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- Question
- If 2p + 3q = 17 and 2p + 2 - 3q + 1 = 5, then, find the value of p and q?
Options- A. -2 , 3
- B. 2, -3
- C. 3, 2
- D. 2, 3
- Correct Answer
- 3, 2
ExplanationApply the law of Fractional Exponents and Laws of Exponents
(am) x (an) = am + n
a-m = 1/am
p0 = 1
and if pX = pY then X will be equal to Y. means X = Y;
(am)n = am x n
(am) x (an) = am + n
am ÷ an = am ? n
Or
am/an = am ? n
Given equation is
2p + 3q = 17 ----------------(i)
2p + 2 - 3q + 1 = 5
? 2p x 22 - 3q x 3 = 5
? 2p x 4 - 3q x 3 = 5
? 4 x 2p - 3 x 3q = 5---------------(ii)
On multiplying Eq. (i) by 3 and adding it, with Eq. (ii), we get
3 x 2p + 3 x 3q = 51
4 x 2p - 3 x 3q = 5
_____________________________
7 x 2p = 56
? 7 x 2p = 7 x 8
? 2p = 8
? 2p = 23
? p = 3
On substituting the value of p in Eq. (i) . we get
23 + 3q = 17
? 8 + 3q = 17
? 3q = 17 - 8
? 3q = 9
? 3q = 32
? q = 2 - 1. How much does a watch gain or lose per day, if its hands coincide in every 64 minutes?
Options- A. 32 8 minutes gain 11
- B. 34 2 minutes gain 11
- C. 32 8 minutes loss 11
- D. None of these Discuss
- 2. At what time between 3 o'clock and 4 o'clock will the hands of a clock be together?
Options- A. 163/11 min past 3
- B. 143/11 min past 3
- C. 132/11 min past 3
- D. 164/11 min past 3 Discuss
- 3. Moving 6/7 of its usual speed a train is 10 min late. Find its usual time to cover the journey.
Options- A. 25 min
- B. 15 min
- C. 35 min
- D. 60 min Discuss
- 4. The square root of (1/4) x (1/49) ÷ (25/121) is
Options- A. 11/5
- B. 11/70
- C. 7/11
- D. 11/7 Discuss
- 5. Find the least number which when multiplied with 74088 will make it a perfect square.
Options- A. 42
- B. 44
- C. 46
- D. 48 Discuss
- 6. If 1/5 : 1/N = 1/N : 1/1.25, then the value of N is?
Options- A. 1.25
- B. 1.5
- C. 2.5
- D. 2.25 Discuss
- 7. One-fourth of the boys and three-eight of the girls in a school participated in the annual sports. What proportional part of the total student population of the school participated in the annual sports?
Options- A. 4/12
- B. 5/8
- C. 8/12
- D. Data inadequate Discuss
- 8. The ages of Vivek and Sumit are in the ratio 2 : 3. After 12 years, their ages wiil be in the ratio 11:15. The age of Sumit is?
Options- A. 32 years
- B. 42 years
- C. 48 years
- D. 56 years Discuss
- 9. Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.?
Options- A. 1400 cm3
- B. 1553 cm3
- C. 12320 cm3
- D. 13320 cm3 Discuss
- 10. Which of the following is not a leap year?
Options- A. 700
- B. 800
- C. 1200
- D. 2000 Discuss
More questions
Correct Answer: 32 8 minutes gain 11
Explanation:
Correct Answer: 164/11 min past 3
Explanation:
Here, n = 3 and (n + 1) = 4
? Two hands will coincide at 60n / 11 min past n
? 60 x 3 / 11 min past 3
? 180 /11 min past 3.
? 164/Sub>11 min past 3
Correct Answer: 60 min
Explanation:
New speed = 6/7 of usual speed
Now, time taken = 7/6 of usual time
(7/6 of the usual time) - (usual time) = 10 min
? 1/6 of the usual time = 10 min
? Usual time = 60 min
Correct Answer: 11/70
Explanation:
Square root of (1/4) x (1/49) ÷ (25/121)
= ?(1/4) x (1/49) x (121/25)
= 11 / (2 x 7 x 5)
= 11/70
Correct Answer: 42
Explanation:
74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
= (2x2) x (3x3) x (7x7) x (2x3x7)
Least number which should be multiplied to 74088 to make it a Perfect square = 2 x 3 x 7 = 42
Correct Answer: 2.5
Explanation:
Given 1/5 : 1/N = 1/N : 1/1.25
? 1/5 x 1/1.25 = 1/N x 1/N
? N2 = 5 x 1.25 = 6.25
? N = 2.5
Correct Answer: Data inadequate
Explanation:
Data inadequate
Correct Answer: 48 years
Explanation:
Let their ages be 2x and 3x years
(2x + 12) / (3x + 12) = 11 /15
? 15(2x + 12) = 11(3x + 12)
? 3x = 48
? x = 16
? age of sumit = 3x = 48 years
Correct Answer: 12320 cm3
Explanation:
Given, r = 7 cm, h = 80 cm
Volume = ?r2h = (22/7) x 7 x 7 x 80
= 12320 cm3
Correct Answer: 700
Explanation:
The century divisible by 400 is a leap year.
∴ The year 700 is not a leap year.
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