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- Question
- Find the quotient when (a-1 - 1) is divided by (a - 1).
Options- A. 2/a
- B. 2a
- C. a/2
- D. -1/a
- Correct Answer
- -1/a
ExplanationGiven equation is
a-1 - 1
Apply the law of Fractional Exponents and Laws of Exponents
x-y = 1/xy
? a-1 - 1 = 1/a - 1
? a-1 - 1 = (1 - a)/a
Now divide by a - 1 in above equation,
? ( a-1 - 1 ) ÷ (a - 1) = (1 - a)/a ÷ (a - 1)
? ( a-1 - 1 ) ÷ (a - 1) = (1 - a)/a x 1/ (a - 1)
? ( a-1 - 1 ) ÷ (a - 1) = -1x (a - 1)/a x 1/ (a - 1)
? ( a-1 - 1 ) ÷ (a - 1) = -1/a
? Required quotient = -1/a. - 1. In a two digit positive number the unit digit is equal to the square of ten's place digit. The difference between the original number and the number formed by interchanging the digit is 54. What of 40% of the original number?
Options- A. 64
- B. 73
- C. 84
- D. Couldn't be determined Discuss
- 2. In the given figure ?QPR = 90°, QR = 26 cm, PM = 6 cm, MR = 8 cm and ?PMR = 90°, find the area of ?PQR.
Options- A. 180 cm2
- B. 240 cm2
- C. 120 cm2
- D. 150 cm2 Discuss
- 3. The average temperature of Monday, Tuesday, Wednesday, and Thursday was 38° C and that of Tuesday, Wednesday, Thursday and Friday was 40° C, if the temperature on Monday was 30° C, the temperature of Friday was?
Options- A. 40°
- B. 39°
- C. 38°
- D. 30° Discuss
- 4. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Options- A. 0°
- B. 10°
- C. 5°
- D. 20° Discuss
- 5. A, B, C are the three angles of a ?. If A ? B = 15° and B ? C = 30°. Then ?A is equal to :
Options- A. 65°
- B. 80°
- C. 75°
- D. 85° Discuss
- 6. 8, 27, 64, 100, 125, 216, 343
Options- A. 27
- B. 100
- C. 125
- D. 343 Discuss
- 7. The G.C.D. of 1.08, 0.36 and 0.9 is:
Options- A. 0.03
- B. 0.9
- C. 0.18
- D. 0.108 Discuss
- 8. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
Options- A. 123
- B. 127
- C. 235
- D. 305 Discuss
- 9. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
Options- A. 3500
- B. 4000
- C. 4050
- D. 5000 Discuss
- 10. In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?
Options- A. 100
- B. 200
- C. 300
- D. 400 Discuss
More questions
Correct Answer:
Explanation:
Let ten's place digit be a and unit's place digit be a2
Original number = 10 x a + 1 x a2 = 10a + a2
The number formed by interchanging the digits,
New number = 10 x a 2 + 1 x a = 10a 2 + a
According to the question
(10a2 + a) - ( 10a + a2) = 54
? 10a2 + a - 10a - a 2 = 54
? 9a2 - 9a = 54
? 9( a2 - a) = 54
? ( a2 - a) = 54/9
? ( a2 - a) = 6
? a2 - a - 6 = 0
? a2 - 3a + 2a - 6 = 0
? a (a - 3) + 2 (a - 3) = 0
? (a - 3) (a + 2) = 0
? a = 3, - 2
? Ten,s digit = a = 3
Unit's digit = a2 = 32 = 9
Original number = 39
? Required number = 39 x 40/100 = 15.6
Correct Answer: 120 cm2
Explanation:
Given in the question, QR = 26 cm, PM = 6 cm, MR = 8 cm
According to question, in ? PMR
(Pythagoras Theorem)
PR = ?PM2 + MR2 = ?36 + 64 = ? 100 = 10 cm
According to question, in ? PQR
(Pythagoras Theorem)
PQ = ?QR2 - PR2 = ?262 - 102 = ?576 - 100 = ? 476 = 24
? area of triangle ?PQR = Base length x Height / 2
? area of triangle ?PQR = PR x PQ / 2
? area of triangle ?PQR = 10 x 24 / 2 = 10 x 12
? area of triangle ?PQR = 120
Correct Answer: 38°
Explanation:
From question
M + T + W + TH = 4 x 38° = 152°
? T + W + TH =152° ? 30° = 122°
Again from question
? T + W + TH + F = 4 x 40° = 160°
? F = 160° ? 122°
= 38°
Correct Answer: 10°
Explanation:
| Angle traced by hour hand in | 13 | hrs = | ❨ | 360 | x | 13 | ❩ | ° | = 130°. |
| 3 | 12 | 3 |
| Angle traced by min. hand in 20 min. = | ❨ | 360 | x 20 | ❩ | ° | = 120°. |
| 60 |
∴ Required angle = (130 - 120)° = 10°.
Correct Answer: 80°
Explanation:
Since A, B and C are the angles of a ?,
? A + B + C = 180° .......................................... (1)
According to question,
A ? B = 15° ;
? A = B + 15°....................................................(2)
B ? C = 30°;
? B = C + 30°;...................................................(3)
Put the value of B from equation (2) in Equation (1), we will get
? A = B + 15°
A = C + 30° + 15°
A = C + 45° ........................................................(4)
From a equation,
? A + B + C = 180°
? (C + 45°) + (C + 30°) + C = 180°
? 3C + 45° + 30° = 180°
? 3C = 180° ? 75° = 105°
? C = 35° ..........................................................(5)
From equation (4)
A = C + 45°
Put the value of C from equation (5) , we will get
? ?A = 35° + 45° = 80°.
Correct Answer: 100
Explanation:
Correct Answer: 0.18
Explanation:
Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18,
∴ H.C.F. of given numbers = 0.18.
Correct Answer: 127
Explanation:
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.
Correct Answer: 4000
Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
∴ P's monthly income = Rs. 4000.
Correct Answer: 100
Explanation:
Suppose, P points make the game.
Clearly, when A scores P points, B scores (P - 20) points and C scores (P - 32) points.
Now, when B scores P points, C scores (P - 15) points.
When B scores (P - 20) points,
C scores [( P - 15 ) / P * P (P - 20)] points
? (P - 15)( P - 20) / P = P - 20 or, P = 100
Hence, 100 points make the game.
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