• 1296
• 1494
• 1530
• 1480
• 1620
• #### 2.  The number of ways in which 6 different marbles can be put in two boxes of different sizes so that no box remains empty is

• 62
• 64
• 36
• 60
• None of these
• #### 3.  There are 10 people seated in two rows (5 in 1 row) and there are two types of food items. Each row can be served any of the two food items but it must be different from the other row. In how many ways the food can be served?

• 6453300
• 2441200
• 7257600
• 6265800
• None of the above

• 18
• 24
• 64
• 192
• 256

• 1512
• 2276
• 3024
• 4118
• 3022
• #### 6.  Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose the possible answer. Quantity A∶ Suppose there are 4 teachers, 6 students and 3 guardians. What are the various ways in which a committee of 7 members can be formed, such that the committee has at least 3 students and 2 guardians? Quantity B∶ 590.

• Quantity A > Quantity B
• Quantity A < Quantity B
• Quantity A ≥ Quantity B
• Quantity A ≤ Quantity B
• Quantity A = Quantity B or No relation.

• 15
• 16
• 21
• 35
• 56
• #### 8.  In how many ways we can arrange the letters of the word “ARRAGEET”?

• 4050
• 2520
• 10080
• 5040
• None of these

• 676
• 17576
• 456976
• 30522

• 9 : 1
• 72 : 1
• 10 : 1
• 8 : 1
• 20 : 1

• 200
• 216
• 235
• 256
• 228

• 15
• 16
• 17
• 18
• 29

• 56
• 60
• 68
• 72
• 79
• #### 14.  There are 3 bowls and 5 nuts. All these nuts are to be distributed into three bowls where any bowl can contain any number of nuts. In how many ways these nuts can be distributed into these bowls if all the bowls and all the nuts are different?

• 35
• 53
• $$_5^3P$$
• $$_3^5P$$
• None

• 15
• 16
• 17
• 12
• 18

• 729
• 537
• 444
• 637
• 669
• #### 17.  Three pen companies A, B and C launched 6, 5 and 6 different models respectively. Find the ways in which they can be displayed in a case with 17 slots such that the models of no two companies are mixed together.

• (5!)(6!)
• 180
• (6!)3/3!
• (6!)3
• None of these

• 54000
• 56800
• 60480
• 62000
• 67200
• #### 19.  The number of ways in which 20 different flowers of two colors can be set alternately on a necklace, there being 10 flowers of each colour, is

• 9! × 10!
• 5(9!)2
• (9!)2
• (18!)2
• None of these
• #### 20.  In a simultaneous throw of two dice, what is the probability of getting a total of 7?

• 1/2
• 1/3
• 1/4
• 1/6
• None of these
• #### 21.  If a license plate has to be made where the first 4 places are numbers from 0 to 9 and the last two letters are made from the alphabets A to F, how many different license plates are possible where the repetition of any letter or number is not allowed?

• 125000
• 130000
• 153000
• 151200
• None of the above
• #### 22.  How many different words can be formed with the letters of the word ‘M A I M I T A L’ such that each of the word begins with L and ends with T?

• 78
• 128
• 180
• 90
• None of these

• 80
• 70
• 71
• 65
• 60

• 80
• 78
• 71
• 69
• 60
• #### 25.  A man has to travel from Allahabad to Lucknow and then from Lucknow to Kolkata. If there are 5 routes from Allahabad to Lucknow and 4 routes to go from Lucknow to Kolkata, then how many options are available for the man to travel from Allahabad to Kolkata via Lucknow?

• 54
• 20
• 45
• 54 + 45
• None of the above
• #### 26.  In how many ways can 5 boys and 7 girls be arranged in a row so that no two boys are together?

• 5! × 7!
• 7P5 × 5!
• 7! × 8P5
• 7P5 × 7!
• None of these
• #### 27.  Find the number of possible triangles using points on the sides of any triangle ABC having “a” points on side BC, “b” points on side AC, “c” points on side AB excluding the points at vertices.

• a + b + cC3 + aC3 + bC3 + cC3
• a + b + cC3 + aC3 – bC3 – cC3
• a + b + cC3 – aC3 + bC3 + cC3
• a + b + cC3 – aC3 – bC3 – cC3
• None of these
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