puzzels

By using the letters A, E, O, E, P, Q, T, S, how many words can be formed, if we have to place all the vowels in even places

OPTIONS:

1) 144 2) 2 3) 288 4) 12 5) 24 6) 576 7) 1 8) 40320 9) 20160 10) none of these

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What will be the power of 10 in the product 1*2*3*4*5......*40

OPTIONS:

1) 1 2) 2 3) 3 4) 4 5) 5 6) 6 7) 7 8) 8 9) 9 10) none of these

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next number of the sequence 12, 20, 30, 42, 56, ..... will be

OPTIONS:

1) 58 2) 60 3) 64 4) 66 5) 68 6) 70 7) 72 8) 76 9) 78 10) none of these

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A number a, its square and its cube are in GP. What will be the third term of AP, for which first two terms are obtained by taking the difference of terms of GP in 2nd-1st and 3rd-2nd manner?

OPTIONS:

1) 6*sum of all numbers upto (a-1) 2) 6*sum of squares of all numbers upto (a-1) 3) a+a^2+a^3 4) 1+a+a^2+a^3 5) 6*sum of all numbers upto a 6) 6*sum of squares of all numbers upto a 7) 6*sum of cubes of all numbers upto (a-1) 8) 6*sum of cubes of all numbers upto a 9) always a fixed number 10) none of these

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By using the letters A, E, O, E, P, Q, T, S, how many words can be formed, if we have to place all the vowels in even places

OPTIONS:

1) 144 2) 2 3) 288 4) 12 5) 24 6) 576 7) 1 8) 40320 9) 20160 10) none of these

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Sum of the ages of a boy and his father is 70 years. Before 20 years Father\'s age was 14 times the age of the boy. What was the age of father at the time of birth of the child?

OPTIONS:

1) 22 2) 25 3) 26 4) 27 5) 29 6) 31 7) 34 8) 36 9) 38 10) none of these

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Solution

( 4 ) E1 = 39 E2 = 84 E3 = 155 now E1 - E2 = 39 - 84 = -45 its modulus means numerical value = 45 and E2 - E3 = 84 - 155 = -71 its modulus means numerical value = 71 so sum = 45+71 = 116

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PUZZLE:

If x = 3, y = 4, z = 5, then sum of the modulus of the numbers obtained by differences in the manner E1 - E2 and E2 - E3 Meaning of operations are E1 : sum of x,x^2,x^3; E2 : sum of y,y^2,y^3 and E3 : sum of z,z^2,z^3

OPTIONS:

1) 96 2) 104 3) 110 4) 116 5) 129 6) 134 7) 140 8) 148 9) 152 10) none of these

Click Here to Submit Your Answer                                              Solution ( 6 ) Maximum no. of intersecting points = 5*4/2 = 10 minimum no. of intersecting points = 1  PUZZLE: If x = 3, y = 4, z = 5, then sum of the modulus of the numbers obtained by differences in the manner E1 - E2 and E2 - E3 Meaning of operations are E1 : sum of x,x^2,x^3; E2 : sum of y,y^2,y^3 and E3 : sum of z,z^2,z^3 OPTIONS: 1) 96 2) 104 3) 110 4) 116 5) 129 6) 134 7) 140 8) 148 9) 152 10) none of these Click Here to Submit Your Answer                                                                                                   Solution ( 3 ) Let present age of father and the son are x and y then according to the given condition x+y = 70 before 20 years (x-20) = 14(y-20) so 70-y-20 = 14(y-20) or 50-y = 14y-280 or 15y = 330 or y = 22 and x = 48 so at the time of birth of child, age of father = 48-22 = 26  PUZZLE: Two positive integers x and y are possible for which sum of x,x^2,x^3 and similarly y,y^2,y^3 are nearer to 100 than the sum of number, its square and cube for other integers. What will be the positive difference between the sum of x,x^2,x^3 and y,y^2,y^3 OPTIONS: 1) 45 2) 54 3) 58 4) 63 5) 68 6) 70 7) 71 8) 75 9) 87 10) none of these Click Here to Submit Your Answer                                                                                                Solution( 7 ) The value of sum (x+x^2+x^3) for 3, 4, 5 and 6 are 39, 84, 155 and 258 respectively. Nearer to 100 are 84 and 155, so difference = 155-84 = 71                                                                                                 PUZZLE: What will be the probability that k1*k2*k3 is an even number, if k1, k2, k3 are 3 positive integers taken randomly.OPTIONS:1) 1/8 2) 1/4 3) 3/8 4) 1/2 5) 5/8 6) 3/4 7) 7/8 8) 1 9) 1/3 10) none of these Click Here to Submit Your Answer

There are 5 lines in a plane. Difference between maximum and minimum number of intersecting points. No two lines are parallel

OPTIONS:

1) 2 2) 3 3) 4 4) 5 5) 8 6) 9 7) 10 8) 15 9) 19 10) none of these

Click Here to Submit Your Answer                                                                         Solution ( 3 ) According to the given condition k-12, k^2, k^3, k^4-36 are in AP. so k^2-(k-12) = k^3-k^2 so k^3-2k^2+k-12 = 0 (i) equation (i) has 3 as its real root on taking the value of k, given 4 numbers will be -9,9,27,45 TODAY'S PUZZLE: A business has two steps. In first step, there is 40 % profit in total investment and in second step, there is 12 % loss in the total output after first step. Overall percentage profit in the initial investment will be OPTIONS: 1) 23.2 2) 24.4 3) 25 4) 25.8 5) 26.2 6) 27.4 7) 27.8 8) 29 9) 32.4 10) none of these Click Here to Submit Your Answer k % of 90 = 80 % of y relation between k and y will be OPTIONS: 1) k=y 2) 3k=2y 3) 3k=8y 4) 9k=4y 5) 9k=8y 6) 8k=9y 7) 9k=10y 8) 10k=9y 9) 2k=9y 10) none of these Click Here to Submit Your Answer  Solution ( 5 ) 90k/100 = 80y/100 or 9k = 8y There are 4 positive numbers k, k^2, k^3, k^4. If we subtract 12 by first number and 36 by last number, we will get an AP of 4 numbers. Calculate k? OPTIONS: 1) 1 2) 2 3) 3 4) 4 5) 5 6) 6 7) 7 8) 8 9) 9 10) none of these Click Here to Submit Your Answer Solution ( 7 ) if you take all odd numbers, then product will be odd. In all other 7 cases, it will be even so probability = 7/8