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If we can generate a maximum of 4 Boolean functions using n Boolean variables, what will be minimum value of n?

NIMCET PREVIOUS YEAR QUESTION

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A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

What is E's profession?

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A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

How many members of the group are males?

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Wrong number in the series 7, 8, 18, 57, 228, 1165, 6996

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7*1 + 1 = 8

8*2 + 2 = 18

18*3 + 3 = 57

57*4 + 4 = 232

232*5 + 5 = 1165

1165*6 + 6 = 6996

so 228 is wrong

The mean of 5 observation is 5 and their variance is 12.4. If three of the observations are 1,2 and 6; then the mean deviation from the mean of the data is:

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In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did not for either. How may experts were there in all.

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Let the total number of experts be .

is the set of experts who voted for miss .

is the set of experts who voted for miss .

Since did not vote for either, n.

and

.

So,

Solving the above equation gives

is the set of experts who voted for miss .

is the set of experts who voted for miss .

Since did not vote for either, n.

and

.

So,

Solving the above equation gives

The value of non-zero scalars α and β such that for all vectors and such that is

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A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1 . The magnitude of its moment about the line joining the origin to the point (12,3,4) is

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Number of real solutions of the equation is

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The sum of infinite terms of a decreasing GP is equal to the greatest value of the function in the interval [-2,3] and the difference between the first two terms is f'(0). Then the common ratio of GP is

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Number of onto (surjective) functions from A to B if n(A)=6 and n(B)=3, is

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If $|z|<\sqrt{3}-1$, then $|z^{2}+2z cos \alpha|$ is

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A computer producing factory has only two plants T_{1} and T_{2} produces 20% and plant T_{2} produces 80% of the total computers produced. 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant T_{1} 10P(computer turns out to be defective given that it is produced in plant T_{2} ). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T_{2} is

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If A > 0, B > 0 and A + B = $\frac{\pi}{6}$ , then the minimum value of $tanA + tanB$

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x= tanA + tan(π/6-A)

we get :

dx/dA = sec²A-sec²(π/6-A)

now putting

dx/dA=0

we get

cos²(A) = cos²(π/6-A) so 0≤A≤π/6

therefore

A=π/6-A from here we get A = π/12 = B

so minimum value of that function is

2tanπ/12 which is equal to 2(2-√3)

The tangent at the point (2, -2) to the curve $x^2 y^2-2x=4(1-y)$ does not passes through the point

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The integral $\int \sqrt{1+2 cot x(cosec x+cotx)} dx$ , $(0<x<\frac{\pi}{2})$ (where C is a
constant of integration) is equal to

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If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in English Dictionary, then the position of the word QUEEN is

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Letters of the word QUEEN are E,E,N,Q,U

Words beginning with E (4!) = 24

Words beginning with N (4!/2!)=12

Words beginning with QE (3!) = 6

Words beginning with QN (3!/2!)= 3

Total words = 24+12+6+9=45

QUEEN is the next word and has rank 46th.

The curve satisfying the differential equation and passing through the point (1,1) also passes through the point __________

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If S and S' are foci of the ellipse , B is the end of the minor axis and BSS' is an equilateral triangle, then the eccentricity of the ellipse is

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The equation of the circle passing through the point (4,6) and whose diameters are along x + 2y - 5 =0 and 3x - y - 1=0 is

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In a parallelogram ABCD, P is the midpoint of AD. Also, BP and AC intersect at Q. Then AQ : QC =

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The median AD of ΔABC is bisected at E and BE is extended to meet the side AC in F. The AF : FC =

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Let $X_i, i = 1,2,.. , n$ be n observations and $w_i = px_i +k, i = 1,2,
,n$ where p and k are constants. If the mean of $x_i 's$ is 48 and the standard deviation is 12, whereas the mean of $w_i 's$ is 55 and the standard deviation is 15, then the value of p and k should be

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If , then the values of A_{1}, A_{2}, A_{3}, A_{4} are

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Equation of the tangent from the point (3,−1) to the ellipse 2x^{2} + 9y^{2} = 3 is

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The position vectors of the vertices

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The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x

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Not Available right now

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In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is

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Suppose A_{1} , A_{2} , A_{3} , …..A_{30} are thirty sets each having 5 elements with no common elements across the sets and B_{1} , B_{2} , B_{3} , ..... , B_{n} are

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Let ,where [x]denotes the greatest integer

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Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following statements is true?

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If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabilities 0.001 and 0.003 respectively. What should be a fair price to pay for the ticket?

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Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both statements and

- Give the answer (U) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- Give the answer (V) if the data in statement I| alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- Give the answer (W) if the data either in Statement I or in Statement II alone are sufficient to the answer of the question.
- Give the answer (X) if the data in both statements I and II together are not sufficient to answer the question.
- Give the answer (Y) if the data in both statements I and II together are are necessary to answer the question.

