * 1 / √3 = 100
⇒ (10 + CD) = 100√3
⇒ CD = 100√3 - 100 = 100 (1.732 - 1) = 100 x 0.732 = 73.2 m

Therefore, the answer is Option A.

Let the numbers be 37a and 37b.

Then, 37a x 37b = 4107

 ab = 3.

Now, co-primes with product 3 are (1, 3).

So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).

 Greater number = 111.

SP = 106.25% of the CP.
Thus, CP = 29.75/1.0625 = Rs. 28

So option D is correct

Let's denote the cost price of the first TV as CP1, the cost price of the second TV as CP2, and the selling price of the second TV as SP2.

The man makes a profit of 10% on the first TV, so we can write the selling price of the first TV as:

SP1 = CP1 + 10% of CP1
33000 = CP1 + 0.1 * CP1
33000 = 1.1 * CP1
CP1 = 33000 / 1.1
CP1 = 30000

He sells the second TV at a loss of 20%, so we can write the selling price of the second TV as:

SP2 = CP2 - 20% of CP2
SP2 = 0.8 * CP2

Since he neither gains nor loses on the whole, the total cost price equals the total selling price:

CP1 + CP2 = SP1 + SP2

We already know the values of CP1 and SP1, so we can substitute them in the equation:

30000 + CP2 = 33000 + SP2

We also know that SP2 = 0.8 * CP2, so we can substitute that as well:

30000 + CP2 = 33000 + 0.8 * CP2

Now, we can solve for CP2:

0.2 * CP2 = 3000
CP2 = 15000

Now that we have the cost price of the second TV, we can find its selling price using the relation we found earlier:

SP2 = 0.8 * CP2
SP2 = 0.8 * 15000
SP2 = 12000

So the selling price of the second TV set is Rs. 12000.

Given, P = Rs.900

SI = Rs.81

T = ?

R = 4.5%

Simple Intrest = SI = PRT/100
Where P = Principal, R = Rate of intrest and T = time period
Total SI = SI from SBI and SI from ICICI
∴ 220 = (500 x R x 2)/100 + (300 x R x 4)/100
⇒ 220 = 10R + 12R
⇒ R = 10% = Rate of intrest

Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)

• Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 x 6 = 36

E = Getting a sum of 9 when the two dice fall = {(3,6), (4,5), (5,4), (6,3)}

• Hence, n(E) = 4

Total number of cards, n(S) = 52
Total number of black cards, n(E) = 26

• Since log_a a = 1, so log₁₀ 10 = 1.
• log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3 
  ∴ log (2 + 3) ≠ log (2 x 3)
• Since loga 1 = 0. so logio 1 = 0.
• log (1 + 2 + 3) = log 6 
   log (1 x 2 x 3) = log 1 + log 2 + log 3=log (6). 

So. option (b) is incorrect.

⇒ - log₁₀ (7 x 10)
⇒ - (log₁₀ 7 + log₁₀ 10)
⇒ - (a + 1)

Explanation:

a/b + b/a = (a² + b²)/ab = (a² + b² + a + b)/ab 
= [(a + b)² - 2ab]/ab
a + b = -8/1 = -8
ab = 4/1 = 4
Hence a/b + b/a = [(-8)² - 2(4)]/4 = 56/4 = 14.

Explanation:

I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b