McqMate
These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Computer Science Engineering (CSE) .
| 101. |
A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as |
| A. | direct proof |
| B. | contrapositive proofs |
| C. | vacuous proof |
| D. | proof by cases |
| Answer» C. vacuous proof | |
| 102. |
A proof that p → q is true based on the fact that q is true, such proofs are known as |
| A. | direct proof |
| B. | contrapositive proofs |
| C. | trivial proof |
| D. | proof by cases |
| Answer» C. trivial proof | |
| 103. |
In the principle of mathematical induction, which of the following steps is mandatory? |
| A. | induction hypothesis |
| B. | inductive reference |
| C. | induction set assumption |
| D. | minimal set representation |
| Answer» A. induction hypothesis | |
| 104. |
For m = 1, 2, …, 4m+2 is a multiple of is known as |
| A. | lemma |
| B. | corollary |
| C. | conjecture |
| D. | none of the mentioned |
| Answer» A. lemma | |
| 105. |
For any integer m>=3, the series 2+4+6+… +(4m) can be equivalent to |
| A. | m2+3 |
| B. | m+1 |
| C. | mm |
| D. | 3m2+4 |
| Answer» A. m2+3 | |
| 106. |
For every natural number k, which of the following is true? |
| A. | (mn)k = mknk |
| B. | m*k = n + 1 |
| C. | (m+n)k = k + 1 |
| D. | mkn = mnk |
| Answer» A. (mn)k = mknk | |
| 107. |
For any positive integer m is divisible by 4. |
| A. | 5m2 + 2 |
| B. | 3m + 1 |
| C. | m2 + 3 |
| D. | m3 + 3m |
| Answer» D. m3 + 3m | |
| 108. |
What is the induction hypothesis assumption for the inequality m ! > 2m where m>=4? |
| A. | for m=k, k+1!>2k holds |
| B. | for m=k, k!>2k holds |
| C. | for m=k, k!>3k holds |
| D. | for m=k, k!>2k+1 holds |
| Answer» B. for m=k, k!>2k holds | |
| 109. |
A polygon with 7 sides can be triangulated into |
| A. | 7 |
| B. | 14 |
| C. | 5 |
| D. | 10 |
| Answer» C. 5 | |
| 110. |
A polygon with 12 sides can be triangulated into |
| A. | 7 |
| B. | 10 |
| C. | 5 |
| D. | 12 |
| Answer» B. 10 | |
| 111. |
Which amount of postage can be formed using just 4-cent and 11-cent stamps? |
| A. | 2 |
| B. | 5 |
| C. | 30 |
| D. | 10 |
| Answer» D. 10 | |
| 112. |
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true. |
| A. | p(3) |
| B. | p(2) |
| C. | p(4) |
| D. | p(6) |
| Answer» A. p(3) | |
| 113. |
Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true. |
| A. | p(1) |
| B. | p(2) |
| C. | p(4) |
| D. | p(n) |
| Answer» D. p(n) | |
| 114. |
A polygon with 25 sides can be triangulated into |
| A. | 23 |
| B. | 20 |
| C. | 22 |
| D. | 21 |
| Answer» A. 23 | |
| 115. |
How many even 4 digit whole numbers are there? |
| A. | 1358 |
| B. | 7250 |
| C. | 4500 |
| D. | 3600 |
| Answer» C. 4500 | |
| 116. |
In a multiple-choice question paper of 15 questions, the answers can be A, B, C or D. The number of different ways of answering the question paper are |
| A. | 65536 x 47 |
| B. | 194536 x 45 |
| C. | 23650 x 49 |
| D. | 11287435 |
| Answer» A. 65536 x 47 | |
| 117. |
Neela has twelve different skirts, ten different tops, eight different pairs of shoes, three different necklaces and five different bracelets. In how many ways can Neela dress up? |
| A. | 50057 |
| B. | 14400 |
| C. | 34870 |
| D. | 56732 |
| Answer» B. 14400 | |
| 118. |
For her English literature course, Ruchika has to choose one novel to study from a list of ten, one poem from a list of fifteen and one short story from a list of seven. How many different choices does Rachel have? |