How much time will the leak take to empty the full cistern?

- The cistern is normally filled in 9 hours.
- It takes one hour more than the usual time to fill the cistern because of a leak in the bottom.

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If the mean deviation 1, 1+d, 1+2d, … , 1+100d from their mean is 255, then d is equal to

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Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both statements and

- Give the answer (U) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- Give the answer (V) if the data in statement I| alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- Give the answer (W) if the data either in Statement I or in Statement II alone are sufficient to the answer of the question.
- Give the answer (X) if the data in both statements I and II together are not sufficient to answer the question.
- Give the answer (Y) if the data in both statements I and II together are are necessary to answer the question.

How will long it take to empty the tank if both the inlet pipe P1 and the outlet pipe P2 are opened simultaneously?

- P1 can fill the tank in 16 minutes.
- P2 can empty the full tank in 8 minutes.

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If and , then a possible value of n is among the following is

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Let S be the set $\{a\in Z^+:a\leq100\}$.If the equation
$[tan^2 x]-tan x - a = 0$ has real roots (where [ . ] is the greatest
integer function), then the number of elements is S is

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How many people (from the group surveyed) read both Indian Express and Times of India?

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The solution set of the inequality is

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If **137+ 276 = 435**, how much is **731 + 672/**** ?**

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Hence, 731+672=6123

If $a, b, c$ are in GP and $log a - log 2b$, $log 2b - log 3c$ and $log 3c - log a$ are in AP, then $a, b, c$are the lengths of the sides of a triangle which
is

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Study the information carefully and answer the questions given below:

If we arrange the alphabets in the word "RATE" in the English alphabetical order, word "AERT" is formed. Then the third alphabet from the left in this word is "R". similarly, from the word "OPEN" we get - "ENOP" and the third alphabet from the left is "O". From the word "CHEF" we get - "CEFH" the third alphabet from the left "F". From the word "TOY" we get - "OTY" and the third alphabet from the left is "Y". If we use all these letters, then a meaningful English word "FORTY" can be formed.

Now find which of the following word set DOES NOT give a meaningful word in the similar way.

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Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?

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The distance between Ahmedabad and Baroda is 100 Km

Navjivan express starts at 6:30 am at 50 Km/hr and Howrah expresses starts at7:00 am at 40 Km/hr.

Distance covered by Navjivan express in 30 minutes (by 7 am) is 25 Km/hr.

So, at 7 am, the distance between the two trains is 75 Kms and they aretravelling towards each other a relative speed of 50+40=90 Km/hr.

So, time taken them to meet is 75/90*60 = 50 minutes.

As, Mr. Shah realizes the problem after thirty minutes, time left to avoid collision is 50-30 = 20 minutes

If (1 + x – 2x^{2})^{6 }= 1 + a_{1}x + a_{2}x^{2 }+ ... + a_{12}x^{12},
then the value a_{2 }+ a_{4 }+ a_{6 }+ ... + a_{12}

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In IEEE single precision floating point representation, exponent is represented in ______

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With 4-bit 2's complement arithmetic, which of the following addition will result in overflow?

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A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps, he is one step away from the starting point is

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If the 2's complement representation of a number is (011010)_{2} , what is its equivalent hexadecimal representation?

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If x, y, z are distinct real numbers then = 0, then xyz=

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For the circuit shown below, the complement of the output F is _________

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If N is a 16-bit signed integer, then 2's complement representation of N is (F87B)_{16}. The 2's complement representation of 8*N is

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If $a, a, a_2, ., a_{2n-1},b$ are in AP, $a, b_1, b_2,...b_{2n-1}, b $are in GP and $a, c_1, c_2,... c_{2n-1}, b $ are in HP, where a, b are positive, then the
equation $a_n x^2-b_n+c_n$ has its roots

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The base ( or radix) of the number system such that the following equation holds 312/20 = 131.1 is

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For the two circles $x^2+y^2=16$ and $x^2+y^2-2y=0$, there is/are

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Which of the following represents (D4)_{16 }?

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How many Boolean expressions can be be formed with 3 Boolean variables?

_{}

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A particle P starts from the point

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In an 8 bit representation of computer system the decimal number 47 has to be subtracted from 38 and the result in binary 2's complement is _________

_{}

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If $\Delta=a^2-(b-c)^2$, where $\Delta$ is the are of the triangle ABC, then $tanA=$

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Select the most suitable antonym from the given choices for the word : "SANGFROID"

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Two numbers $a$ and $b$ are chosen are random from a set of the first 30
natural numbers, then the probability that $a^2 - b^2$ is divisible by
3 is

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The word PIN is used in four different ways. Choose the option in which the usage of the word is incorrect or inappropriate?

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Pick the most appropriate substitute to the capitalized word in the following sequence.

