VITEEE PCME Mock Test - 6 - JEE MCQ

Explanation:

• Given that f is continuous at x = 1, it means that the limit of f(x) as x approaches 1 exists and is equal to f(1).


• Since x ≠ 1, the function is defined around x = 1.


• Therefore, if f is continuous at x = 1, then f(1) must be equal to the value of the function at x = 1, which is A: 0, B: 1, C: e, or D: 1e.


• Out of the given options, the value of the natural number e is the most likely value for f(1) when x ≠ 1 and f is continuous at x = 1.


• Hence, the correct answer is C: e.

 

Determinant of skew symmetric matrix is always 0.

Initial distance = 25 dog leaps
Per-minute dog makes 5 dog leaps and cat makes 6 cat leaps = 3 dog leaps
⇒  Relative speed = 2 dog leaps / minutes
⇒  An initial distance of 25 dog leaps would get covered in 12.5 minutes.

So Option D is correct

Let distance between the two places = d km
Let total time taken by faster horse = t hr
⇒ Total time taken by slower horse = (t + 5) hr,

Therefore,
speed of the faster horse = d/t km/hr
speed of the slower horse = d/(t + 5) km/hr 
The two horses meet each other in 3 hour 20 min i.e. in 3(1/3) hr = 10/3 hr
In this time, total distance travelled by both the horses together is d. 

∴ d/(t+5) * 10/3 + d/t * 10/3 = d
⇒ 10/(3(t+5)) + 10/3t = 1
⇒ 10t + 10(t+5) = 3t(t+5)
⇒ 20t + 50 = 3t² + 15t
⇒ 3t² − 5t − 50 = 0
⇒ 3t² + 10t − 15t − 50 = 0
⇒ t(3t + 10) − 5(3t + 10) = 0
⇒ (3t + 10)(t − 5) = 0
⇒ t = 5 (ignoring -ve value) 

Thus, Total time taken by slower horse = 5 + 5 = 10 hr

So Option B is correct

Time take for reaching B for ram is T = 5/5 = 1hr
Time taken for reaching B for Shyam is T = 5/10 = 1/2 hr

Its 10 am when ram reaches B and 10: 15 when Shyam reaches B , so they must meet each after 10 and before 10:15 for sure as ram starts back after reaching B

if we see for options 10: 10 am is the only answer

Since the second rabbit covers 7/120 of the distance in 2 hours 30 minutes
⇒ it covers 8.4 / 120 = 7% of the distance in 3 hours.

Thus, in 3 hours both rabbits together cover 15% of the distance which means 5% per hour so they will meet in 20 hours.

The ratio of speeds = 8 : 7.
⇒ the second rabbit would cover 700 ft to the meeting point in 20 hours and its speed would be 35 feet/hr.

So Option D is correct

Tax on income of Rs. 2000 = 1% of 2000 = Rs. 20
Tax on income of Rs. 9000 = 2% of 9000 = Rs. 180
Total tax on an income of Rs. 2000 and an income of Rs. 9000 = 20 + 180 = Rs. 200

Tax on an income of Rs. 15,550 = 3% of 15,550 = 3/100 x 15,550 = 3/2 x 311 = Rs.933/2 

Tax on an income of Rs. 16,550 = 5% of 16,550 = 5/100 x 16.550 = 1655/2

Required ratio = 933/2 : 1655/2 = 933 : 1655

Number of applications received by colleges A, B and C in 2013 = 1200 + 1500 + 1850 = 4550
Number of applications received by colleges A, B and C in 2016 = 2000 + 1750 + 1500 = 5250
Ratio = 4550 : 5250 = 91 : 105 = 13 : 15

Number of applications received by college C during 2013-2016 = 1200 + 1650 + 2300 + 1750 = 6900
Number of applications received by college A during 2012-2015 = 1800 + 1500 + 1350 + 1100 = 5750
Difference = 6900 - 5750 = 1150

Let’s say the cost of the cloth is x rs per metre. Because of the faulty meter, he is paying x for 120 cms when buying.

So cost of 100 cms = 100x/120.

He is selling 80 cms for x, so selling price of 100cms of cloth is 100x/80.

discount = 20%

so the effective selling price is .8*100x/80= x

profit = SP-CP= x – 100x/120 = x/6

Profit % = x/6 divided by 100x/120 = 20%

Let total sales be ‘x’

The commission that Sailesh will get is x – 265000

He gets 6% on sales upto 100000 and 5% on sales greater than that.

Calculating his commission on total sales:

0.06*100000 + 0.05(x-100000)

Equating,

0.05x + 1000 = x – 265000

0.95x = 266000

x= 280000

Hence, his sales were worth 280,000