| A. | 34900 |
| B. | 26500 |
| C. | 12000 |
| D. | 10500 |
| Answer» D. 10500 | |
| 119. |
The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated. |
| A. | 874261140 |
| B. | 537856330 |
| C. | 549872700 |
| D. | 456976000 |
| Answer» D. 456976000 | |
| 120. |
Amit must choose a seven-digit PIN number and each digit can be chosen from 0 to 9. How many different possible PIN numbers can Amit choose? |
| A. | 10000000 |
| B. | 9900000 |
| C. | 67285000 |
| D. | 39654900 |
| Answer» A. 10000000 | |
| 121. |
A head boy, two deputy head boys, a head girl and 3 deputy head girls must be chosen out of a student council consisting of 14 girls and 16 boys. In how many ways can they are chosen? |
| A. | 98072 |
| B. | 27384 |
| C. | 36428 |
| D. | 44389 |
| Answer» B. 27384 | |
| 122. |
A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks? |
| A. | 18 |
| B. | 35 |
| C. | 28 |
| D. | 14 |
| Answer» D. 14 | |
| 123. |
When four coins are tossed simultaneously, in number of the outcomes at most two of the coins will turn up as heads. |
| A. | 17 |
| B. | 28 |
| C. | 11 |
| D. | 43 |
| Answer» C. 11 | |
| 124. |
How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7? |
| A. | 14 |
| B. | 5 |
| C. | 9 |
| D. | 24 |
| Answer» B. 5 | |
| 125. |
During a month with 30 days, a cricket team plays at least one game a day, but no more than 45 games. There must be a period of some number of consecutive days during which the team must play exactly number of games. |
| A. | 17 |
| B. | 46 c) 124 |
| C. | d |
| D. | 24 |
| Answer» D. 24 | |
| 126. |
In how many ways can 8 different dolls be packed in 5 identical gift boxes such that no box is empty if any of the boxes hold all of the toys? |
| A. | 2351 |
| B. | 365 |
| C. | 2740 |
| D. | 1260 |
| Answer» D. 1260 | |
| 127. |
A group of 20 girls plucked a total of 200 oranges. How many oranges can be plucked one of them? |
| A. | 24 |
| B. | 10 |
| C. | 32 |
| D. | 7 |
| Answer» A. 24 | |
| 128. |
In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party? |
| A. | 15 |
| B. | 14 |
| C. | 16 |
| D. | 17 |
| Answer» B. 14 | |
| 129. |
A bag contains 25 balls such as 10 balls are red, 7 are white and 8 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour? |
| A. | 10 |
| B. | 18 |
| C. | 63 |
| D. | 35 |
| Answer» B. 18 | |
| 130. |
The number of diagonals can be drawn in a hexagon is |
| A. | 9 |
| B. | 32 |
| C. | 16 |
| D. | 21 |
| Answer» A. 9 | |
| 131. |
A number lock contains 6 digits. How many different zip codes can be made with the digits 0–9 if repetition of the digits is allowed upto 3 digits from the beginning and the first digit is not 0? |
| A. | 254307 |
| B. | 453600 |
| C. | 458760 |
| D. | 972340 |
| Answer» B. 453600 | |
| 132. |
In how many ways can 10 boys be seated in a row having 28 seats such that no two friends occupy adjacent seats? |
| A. | 13p5 |
| B. | 9p29 |
| C. | 19p10 |
| D. | 15p7 |
| Answer» C. 19p10 | |
| 133. |
How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes? |
| A. | 40325 |
| B. | 40320 |
| C. | 40520 |
| D. | 40720 |
| Answer» B. 40320 | |
| 134. |
There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex heptagons of distinctly different areas can be drawn using these points as vertices? |
| A. | 7! * 6 |
| B. | 7c5 |
