SRMJEE Aptitude Mock Test - 2 - JEE MCQ

T₅ = 1
In an AP,
T_n = a + (n - 1)d
a + 4d = 1 --- (i)
Also, T₈ = -17
a + 7d = -17 --- (ii)
(ii) - (i):
3d = -18
d = -6
Using (i), a = 1 - 4 × (-6) = 1 + 24 = 25
So, sum of n terms,

a² + b² + c² + 27 = 6(a + b + c)
a² - 6a + 9 + b² - 6b + 9 + c² - 6c + 9 = 0
(a - 3)² + (b - 3)² + (c - 3)² = 0
It gives a = 3, b = 3 and c = 3.
Put this in .

= 3

6x = 2x² + 5x - 2
2x² - 2 = x

All the figures given below are in thousands.
Total number of cars sold by companies A in 2017 and C in 2013 = 52 + 65 = 117
Total number of cars sold by all four companies in 2013 = 45 + 63 + 65 + 67 = 240
Total number of cars sold by all four companies in 2016 = 72 + 58 + 70 + 63 = 263
Total number of cars sold by all four companies in 2013 and 2016 = 240 + 263 = 503
Required percentage = (117/503) × 100 = 23.26% ~ 23.3%
Hence, answer option 4 is correct.

Total number of cars sold by company C in 2018 = 76,000
Total number of cars sold by company A during 2014-2018 = 52,000 + 61,000 + 72,000 + 52,000 + 63,000 = 3,00,000
Average number of cars sold by company A during 2014-2018 = 3,00,000/5 = 60,000
Required number = 76,000 - 60,000 = 16,000
Hence, answer option 3 is correct.

Total number of cars sold by company B during 2015, 2017 and 2018 (in thousands) = 60 + 53 + 67 = 180
Total number of cars sold by company C in 2013, 2015, 2017 and 2018 (in thousands) = 65 + 66 + 63 + 76 = 270
Required percentage = (270 - 180)/270 × 100 =
Hence, answer option 2 is correct.

Total number of cars sold by companies A, B and D in 2017 (in thousands) = 52 + 53 + 75 = 180
Total number of cars sold by all four companies in 2018 (in thousands) = 63 + 67 + 76 + 74 = 280
Ratio of the total number of cars sold by companies A, B and D in 2017 to the total number of cars sold by all four companies in 2018 = 180 : 280 = 9 : 14
Hence, answer option 3 is correct.

Let the total work be 96 units.
(LCM of 24, 16 and 32 = 96)
Work done by A in 1 day = 96 units/24 = 4 units
Work done by B in 1 day = 96/16 units = 6 units
Work done by C in 1 day = 96/32 units = 3 units
Working together, work done by A and C in 1 day = 4 units + 3 units = 7 units
Work done by A and C in 6 days = 7 units × 6 = 42 units
Remaining work = 96 units - 42 units = 54 units
Time taken by B to complete 54 units of work = (54/6) days = 9 days
Hence, answer option 2 is correct.

Let a = 20 cm
b = 30 cm

Area of isosceles triangle
= 75√7

2 sinθ - 8 cos²θ + 5 = 0
⇒ 2 sinθ - 8 (1 - sin²θ) + 5 = 0
⇒ 8 sin²θ + 2sinθ - 3 = 0
⇒ 8 sin²θ - 4sinθ + 6 sinθ - 3 = 0
⇒ 4 sinθ (2sinθ - 1) + 3 (2 sinθ - 1) = 0
⇒ (4 sinθ + 3) (2 sinθ - 1) = 0
⇒ sinθ = 1/2
⇒ θ = 30°
(tan 2θ + cosec 2θ),
= (tan 2 × 30° + cosec 2 × 30°)
= (tan 60° + cosec 60°)

Hence, option (4) is correct.

• Number of students in science and vocational subjects = 35 + 18 + 10 + 30 = 93
• Total students = 35 + 18 + 25 + 47 + 45 + 40 + 10 + 30 = 250
• The percentage of students studying in science and vocational subjects = × 100 = 37.2%
• Hence, option (3) is correct.

Simple interest (in Rs.) = prt/100
p = principal (in Rs.)
r = rate of interest
t = time
Simple interest for 10 years = Rs.1,850
Simple interest for 4 years at 5% + Simple interest for 3 years at 8% + Simple interest for 3 years at 10% = 1,850

p(20 + 24 + 30) = 1,85,000
p = 1,85,000/74 = 2,500 
∴ The sum is Rs. 2,500.
Hence, answer option 4 is correct.