The weapon inspector's report was not expected to provide INCONTROVERTIBLE evidence of weapons of mass destruction.

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In the sentence given below, a part of sentence is underlined. Four different ways of phrasing the underlined part are indicated as four choices. Choose the best alternative and mark its corresponding letter as your answer.

A nation is built not be legislation but by the stirrings in the heart of the people.

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Select the most suitable synonym for the underlined word in the sentence.

All the members of organization expressed implacable opposition to the move.

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Choose the phrasal verb to replace the explanation in brackets.

"We must (be quick) ________ or we'll be late for school"

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Anne had to pay everything because as usual, Peter __________ his wallet at home.

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Extreme old age when a man behaves like a child.

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Identify the word that means "To try to achieve something is difficult circumstances despite a setbacks".

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In the following a part of the sentence is underlined. Four different ways of phrasing the underlined part are indicated below. Chose the best alternative among the four choices given.

When he entered the house, it was in sixes and sevens.

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There are two blanks in the sentences given below. From the pairs of word given below the sentences, choose the pair that fills the blank most appropriately.

Private companies supplying 'breakfast cereals' have started ________ in agriculture in poorer countries. This has _________ the spectre of land grabs and political conflicts.

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Use the appropriate phrasal verb and complete the sentence given below.

The new system in education is aimed at ___________ the differences between rich and poor.

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I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our Island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government-every man of them.

That is the will of the parliament of our nation. The British Empire and the French Republic, linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail.

We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old."

What does the term *ride out the storm* mean?

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I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our Island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government-every man of them.

That is the will of the parliament of our nation. The British Empire and the French Republic, linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail.

We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old."

What does *subjugate* mean?

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I have, myself, full confidence that if all do their duty, if nothing is neglected, and if the best arrangements are made, as they are being made, we shall prove ourselves once again able to defend our Island home, to ride out the storm of war, and to outlive the menace of tyranny, if necessary for years, if necessary alone. At any rate, that is what we are going to try to do. That is the resolve of His Majesty's Government-every man of them.

That is the will of the parliament of our nation. The British Empire and the French Republic, linked together in their cause and in their need, will defend to the death their native soil, aiding each other like good comrades to the utmost of their strength. Even though large tracts of Europe and many old and famous States have fallen or may fall into the grip of the Gestapo and all the odious apparatus of Nazi rule, we shall not flag or fail.

We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender, and even if, which I do not for a moment believe, this island or a large part of it were subjugated and starving, then our Empire beyond the seas, armed and guarded by the British Fleet, would carry on the struggle, until, in God's good time, the New World, with all its power and might, steps forth to the rescue and the liberation of the old."

"That is the resolve of His Majesty's Government." What is their resolve?

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Fill in the blanks choosing the correct adjective : The phoenix is a ______Bird.

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Which of the following is the correct passive of the sentence, "JOHN HAS EATEN THE APPLES?"

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Choose one of the words that is most nearly same as meaning of the given word Indemnify

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Select a word from the given alternatives which has the same meaning as the underlined word:

He has a propensity for getting into debt.

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Select the most suitable synonym from the given choices for the word : "ANTEDILUVIAN"

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A clock is set right at 5 AM. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day?

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Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.

Now 23 hrs 44 min. of this clock = 24 hours of correct clock.

356/15 hrs of this clock = 24 hours of correct clock

89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.

= 90 hrs of correct clock.

So, the correct time is 11 p.m

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

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Decide which of the give conclusions logically follow from from the given students(s) :

Statements:

All suns are moons.

Some moons are planets.

Conclusions :

I. All moons are suns.

II. At least some moons are planets.

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Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

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We can get the triangles in
two different ways.

Taking two points from the line having 10 points

(in ^{10}_{}2

So,
the number of triangles here is

Taking
two points from the line having 11 points (in ^{11}_{}2

Total number of triangles, =495+550

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

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= H.C.F. of (1657 - 6) and (2037 - 5)

= H.C.F. of 1651 and 2032 = 127.

Twelve classmates A, B, C, D, E, F, G, H I, J, K and L are sitting on a square table with 3 persons on each side. ABC and GJK are sitting on opposite sides. A and L are adjacent to each other. K is sitting diagonally to C.

If F is sitting between D and E, who is sitting to the left of K?

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Twelve classmates A, B, C, D, E, F, G, H I, J, K and L are sitting on a square table with 3 persons on each side. ABC and GJK are sitting on opposite sides. A and L are adjacent to each other. K is sitting diagonally to C.

If H is sitting between L and F, then he will be facing

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Twelve classmates A, B, C, D, E, F, G, H I, J, K and L are sitting on a square table with 3 persons on each side. ABC and GJK are sitting on opposite sides. A and L are adjacent to each other. K is sitting diagonally to C.

