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Study Stuff for MCA Examinations

Study Stuff for MCA Examinations

If TRANSFER is coded as RTNAFSRE, the ELEPHANT would be coded as

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Which two of the following numbers comes in the next in the following sequence.

61, 57, 50, 61, 43, 36, 61, ………

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Thus, following the same pattern next two terms will be 29
and 22.

How many minimum number of colours will be required to paint all the sides of a cube without the adjacent sides having the same colours?

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In the following sequence, which pair of numbers fill in the blanks?

1, 1, 3, 2, 8, 5, 21, 13

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1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Anthropologists have pieced together the little they know about the history of left-handedness and right-handedness from indirect evidence. Though early men and women did not leave written records, they did leave tools, bones, and pictures. Stone age hand axes and hatchets were made from stones that were carefully chipped away to form sharp cutting edges. In some, the pattern of chipping shows that these tools and weapons were made by right-handed people, designed to fit comfortably into a right hand. Other Stone Age implements were made by or for left-handers Prehistoric pictures, painted on the walls of caves, provide further clues to the handedness of ancient people. A right-hander finds it easier to draw faces of people and animals facing toward the left. Whereas a left-hander finds it easier to draw faces facing toward the right. Both kinds of faces have been found in ancient painting. On the whole, the evidence seems to indicate that prehistoric people were either ambidextrous or about equally likely to be left – or right-handed. But, in the Bronze Age. The picture changed. The tools and weapons found from that period are mostly made for right-handed use. The predominance of right-handedness among humans today had apparently already been established.

What is the indirect evidence through which the preferred handedness of the Stone Age people could be understood?

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Anthropologists have pieced together the little they know about the history of left-handedness and right-handedness from indirect evidence. Though early men and women did not leave written records, they did leave tools, bones, and pictures. Stone age hand axes and hatchets were made from stones that were carefully chipped away to form sharp cutting edges. In some, the pattern of chipping shows that these tools and weapons were made by right-handed people, designed to fit comfortably into a right hand. Other Stone Age implements were made by or for left-handers Prehistoric pictures, painted on the walls of caves, provide further clues to the handedness of ancient people. A right-hander finds it easier to draw faces of people and animals facing toward the left. Whereas a left-hander finds it easier to draw faces facing toward the right. Both kinds of faces have been found in ancient painting. On the whole, the evidence seems to indicate that prehistoric people were either ambidextrous or about equally likely to be left – or right-handed. But, in the Bronze Age. The picture changed. The tools and weapons found from that period are mostly made for right-handed use. The predominance of right-handedness among humans today had apparently already been established.

According to the passage, a person who is right – handed is more likely to draw people and animals that are facing

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Anthropologists have pieced together the little they know about the history of left-handedness and right-handedness from indirect evidence. Though early men and women did not leave written records, they did leave tools, bones, and pictures. Stone age hand axes and hatchets were made from stones that were carefully chipped away to form sharp cutting edges. In some, the pattern of chipping shows that these tools and weapons were made by right-handed people, designed to fit comfortably into a right hand. Other Stone Age implements were made by or for left-handers Prehistoric pictures, painted on the walls of caves, provide further clues to the handedness of ancient people. A right-hander finds it easier to draw faces of people and animals facing toward the left. Whereas a left-hander finds it easier to draw faces facing toward the right. Both kinds of faces have been found in ancient painting. On the whole, the evidence seems to indicate that prehistoric people were either ambidextrous or about equally likely to be left – or right-handed. But, in the Bronze Age. The picture changed. The tools and weapons found from that period are mostly made for right-handed use. The predominance of right-handedness among humans today had apparently already been established.

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The author implies that which of the following developments occurred around the time of the Bronze Age

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Which of the following refers to the idiom “under the sun”?

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Choose a phrasal verb to replace the explanation in brackets:

When we arrive at the station, we (descend from) ____________ the train.

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Choose the suitable word from the following and fill in the blank :

The medal was awarded for the student's __________ conduct and courage.

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Which of following is a correctly spelt word?

