A = 0.a_{1}a_{1}a_{1} ... and B = 0.a_{2}a_{2}a_{2}, where a_{1 }and a_{2} are multiples of 3 and also, a_{1} and a_{2} are distinct integers from 0 to 8. Then value of A + B is
A. | |
B. | |
C. | 1 |
D. | Cannot be determined |
Option: C Explanation : Similarly, Now, a_{1} and a_{2} are multiples of 3 and are distinct. Also, these values are less than 8. either a_{1} = 3 and a_{2} = 6 or a_{1} = 6 and a_{2} = 3 ∴a_{1} + a_{2} = 9. Click on Discuss to view users comments. |
Which of the following is true?
A. | √2+√5=√7 |
B. | √2+√5 ≤ √7 |
C. | √2+√5<√7 |
D. | √2+√5 > √7 |
Option: D Explanation :
(√2+√5)² = 2 + 2√10 +5 =7+2√10 Click on Discuss to view users comments. |
revise20. If a, b, c, d, p and q are non-zero, unequal integers and (a+bi)/(c+di) equals
A. | p/q |
B. | p2 / q2 |
C. | 1 |
D. | None of the these |
Option: B Explanation : a + bi p c + di q qa + qbi = pc + pdi Equating real and imaginary parts. qa = pc and qb = pd. a = -P/q -c and b = (p/q)d * a²+b² (p²/q²)c + (p²/q²)d² p² ---- = ------------------- = -- c²+d² c²+d² q² Click on Discuss to view users comments. |
revise 47. Which of the following statementls is/are true?
I. Average of a set of values will always lie between lowest and the largest of these values.
II. If each of the values in a set is increased by a constant k, then new average of the set is increased by k.
III. If each of the values in a set is multiplied by a constant m, then new average will also be `m' times the old average
Codes
A. | Only I and II |
B. | Only II and III |
C. | Only I and III |
D. | I, II and III |
Option: D Explanation : I. Average of a set of numbers is greater than smallest and smaller than the greatest number of the set. Thus, I is true. II. Consider five numbers a, b, c, d and e whose average is (a+b+c+d+e) / 5 Now if each of them is increased by k, then we have average =a+k+b+k+c+k+d+k+e+k 5 =a+b+c+d+e + 5k = old average +k. 5 5 Thus, II is true III. Consider three numbers x,y and z whise average is (x+y+z) /3 Now each of them is multiplies by m then new average =(xm +ym+zm) / 3 = m((x+y+x)/3) = 3xodd average Thus III is true Click on Discuss to view users comments. |
What is the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder?
A. | 2987 |
B. | 3601 |
C. | 3600 |
D. | 2986 |
Option: B Explanation :
L.C.M. of 5, 6, 8, 9 and 12 is 360 Click on Discuss to view users comments. |