If G and E are facing C and H respectively, the neighbours of K are

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The integers 34041 and 32506, when divided by a 3 - digit integer n, leave the same remainder. What can be the value of n?

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34041 - 32506 = 1535

So n should be a factor of 1535.

Factors of 1535:-
1, 5, 307, 1535

Here, 307 is a three digit factor of 1535. So n = 307
34041 and 32506 divided by 307 leaves remainder 271.

So 307 is the answer.

The number of solid spheres ,each of diameter 3 cm that could be moulded to form a solid metal cylinder of height 54cm and diameter 4 cm is?

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1.All chickens are birds.

2. Some chickens are hens.

3. Female birds lay eggs.

If the above three statements are facts, which of the following statement must also be a fact?

I. All birds lay eggs.

II. Hens are birds.

III. Some chickens are not hens.

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The number that comes next in the series 1, 2, 3, 6, 11, 20, 37, 68,...

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1 + 2 + 3 = 6

2 + 3 + 6 = 11

3 + 6 + 11 = 20

6 + 11 + 20 = 37

11 + 20 + 37 = 68

so next number in the sequence would be;20 + 37 + 68 = 125

Using only 2, 5, 10, 25 and 50 paise coins, the smallest number of coins required to pay exactly 79 paise, 66 paise and Re 1.01 to three different persons is

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25 paise × 3 coins + 2 paise × 2 coins
Total number of coins for 79 paise = 5

Coins
For 66 Paise :

50 paise × 1 coin + 10 paise × 1 coin + 2 paise × 3 coin

Total number of coins for 66 paise = 5 coins

For 1.01 Paise :

50 paise × 1 coin + 25 paise × 1 coin + 10 paise × 2 coin
+ 2 paise × 3 coin

Total number of coins for Rs. 1.01 paise = 7 coins

So, total coins used = (5 + 5 + 7) coins

= 17 coins

Ans.(A) (because given that smallest no. of coin)

What pair comes next in the following sequence 99, 90, 83, 78, ...

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A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the actual price price were his was the listed price of the article?

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As dealer makes a profit of 20%,

selling price (SP) = 1.2x

But the dealer incurs loss by selling 16 articles at the cost of 12 articles.

So, SP of 16 articles = CP of 12 articles

Loss = 25%

Now, SP = 1.6x

80% of marked (or list) price (MP) = 1.6x

MP = 2x

Hence, list price is 100% above cost price.

A dealer offers sells half of the eggs that he has and another half an egg to Anurag. Then he sells half of the balance eggs and another half an egg to Deepak. Then he sells half of the balance eggs and another half an egg to Sivani. In the end he is left with just 7 eggs and he claims that he never broke an egg. How many eggs did he start with?

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There are eight poets, namely, A, B, C, D, E, F, G and H in respect of whom questions are being asked in the examination. The first four are ancient poets and the last four are modern poets. The question on ancient and modern poets is being asked in alternate years. Those who like W also like V, those who like S like R also. The examiner who sets question is not likely to ask question on S because he has written an article on him. But he likes S. Last year a question was asked on U. Considering these facts, on whom the question is most likely to be asked this year ?

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A team must be selected from ten probables – A, B, C, D, E, F, G, H, I and J. Of these, A, C, E and J are forwards, B, G and H are point guards and D, F and I are defenders. The team must have at least one forward, one point guard and one defender. If the team includes J, it must also include F. The team must include E or B, but not both. If the team includes G, it must also include F. The team must include exactly one among C, G and I. C and F cannot be members of the same team.D and H cannot be members of the same team. The team must include both A and D or neither of them. There is no restriction on the number of members in the team. What could be the maximum size of the team that includes G?

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How many 4 - digit numbers that can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

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In a family of six persons, there are people from three generations. Each person has separate profession and also they like different colours. There are two couples in the family. Rohan is a CA and his wife neither is a doctor nor likes green colour. Engineer likes red colour and his wife is a teacher. Mohini is mother-in-law of Savita and she likes orange colour. Deepak is grandfather of Titu and Titu, who is a principal, likes black colour. Nerru is grand-daughter of Mohini and she likes blue colour. Nerru's mother likes white colour. Savita is a

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How many positive numbers less than 10,000 are such that the product of their digits is 210?

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(Only 2*3 makes the single digit 6).

So, four digit numbers with combinations of the digits {1,6,5,7} and {2,3,5,7} and three digit numbers with combinations of digits {6,5,7} will have the product of their digits equal to 210.

{1,6,5,7} # of combinations 4!=24

{2,3,5,7} # of combinations 4!=24

{6,5,7} # of combinations 3!=6

24+24+6=54.

Each of the five people K, L, M, P and Q is of a different weight. It is known that the number of people heavier than P is the same as the number of people lighter than Q. L is the heaviest and K is not the lightest. Who is the lightest?

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