| C. | 7! |
| D. | same area |
| Answer» D. same area | |
| 135. |
How many ways are there to arrange 7 chocolate biscuits and 12 cheesecake biscuits into a row of 19 biscuits? |
| A. | 52347 |
| B. | 50388 |
| C. | 87658 |
| D. | 24976 |
| Answer» B. 50388 | |
| 136. |
If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d, e) possible such that a+b+c+d+e=75. |
| A. | 65c5 |
| B. | 58c6 |
| C. | 72c7 |
| D. | 74c4 |
| Answer» D. 74c4 | |
| 137. |
There are 15 people in a committee. How many ways are there to group these 15 people into 3, 5, and 4? |
| A. | 846 |
| B. | 2468 |
| C. | 658 |
| D. | 1317 |
| Answer» D. 1317 | |
| 138. |
There are six movie parts numbered from 1 to 6. Find the number of ways in which they be arranged so that part-1 and part-3 are never together. |
| A. | 876 |
| B. | 480 |
| C. | 654 |
| D. | 237 |
| Answer» B. 480 | |
| 139. |
How many ways are there to divide 4 Indian countries and 4 China countries into 4 groups of 2 each such that at least one group must have only Indian countries? |
| A. | 6 |
| B. | 45 |
| C. | 12 |
| D. | 76 |
| Answer» A. 6 | |
| 140. |
Find the number of factors of the product 58 * 75 * 23 which are perfect squares. |
| A. | 47 |
| B. | 30 |
| C. | 65 |
| D. | 19 |
| Answer» B. 30 | |
| 141. |
From a group of 8 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done? |
| A. | 686 |
| B. | 438 |
| C. | 732 |
| D. | 549 |
| Answer» A. 686 | |
| 142. |
What is the recurrence relation for 1, 7, 31, 127, 499? |
| A. | bn+1=5bn-1+3 |
| B. | bn=4bn+7! |
| C. | bn=4bn-1+3 |
| D. | bn=bn-1+1 |
| Answer» C. bn=4bn-1+3 | |
| 143. |
Find the value of a4 for the recurrence relation an=2an-1+3, with a0=6. |
| A. | 320 |
| B. | 221 |
| C. | 141 |
| D. | 65 |
| Answer» C. 141 | |
| 144. |
What is the solution to the recurrence relation an=5an-1+6an-2? |
| A. | 2n2 |
| B. | 6n |
| C. | (3/2)n |
| D. | n!*3 |
| Answer» B. 6n | |
| 145. |
Determine the value of a2 for the recurrence relation an = 17an-1 + 30n with a0=3. |
| A. | 4387 |
| B. | 5484 |
| C. | 238 |
| D. | 1437 |
| Answer» D. 1437 | |
| 146. |
Determine the solution for the recurrence relation an = 6an-1−8an-2 provided initial conditions a0=3 and a1=5. |
| A. | an = 4 * 2n – 3n |
| B. | an = 3 * 7n – 5*3n |
| C. | an = 5 * 7n |
| D. | an = 3! * 5n |
| Answer» B. an = 3 * 7n – 5*3n | |
| 147. |
What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+⋯? |
| A. | 10, 4, 0, 16, 25, … |
| B. | 0, 4, 15, 10, 16, 25,… |
| C. | 4, 0, 15, 10, 25, 16,… |
| D. | 4, 10, 15, 25,… |
| Answer» C. 4, 0, 15, 10, 25, 16,… | |
| 148. |
What is multiplication of the sequence 1, 2, 3, 4,… by the sequence 1, 3, 5, 7, 11,….? |
| A. | 1, 5, 14, 30,… |
| B. | 2, 8, 16, 35,… |
| C. | 1, 4, 7, 9, 13,… |
| D. | 4, 8, 9, 14, 28,… |
| Answer» A. 1, 5, 14, 30,… | |
| 149. |
What will be the sequence generated by the generating function 4x/(1-x)2? |
| A. | 12, 16, 20, 24,… |
| B. | 1, 3, 5, 7, 9,… |
| C. | 0, 4, 8, 12, 16, 20,… |
| D. | 0, 1, 1, 3, 5, 8, 13,… |
| Answer» C. 0, 4, 8, 12, 16, 20,… | |
| 150. |
Find the sequence generated by 1/1−x2−x4.,assume that 1, 1, 2, 3, 5, 8,… has generating function 1/1−x−x2. |
| A. | 0, 0, 1, 1, 2, 3, 5, 8,… |
| B. | 0, 1, 2, 3, 5, 8,… |
| C. | 1, 1, 2, 2, 4, 6, 8,… |
| D. | 1, 4, 3, 5, 7,… |
| Answer» A. 0, 0, 1, 1, 2, 3, 5, 8,… | |
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