UGEE REAP Mock Test- 1 - JEE MCQ

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

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x)

⇒ 28x - 22x = 350800 - (13900 * 22)
⇒ 6x = 45000
⇒ x = 7500
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400

Let the number of total employees in the company be 100x, and the total salary of all the employees be 100y.

It is given that 20% of the employees work in the manufacturing department, and the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company.

Hence, the total number of employees in the manufacturing department is 20x, and the total salary received by them is (100y/6)

Average salary in the manufacturing department = (100y/6*20x) = 5y/6x

Similarly, the total number of employees in the nonmanufacturing department is 80x, and the total salary received by them is (500y/6)

Hence, the average salary in the nonmanufacturing department = (500y/6*80x) = 25y/24x

Hence, the ratio is:- (5y/6x): (25y/24x) 

=> 120: 150 = 4:5

The correct option is D

1st term = 2
2nd term = 2 + 1 = 3
3rd term = 3 * 1 = 3
4th term = 3 + 2 = 5
5th term = 5 * 2 = 10
6th term = 10 + 3 = 13...

⇒ For every term at even position, previous term is added with half of the position
⇒ For every term at odd position, previous term is multipiled with the same numeber that was added in previous term

So, missing term = 13 x 3 = 39.

Shortcut:
The decrease in weight would be 20kgs (10people’s average weight drops by 2 kgs). Hence, the new person’s weight = 140 - 20 = 120.

Detailed Solution:

Let weight of 9 men =x.
Weight of new men =y

According to the question:

((x+140)/10) ​− 2 = (x+y​)/10
y = 120

P - M → P is the brother of M
M + N → M is the mother of N
N × Q → N is the sister of Q
Therefore, P is the maternal uncle of Q.

option D.

P*Q^R@S#T*P: P is elder than Q, Q is child of R, R is brother of S, S is younger than T, T is elder than P.
The age of Q is 22 years and age of T is 33 years.

T(33) > P > Q
Hence, the age of P is 29 years.

Explanation:

Given Information:
- P!Q - P is the parent of Q
- P^Q - P is the child of Q
- P*Q - P is elder to Q
- P#Q - P is younger to Q
- P@Q - P is brother of Q
- P&Q - P is wife of Q
- P+Q - P is sister-in-law of Q

Given:
A!B^C+D&E@F^GIA

Since G is the wife of H, we can infer that G&H.

Now, we need to find the relationship between G and C.

Since H is the parent of G, and C is the child of B, and B is the parent of C, then we can conclude that G is the mother-in-law of C.

Therefore, the correct answer is B: Mother-in-law.A ! B ∧ C + D & E @ F ^ G! A: A is parent of B, B is child of C, C is sister-in-law of D, D is wife of E, E is brother of F, F is child of G, G is parent of A.

This is a simple alternating addition and subtraction series.

In the first pattern, 3 is added. In the second, 2 is subtracted.

► 7 + 3 = 10,
► 10 - 2 = 8,
► 8 + 3 = 11,
► 11 - 2 = 9,
► 9 + 3 = 12,
► 12 - 2 = 10.

• The word that is different from the rest is "Trousers" (Option D).

  Explanation: All the other options - Coat, Shirt, Blouse, and Sweater - are upper-body clothing items, while Trousers are a lower-body clothing item. Hence, Trousers are the odd one out.

P sits two seats to the left of R, and Q sits two seats to the right of R. We can represent this information in the diagram below.

On the basis of the diagram that we drew, we find that to accommodate U we have to create a new slot between P and Q.

Hence, choice (c) is the correct answer. Choice (c)

When a person aged 26 years, is replaced by a person aged 56 years, the total age of the group goes up by 30 years.

Since this leads to an increase in the average by 6 years, it means that there are 30 / 6 = 5 persons in the group.

If the number of swifts sold by R and S is to be minimum, R and S should sell a maximum number of Baleno and Zen.

The share of R and S in total sales is 40%.

So even if they sell all Baleno’s and Zen that will account to only 24%, so they together will sell 16% Swifts.

The total share of swifts is 27% so they sold 16%.

Hence percentage share would be 16/27 × 100

= 59.25% which on rounding off becomes 59%. So correct answer is 59.

Let the two consecutive positive integers be x and x + 1.

⇒ x² + (x + 1)² - x(x + 1) = 91
⇒ x² + x - 90 = 0
⇒ (x + 10)(x - 9) = 0
⇒ x = -10 or 9.
x = 9 [∵ x is positive]

Hence the two consecutive positive integers are 9 and 10.

We have, p² + 5 < 5p + 14

=> p² – 5p – 9 < 0

=> p<6.4 or p>-1.4
Hence, p ≤ 6, p > −1 will satisfy the inequalities

We know that,
h² = p² + b² Given, p and b are positive integer, so h2 will be sum of two perfect squares.

We see 
a) 7² + 5² = 74
b) 6² + 4² = 52
c) 3² + 2² = 13
d) Can’t be expressed as a sum of two perfect squares

Therefore the answer is Option D.

• Total number of cards, n(S) = 52
• Total number of face cards, n(E) = 12 (4 Jacks, 4 Queens, 4 Kings)

Step 1:

• We now need to obtain the digital root of the number. Here's how you do it:
• Split the number up and add each digit together:
  1 + 6 + 6 + 4 + 1 = 18
• If the answer is more than one digit, you would add each digit of the answer together again:
  1 + 8 = 9
• What is the digital root of number 16,641?
  Answer: 9

Step 2:

• So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
• Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!

Factoring

• OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.
• Here are all of the factors of 16,641:
  (1 x 16,641) (3 x 5,547) (9 x 1,849) (43 x 387) (129 x 129)

Hence the answer is 129.
 

If whenever my mother scolds me, I either hide behind my father or complain to my grandma. Then, if I did not complain to my grandma & did not hide behind my father, my mother must not have scolded me. Correct option is (a) 

Hence, the correct ans is UIJOL which is option b.

15 past 5 means quarter past 5 = (5:15)
⇒ (11*15 - 60*5)/2 = 67.5

Priya’s days work = (½)/8 = 1/16

Preeti’s days work

⇒ (⅓)/6 = 1/18 days

Together they can finish in.

= (5 x (5/18))m/sec = (25/18) m/sec

Total distance covered = Sum of the length of trains = 350 m

∴ Time taken = (350 x (18/25))sec = 252 sec.