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Which of the following statement is grammatically correct?

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Choose the set words from among the alternatives given. Which when inserted in the sentence best suit the meaning of the sentence.

The _________ of evidence was on the side of plaintiff since all but one witness testify his story was __________

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Choose the one which is nearest in meaning to the word “TURN UP”?

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The phrase “Ready to believe” means

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Choose the appropriate word from among the choice to fill in the blank in sentence:

”If you drink too much, it will _____________ your judgement”

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Choose the set of words for each blank that best fits the meaning of the following sentence as a whole :

_________ green and black tea are obtained from the same plant, there are quite a few significant difference __________ them.

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Choose the correct alternative which can be substituted for the given word/sentence A person who travels to a sacred place as an act of religious devotion.

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Pick out the most effective word from the given words to fill in the blanks to make the sentence meaningfully complete:

Some people ________ themselves into believing that they are indispensable to the organization they work for.

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Fill in the blanks with appropriate phrase to make the sentence meaningfully complete.

__________ bad weather, the trip will be postponed to next week.

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In the following sentence, choose the most suitable one word for the expression:

“A book containing summarized information on all branches of knowledge”

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Pick out the most effective word from the given words to fill in the blanks to make the sentence meaningful completely:

The man was about to move his bike into the compound of his apartment when a passer by ________ down the motor cycle

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Which one of the following Boolean algebraic rule is correct?

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A + A'B = (A + A') . (A + B)

= 1 . (A + B)

= A + B

The representation of a floating point binary number +1001.11 in 8 bit fraction and 6 bit exponent format is

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Which term is redundant in the expression AB + A'C + BC ?

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Let the memory access time is 10 miliseconds and cache hit ratio 15%. The effective memory access time is

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Which of the following is the representation of decimal number (- 147) in 2's compliment notation on a 12-bit machine?

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The first instruction of bootstrap loader program of an operating system is stored in

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Consider the equation (40)_{x} = (132)_{y} is some bases x and y. Then a possible set of value of x and y are

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The smallest integer that can be represented by an 8 bit number in 2's complement form is

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Which of the following in a functionally complete set of gates?

I. NAND II. NOR

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The total number binary function that can be defined using n Boolean variables is

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A and B are independent witness in a case. The chance that A speaks truth is x and B speaks
truth is y. If A and B agree on certain statement, the probability that the statement is true is

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P(B speaks truth) = y

Since, both A and B agree on certain statement.

Hence, Total Probability =P(A)P(B)+P(A')P(B')

=xy + (1-x)(1-y)

If statement is true then it means both A and B speaks truth.

∴ Required Probability =

The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A+G^{2} = 27, then the two numbers are

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In an entrance test there are multiple choice questions, with four possible answer to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If the student gets the correct answer to a question, then the probability that he as guessing is

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A man is known to speak the truth 2 out of 3 times. He threw a dice cube with 1 to 6 on its faces and reports that it is 1. Then the probability that it is actually 1 is

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Let A and B be two events such that , and

where stands for the complement of event A. Then the events A and B are

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The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively. The P(X = 1) is

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np = 4

npq = 2

q = 1/2, p = 1/2, n = 8

p(X = 1) = 8C1 (1/2)(1/2)7

If is the mean of distribution of x, then usual notation is

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If E_{1} and E_{2} are two events associated with a random experiment such that P (E_{2}) = 0.35, P (E_{1} or E_{2}) = 0.85 and P (E_{1} & E_{2}) = 0.15 then P(E_{1}) is

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Find a matrix X such that 2A + B + X = 0, whose A = and B =

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If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in HP, then sin A, sin B, sin C are in

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If altitudes of a triangle are in HP then its side will be in AP because sides are inverse proportion to height as area is constant. a, b, c are sides of triangle.

a, b, c are in A.P.

sin A, sin B, sin C are in A.P.

α, β are the roots of the an equation $x^2- 2x cosθ + 1 = 0$, then the equation having roots αn and βn is

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The equation (x-a)^{3}+(x-b)^{3}+(x-c)^{3} = 0 has

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Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then resulting numbers are in geometric progression. Then which of the following is not among the three numbers?

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Let the three terms in A.P. be a – d, a, a + d.

given that a – d + a + a + d = 21

a = 7

then the three term in A.P. are 7 – d, 7, 7 + d

According to given condition 9 – d, 9, 21 + d are in G.P.

(9)^{2} = (9 – d) (21 + d)

81 = 189 + 9d – 21d – d^{2}

81 = 189 – 12d – d^{2}

d^{2} + 12d – 108 = 0

d(d + 18) – 6 (d + 18) = 0

(d – 6) (d + 18) = 0

We get, d = 6, –18

Putting d = 6 in the term 7 – d, 7, 7 + d we get 1, 7, 13.

The value of A that satisfies the equation asinA + bcosA = c is equal to

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If tan x = - 3/4 and 3π/2 < x < 2π, then the value of sin2x is

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Find the principal value of is

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If cosθ = 4/5 and cosϕ = 12/13, θ and ϕ both in the fourth quadrant, the value of cos( θ + ϕ )is

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The value of sin36^{o is}

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Express (cos 5x – cos7x) as a product of sines or cosines or sines and cosines,

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If non-zero numbers a, b, c are in A.P., then the straight line ax + by + c = 0 always passes
through a fixed point, then the point is

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Since a, b and c are in A. P. 2b = a + c

a –2b + c =0

The line passes through (1, –2).

If the lines x + (a – 1)y + 1 = 0 and 2x + a^{2}y – 1 = 0 are perpendicular, then the condition satisfies by a is

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In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC,
then 2(r + R) equals

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If x^{2} + 3xy + 2y^{2} – x – 4y – 6 = 0 represents a pair of straight lines, their point of intersection is

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The equation of the tangent line to the curve y = 2x sin x at the point (π/2, π), is

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If the graph of y = (x – 2)^{2} – 3 is shifted by 5 units up along y-axis and 2 units to the right along
the x-axis, then the equation of the resultant graph is

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When y= f (x) is shifted by k units to the right along x

– axis, it become y= f (x - k )

Hence, new equation of

graph is y = (x - 4)^{2} + 2

The direction cosines of the vector a = (- 2i + j – 5k) are

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The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and
one focus (0, 4) is

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If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are vectors such that $\vec{a}$+$\vec{b}$+$\vec{c}$ = 0 and |$\vec{a}$| =7, $\vec{b}$=5, |$\vec{c}$| = 3, then the angle between the vectors $\vec{b}$ and $\vec{c}$

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If , and

, (a ≠ b ≠ c ≠ 1) are co-planar, then the value of is

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Let **a**, **b** and **c** be three vectors having magnitudes 1, 1 and 2 respectively. If **a** x (**a** x **c**) - **b** = 0, then the acute angle between **a** and **c** is

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Let , and be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value of .+.+. is

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If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )

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The number of elements in the power set P(S) of the set S = [2, (1, 4)] is

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If (1 - x + x^{2 })^{n} = a + a_{1}x + a_{2}x^{2} + ... + a_{2n}x^{2n} , then a_{0} + a_{2} + a_{4} + ... + a_{2n} is

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m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small
cages and p large animal (n < p < m). The large animals are so large that they do not fit in small
cage. However, small animals can be put in any cage. The number of putting the animals into
cage is

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Let A and B two sets containing four and two elements respectively. The number of subsets of
the A × B, each having at least three elements is

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n(B) = 2

Then the number of subsets in A*B is 2^{8 }= 256

The slope of the function

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What is the largest area of an isosceles triangle with two edges of length 3?

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The value of is

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Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2. If $\lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3$, then f(2) is

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⇒f′(1)=0 and f′(2)=0

Given f(x) is a fourth degree polynomial

Let $f(x)=a{x}^4+b{x}^3+c{x}^2+dx+e$

Given

$\lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3$

$\lim _{{x}\rightarrow0}\lbrack1+\frac{a{x}^4+b{x}^3+c{x}^2+\mathrm{d}x+e}{{x}^2}\rbrack=3$

$\lim _{{x}\rightarrow0}\lbrack1+a{x}^2+bx+c+\frac{d}{x}+\frac{e}{{x}^2}\rbrack=3$

For limit to have finite value, value of 'd' and 'e' must be 0⇒d=0 & e=0

Substituting x=0 in limit

⇒ c+1=3

⇒ **c=2**

$f^{\prime}(x)=4a{x}^3+3b{x}^2+2cx+d$

$x=1$ and $x=2$ are extreme values,

⇒$f^{\prime}(1)=0$ and $f^{\prime}(2)=0

⇒ $4a+3b+4=0$ and $32a+12b+8=0$

By solving these equations

we get, $a=\frac{1}{2}$ and $b=-2$

So,

$f(x)=\frac{x^{4}}{2}-2x^{3}+2x^{2}$

⇒$f(x)=x^{2}(\frac{x^{2}}{2}-2x+2)$

⇒$f(2)=2^{2}(2-4+2)$

⇒$f(2)=0$

The maximum value of 4 sin^{2 }x + 3 cos^{2 }x + sin(x/2) + cos(x/2) is

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The solution of (e^{x} + 1) y dy = (y + 1) e^{x }dx is

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Evaluate dx

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Using Property

The critical point and nature for the function f(x, y) = x^{2} –2x + 2y^{2} + 4y – 2 is

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If y = cos^{2 }x^{2 }, find dx/dy

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= 2 (cos x2) sin x2 .2x

= -4 (cos x2) sin x2

The derivative of (x^{3} + e^{x} + 3^{x} + cotx) with respect to x is

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Now,

= 3x^{2 }+ e^{x }+ 3^{x} log3 - cosec^{2} x

The solution of the differential equation is

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Variable separable

Integrating

Differentiate [- log(log x), x > 1] with respect to x

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On differentiating both sides,

= - (log (log x))

= (log x)

=

=

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=

Again apply L'Hospital Rule,

=

Putting x = 0, we get

Two persons S and M have made the following statements among themselves.

S says that I am certainly not over 40 years.

M says that I am 38 years and you are at least 5 year old than me.

S says you are at least 39 years.

If all the above statements are wrong, what are the ages of M and S?

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What is the largest number of positive integers to be picked up randomly so that the sum of
difference of any two of the chosen numbers is divisible by 10?

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Five children were administered psychological tests to know their intellectual levels. In the report psychologists pointed that child A is less intelligent than child B. The child C is less intelligent child D. The child B is less intelligent than child C and child A is less intelligent than child E. Which child is most intelligent?

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From a group of 7 men and 6 women, a committee of 5 persons with more males than females is to be formed. In how many ways can this be done?

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A, B, C, D, E are a group of 7 friends from a club. There are two houses wives, one lecturer, one architect, one accountant and one lawyer in the group. There are two married couples. The lawyer is married to D, who is a housewife. No lady is either an architect or an accountant. C, the accountant is married to F, who is a lecturer. If E is not a housewife, what is the profession of E?

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There are five books A, B, C, D, and E placed on a table. If A is placed below E, C is placed above D, B is placed below A and D is placed above E, then which of the following books touches the surface of the table.

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The following series is obtained by considering representations of decimal 99 in the different number system. The next two numbers in the sequence are

99, 90, 83, 78, ____, ____

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In a family of six-person A, B, C, D, E, and F there are two married couples. D is the grandmother of A and mother of B. C is the wife of B and mother of F. F is the granddaughter of E.

Who is C to A?

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In a family of six-person A, B, C, D, E, and F there are two married couples. D is the grandmother of A and mother of B. C is the wife of B and mother of F. F is the granddaughter of E.

Which of the following is true?

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In a family of six-person A, B, C, D, E, and F there are two married couples. D is the grandmother of A and mother of B. C is the wife of B and mother of F. F is the granddaughter of E.

Who among the following is one of the couples?

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The missing number in the following series 336, 210, 120, 60, ______, 6 is

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If the day after in the day tomorrow is three days before Friday, then today is

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Find the missing term of the following series:

DCXW, HGTS, ________, POLK, TSHG

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Four passengers in a train find that they form an interesting group. Two of them are lawyers and the other two are doctors. Two of them speak Bengali and the other two speak Hindi and no two of the same profession speak the same language. They also found that two of them are Christians and two are Muslims and no two of the same religion speak the same languages. The Hindi speaking doctor is a Christian. Then which of the following statement logically follows?

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In an amusement park seven friends – Feroz, Gautam, Harish, Javed, Kumar, Laxman and Mohan are deciding who will ride the roller coaster. There is time for only one ride before the park closes. If Feroz rides Gautam must ride. If Gautam and Harish both ride, Javed cannot ride. If Harish and Javed both ride, Laxman cannot ride. If Javed rides, either Kumar or Mohan must ride. Kumar and Laxman cannot both ride, but one of them must ride. Kumar and Mohan cannot both ride.

Which of the following is an acceptable combination of riders if only three people ride?

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In an amusement park seven friends – Feroz, Gautam, Harish, Javed, Kumar, Laxman and Mohan are deciding who will ride the roller coaster. There is time for only one ride before the park closes. If Feroz rides Gautam must ride. If Gautam and Harish both ride, Javed cannot ride. If Harish and Javed both ride, Laxman cannot ride. If Javed rides, either Kumar or Mohan must ride. Kumar and Laxman cannot both ride, but one of them must ride. Kumar and Mohan cannot both ride.

If Javed and Mohan both ride, which of the following is true?

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In an amusement park seven friends – Feroz, Gautam, Harish, Javed, Kumar, Laxman and Mohan are deciding who will ride the roller coaster. There is time for only one ride before the park closes. If Feroz rides Gautam must ride. If Gautam and Harish both ride, Javed cannot ride. If Harish and Javed both ride, Laxman cannot ride. If Javed rides, either Kumar or Mohan must ride. Kumar and Laxman cannot both ride, but one of them must ride. Kumar and Mohan cannot both ride.

If Feroz and Harish both ride, what is the greatest number of people who can ride?

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The number of squares in the following 6 × 6 grid is

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A cube is made up of 125 one cm. square cubes placed on a table. How many squares are visible only on three sides?

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Three thieves rob a bakery of bread, one after the other. Each thief takes half of what is present and half bread. If 3 breads remain at the end, what is the number of breads that were present initially?

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caterpillar crawls up a pole of 75 inches high standing from the ground. Each day is crawls up 5 inches and each night it slides down 4 inches. When will it reach the top of the pole?

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A man's investments doubles in every 5 years. If the invested Rs. 5,000 in each of the years 1990, 1995, 2000 and 2005, then what was the total amount received by him in 2010?

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A, B, C, D, E, F, G, and H are sitting around a circular table facing the center. Each one of them has a different profession viz, doctor, engineer, architect, teacher, clerk, shopkeeper, banker and businessman. A sits third to the right of the teacher. D sits second to the left of G. G is not an immediate neighbor of teacher. Only one person sit between B, the shopkeeper and the teacher. The one who is an architect sits third to the right of the shopkeeper. H is sit between architect and engineer. E is not an immediate neighbor of H. Engineer sits third to the right of the clerk. Only one person sits between the businessman and F.

E is neither a businessman nor a doctor. Who amongst the following is the clerk?

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A, B, C, D, E, F, G, and H are sitting around a circular table facing the center. Each one of them has a different profession viz, doctor, engineer, architect, teacher, clerk, shopkeeper, banker and businessman. A sits third to the right of the teacher. D sits second to the left of G. G is not an immediate neighbor of teacher. Only one person sit between B, the shopkeeper and the teacher. The one who is an architect sits third to the right of the shopkeeper. H is sit between architect and engineer. E is not an immediate neighbor of H. Engineer sits third to the right of the clerk. Only one person sits between the businessman and F.

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A, B, C, D, E, F, G, and H are sitting around a circular table facing the center. Each one of them has a different profession viz, doctor, engineer, architect, teacher, clerk, shopkeeper, banker and businessman. A sits third to the right of the teacher. D sits second to the left of G. G is not an immediate neighbor of teacher. Only one person sit between B, the shopkeeper and the teacher. The one who is an architect sits third to the right of the shopkeeper. H is sit between architect and engineer. E is not an immediate neighbor of H. Engineer sits third to the right of the clerk. Only one person sits between the businessman and F.

What is the profession of H?

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Who sits exactly between the architect and businessman?

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Who sits immediately right of the businessman?

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Raghav left his home for office in car. He drove 15
km straight towards North and then turned eastwards
and covered 8 km. He then turned to left and covered
1 km. He again turned left and drove for 20 km and
reached office. How far and in which direction is his
office from the home?

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John is 20 years older than Steve. In 10 years, Steve's age will be half of that of John. What is the present age of Steve?

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Let the age of Steve be “x” then the age of John is x + 20 after 10 years Steve age be (x + 10), John's age is x+ 30. Now,

2(x + 10) = x +3

Therefore, x = 10

Pointing to a boy, Aruna said to Pushpa, “The mother of his father is the wife of your maternal grand-father”. How is Pushpa related to that boy?

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Which of the following pairs of number follow the number in the series 2, 4, 12, 24, 72, _____, _____?

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2 x 2 = 4

4 x 3 = 12

12 x 2 = 24

24 x 3 = 72

72 x 2 = 144

144 x 3 = 432

P, Q, R, S, T and U are sitting in two rows, three in each row facing each other.

R is second to the left of P.

Q and T are facing each other.

S and P are diagonally opposite to each other.

Q is not a neighbor of R

Which of the following are sitting in a row?

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U S Q

PTR in a row.

There are six teachers A, B, C, D, E and F in a school. Each teacher has to teach two subjects, one compulsory and the other optional. D's optional is History, while three others have it as compulsory subject. E and F have Physics as one of their subjects, F's compulsory subject is Mathematics, which is an optional subject of both C and E. History and English are A's subjects but in term of compulsory and optional subjects, they are reverse of D's. Chemistry is an optional subject of one of the teachers. There is only one female teacher, who has English as her compulsory subject.

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Teachers | Compulsory Subject | Optional Subject |

A | History | English |

B | History | Chemistry |

C | History | Maths |

D | English | History |

E | Physics | Maths |

F | Mathematics | Physics |

There are six teachers A, B, C, D, E and F in a school. Each teacher has to teach two subjects, one compulsory and the other optional. D's optional is History, while three others have it as compulsory subject. E and F have Physics as one of their subjects, F's compulsory subject is Mathematics, which is an optional subject of both C and E. History and English are A's subjects but in term of compulsory and optional subjects, they are reverse of D's. Chemistry is an optional subject of one of the teachers. There is only one female teacher, who has English as her compulsory subject.

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Teachers | Compulsory Subject | Optional Subject |

A | History | English |

B | History | Chemistry |

C | History | Maths |

D | English | History |

E | Physics | Maths |

F | Mathematics | Physics |

There are six teachers A, B, C, D, E and F in a school. Each teacher has to teach two subjects, one compulsory and the other optional. D's optional is History, while three others have it as compulsory subject. E and F have Physics as one of their subjects, F's compulsory subject is Mathematics, which is an optional subject of both C and E. History and English are A's subjects but in term of compulsory and optional subjects, they are reverse of D's. Chemistry is an optional subject of one of the teachers. There is only one female teacher, who has English as her compulsory subject.

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Teachers | Compulsory Subject | Optional Subject |

A | History | English |

B | History | Chemistry |

C | History | Maths |

D | English | History |

E | Physics | Maths |

F | Mathematics | Physics |

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Teachers | Compulsory Subject | Optional Subject |

A | History | English |

B | History | Chemistry |

C | History | Maths |

D | English | History |

E | Physics | Maths |

F | Mathematics | Physics |

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