## RRB NTPC Quant quiz for Stage I

**Railway NTPC Quant quiz for (Phase I), RRB (JE), RRB ALP, SSC various exams and other competitive exams.**

Q1. **Six times of a positive integer is equal to 8 less than twice the square of that number. Find the number.**

A) 4

B) 12

C) 24

D) 32

Q2. **In a workshop 18 men and 14 children can complete a work in 30 days. 15 men can complete the same work in 60 days. In how many days will 14 men and 7 children complete that work?**

A) 45

B) 36

C) 40

D) 48

Q3. **If P. cos θ + Q. sin θ = 8 and P. sin θ – Q. cos θ = 5, what is the value of (P ^{2} + Q^{2})?**

A) 89

B) 97

C) 101

D) 99

Q4. **P, Q, and R are the midpoints of the sides AB, BC, and CA respectively of the ΔABC. If the area of ΔPQR is 8 cm², find the area of ΔABC?**

A) 40 sqcm

B) 32 sqcm

C) 16 sqcm

D) 24 sqcm

Q5. **If x + y = 5 and x ^{2} + y^{2} = 25, which one of the following is the value of x^{3} + y^{3}?**

A) 450

B) 361

C) 243

D) 125

Q6. **AB is a diameter and AC is a chord of a circle such that ∠ BAC =30°. The tangent at C intersects AB produced in D. Then,**

A) BC < BD

B) BC > BD

C) BC = BD

D) None of these

Q7. **3 years ago the age of a father was 1 year more than 4 times his son’s age. After 5 years the sum of their ages will be 57 years. Find the present age of the father.**

A) 25 years

B) 36 years

C) 48 years

D) 40 years

Q8. **Four pipes of lengths 75 cm, 100 cm, 125 cm, and 200 cm are to be cut into parts of equal lengths. Each part must be as long as possible. What is the maximum number of pieces that can be cut?**

A) 15

B) 20

C) 30

D) 25

Q9. **If 3 ^{x} + 3^{x+1} = 36, then the value of x^{x} is : **

A) 64

B) 2125

C) 81

D) 4

Q10. **Find the values of k for which 64x ^{2} + kx + 1 = 0 has equal roots.**

A) ± 16

B) ± 14

C) ± 12

D) ± 10

**Solutions**

**Solutions**

Q1. Ans(A)

**Traditional Approach :**

Let the number be x.

Then, according to the question,

6x = 2x^{2} – 8

⇒ 2x^{2} – 6x – 8 = 0

⇒ (x – 4)(2x + 2) = 0

⇒ x = 4, –1

**Elimination Approach :**

Let’s take option A ; 4

6 times of 4 = 24

Square of 4 = 16

∴ Twice of square of 4 = 32

We can clearly observe that 6 times of 4 is 8 less than twice the square of it.

Hence, it gets confirmed that 4 is the answer.

Option A, is hence the correct answer.

Q2. Ans(A)

**……….(1)**

Therefore, 20 Men will also complate the same work in ‘a’ days.

a = 45 days

So, 14 men and 7 children will complete that work in 45 days.

Option A, is hence the correct answer.

^{2}. cos

^{2}θ + Q

^{2}. sin

^{2}θ + 2PQ. sin θ.cos θ = 64

**…… (i)**

^{2}. sin

^{2}θ + Q

^{2}. cos

^{2}θ – 2PQ. sin θ.cos θ = 25

**……… (ii)**

P^{2} + Q^{2} = 89

Option A, is hence the correct answer

⇒ Area of ΔABC = 4 × area of ΔPQR = 4 × 8 = 32 cm²

Option B, is hence the correct answer.

^{2}= x

^{2}+ y

^{2}+ 2xy

⇒ 5^{2} = 25 + 2xy [Given x + y = 5 and x² + y² = 25]

So,

^{3}+ y

^{3}= (x + y) (x

^{2}+ y

^{2}– xy)

^{3}+ y

^{3}= 5 × (25 – 0)

⇒ x^{3} + y^{3} = 125

Option C, is hence the correct answer.

Q6. Ans(C)

∠ ACB = 90° ( ∠ in a semi-circle).

So, ∠ ABC = 60° & ∠ CBD = 120°

Now, ∠ BCD = ∠ BAC = 30°(∠ s in alt. segments)

**∴ **∠ BDC = 180° – ( 30°+120°) = 30°

Thus, ∠ BCD = ∠ BDC . So, BC = BD.

Q7. Ans(B)

Let present age of father be F and son be S.

F – 3 = 4(S – 3) + 1

⇒ F – 3 = 4S – 12 + 1

⇒ F – 3 = 4S – 11

⇒ F = 4 S – 11 + 3 = 4 S – 8

⇒F = 4S – 8 **…(i)**

Also,

(F + 5) + (S + 5) = 57

⇒ F + S + 10 = 57

⇒ F + S = 47

⇒ F = 47 – S ** …(2)**

Putting value of F from eqn.(i) in eqn. (ii), we get:

4 S – 8 = 47 – S

⇒ 5S = 47 + 8 = 55

⇒ S = 11

Age of son = 11

Putting the age of son in eqn. (2), Age of father (F) = 47 – 11 = 36 years

Option B, is hence the correct answer.

Q8. Ans(B)

Now,

H.C.F of 75, 100, 125 and 200 is 25.

As,

200 = 25 × 8

So, the pipe, length of which is 75cm is cut into three equal parts of 25cm each.and similarly pipe of 100cm length cut into 4 equal parts and so on.

∴ Number of pieces = 3 + 4 + 5 + 8 = 20.

3^{x} + 3^{x+1} = 36 ⇒ 3^{x} + 3^{x} × 3^{1} = 36

⇒ 3^{x} (1 + 3) = 36 ⇒ 3^{x} = 9 = 3^{2}

⇒ x = 2 ∴ x^{x} = 2^{2} = 4

Option D, is hence the correct answer.

^{2}+ kx + 1 = 0

^{2}– 4ac = 0

^{2}– 4 × 64 × 1 = 0

^{2}= 256

⇒ k = ± 16

Option A, is hence the correct answer.

**For more RRB NTPC Quant Quiz Click here**

**WhatsApp Group Join here****Mail us at : ambitiousbaba1@gmail.com****Telegram Group:- Click Here**