Mock Test-1 (Paper-1) (Question 101-125)

Total Questions: 25

11. If a two digits number is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by:

Correct Answer: (c) 11-k
Solution:10x + y = k(x + y)

∴  10y + x = 11y + 11x - 10x - y

= 11(x + y) - k(x + y) = (11 - k)(x + y)

12. Twenty five percent of Pranab's annual salary is equal to eighty percent of Surya's annual salary. Surya's monthly salary is forty percent of Dheeru's monthly salary. If Dheeru's annual salary is ₹ 6 lacs, what is Pranab's monthly salary? (At some places annual income and in some place monthly income is given.)

Correct Answer: (d) ₹ 64,000
Solution:Dheeru's monthly salary = 600000/12 = ₹ 50000

Surya's monthly salary = 50000 × 40/100 = ₹ 20000

Pranab's monthly salary = 20000 × 80/25 = ₹ 64000

13. If a sum of amount becomes 3 time in 8 years at compound interest, it will become 9 times in how many years?

Correct Answer: (a) 16 years
Solution:So for next 8 years it again becomes 3 times means 3 × 3 times = 9 times = 16 years

14. Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. 62 cm³ of the melted material is lost due to improper handing. The area (in cm²) of the whole surface of the newly formed cube is

Correct Answer: (a) 294
Solution:Volume of all three cube = 4³ + 5³ + 6³

= 64 + 125 + 216 cm³ = 405 cm³

Now, 62cm³ is lost

∴ Volume of new cube = 405 - 62 = 343

(side of new cube)³ = 343

side of new cube= ³√343 = 7

Total surface area of new cube

= 6(side)² = 6 × (7)² = 6 × 49 = 294 cm²

15. 18, 48, 100, 180, 294, 448, ?

Correct Answer: (d) 648
Solution:

16. If p, q, r are all real numbers, then (p - q)³ + (q - r)³ + (r - p)³ is equal to

Correct Answer: (b) 3 (p - q) (q - r) (r - p)
Solution:If a + b + c = 0 then a³ + b³ + c³ = 3abc

let, a = (p - q), b = (q - r), c - (r - p)

than, a + b + c = p - q + q - r + r - p = 0

∴  (p - q)³ + (q - r)² + (r - p)³

= 3(p - q) (q - r) (r - p) = 0

17. The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is

Correct Answer: (b) 108
Solution:Sum of the digits in the units place

⇒ (4 - 1) ! (3 + 4 + 5 + 6) ⇒ (4 - 1) ! (3 + 4 + 5 + 6)

⇒ 3 ! (3 + 4 + 5 + 6) ⇒ 3 ! (3 + 4 + 5 + 6)

⇒ 6 × 18 ⇒ 6 × 18 = 108

18. 72% of the students of a certain class took Biology and 44% took Mathematics. If each student took at least one subject from Biology or Mathematics and 40 took both, the total number of students in the class is

Correct Answer: (c) 250
Solution:Let the total number of students in the class be x.

∴  72x/100 - 40 + 40 + 44x/100 - 40 = x

⇒ 72x/100 × x + 44x/100 - x = 40 ⇒ x = 250

19. With the vertices of the triangle ABC as centres, three circles are described, each touching the other two externally. If the sides of the triangles are 10 cm, 8 cm and 6 cm find the radii of the circles.

Correct Answer: (c) 4 cm, 6 cm, 2 cm
Solution:

Let radius of 3 circles be r₁, r₂ & r₃

So, r₁ + r₂ = 10

r₂ + r₃ = 8 ;  r₃ + r₁ = 6

After solving, we get

r₁ = 4, r₂ = 6, r₃ = 2

20. Suresh, starting from his house, goes 4 km in the East, then he turns to his right and goes 3 km. What minimum distance will be covered by him to come back to his house?

Correct Answer: (b) 5 km
Solution: