Mock Test-5 (Paper-1) (Question 101-125)

Total Questions: 25

11. ABCD is a square. Draw a triangle QBC on side BC considering BC as base and draw a triangle PAC on AC as it base such that ΔQBC ∼ ΔPAC then (Area of ΔQBC)/(Area of ΔPAC is equal to:)

Correct Answer: (c) 1/2
Solution:

12. Find the third vertex of the triangle whose two vertices are (-3, 1) and (0, -2) and the centroid is the origin.

Correct Answer: (c) (3, 1)
Solution:

Let third vertex is (a, b)
∴ (- 3 + 0 + a)/3 = 0 ⇒ a = 3
and (1 - 2 + b)/3 = 0 ⇒ b = 1
∴ 3ʳᵈ vertex is (3, 1)

13. From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar. Then the height of the pillar is

Correct Answer: (d) 12 m
Solution:

14. Read the information given below and answer the questions that follow. (Question 114 to 115)

(i) 658 failed in Physics
(ii) 166 failed in Physics and Chemistry
(iii) 372 failed in Chemistry, 434 failed in Physics and Maths
(iv) 590 failed in Maths, 126 failed in Maths & Chemistry.

Find the number of people who failed in (assuming that none is passed in all subjects).

We have the following equations:

a + b + c + d + e + f + g = 1000
a + b + d + e = 658b, + d = 166
b + d + c + f = 372.
d + e = 434 as in the figure.
d + e + f + g = 590 d + f = 126. Find the values.

Chemistry but not in Physics.

Correct Answer: (d) 206
Solution:Chemistry but not Physics = c + f = 206 .

15. Read the above statement and give the answer :

Physics or Maths but not in Chemistry.

Correct Answer: (c) 628
Solution:Physics and Maths but not Chemistry = a + e + g = 628.

16. A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways this can be done if the committee should have all the 4 professors and 1 research associate or all 3 trainees and 2 professors?

Correct Answer: (d) 12
Solution:

Number of committees,
= ⁴C₄ × ⁶C₁ + ³C₃ × ⁴C₂
= 1 × 6 + 1 × (4 × 3)/(1 × 2) = 6 + 6 = 12

17. .

Correct Answer: (d)
Solution:

18. Given below is the sequence of series. Analyze the pattern of the series and answer the given following questions.

4, 2, 2, 3, 6, 15, 45

If (2835)n is the term of the sequence where n is the nth term of sequence then find 'n'.

Correct Answer: (c) 10ᵗʰ
Solution:

19. The shape of an object is a right circular cylinder with a hemisphere on bottom and a right circular cone on the top. The radius of the cylinderical part is 5 cm and the height of cylinder part is 2.6 times the radius. What is the total height of the object, if the surface area of the object is770 cm²?

Correct Answer: (d) 30 cm
Solution:

20. Aman invested a certain sum - ₹ 'x' for two years in scheme A offering compound interest at 20% p.a. (compounded annually). He also invested ₹ (x - 1600) in scheme B for three years offering simple interest at 10% p.a. The interest he received from scheme A was twice the interest he received from scheme B. What is the sum of money that Aman had invested in scheme B?

Correct Answer: (a) ₹ 4400
Solution: