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Study Stuff for MCA Examinations

Study Stuff for MCA Examinations

Inverse of the function $f(x)=\frac{10^x-10^{-x}}{10^{x}+10^{-x}}$ is

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⇒ $\frac{10^x-10^-x}{10^x+10^-x}=y$

⇒ $\frac{10^{2x}-1}{10^{2x}+1}=y$

⇒ $10^{2x}=\frac{1+y}{1-y}$ By Componendo Dividendo Rule

⇒ $x=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+y}{1-y}\Bigg{)}$

⇒ ${f}^{-1}(y)=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+y}{1-y}\Bigg{)}$

⇒ ${f}^{-1}(x)=\frac{1}{2}\log _{10}\Bigg{(}\frac{1+x}{1-x}\Bigg{)}$

Let $\vec{a}, \vec{b}, \vec{c} $ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$ , $\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then c is

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$\Rightarrow\begin{vmatrix}{a} & {a} & {c} \\ {1} & {0} & {1} \\ {c} & {c} & {b}\end{vmatrix}=0$

$\Rightarrow-ac-ab+ac+{c}^2=0$

$\Rightarrow{c}^2=ab$

The correct expression for $cos^{-1} (-x)$ is

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Suppose that the temperature at a point (x,y), on a metal plate is $T(x,y)=4x^2-4xy+y^2$, An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

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The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are

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Angles of elevation of the top of a tower from
three points (collinear) A, B and C on a road
leading to the foot of the tower are 30°, 45°
and 60° respectively. The ratio of AB and BC is

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If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ are coincide, then the value of $b^2$

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A particle is at rest at the origin. It moves
along the x −axis with an acceleration $x-x^2$
, where x is the distance of the
particle at time t. The particle next comes to
rest after it has covered a distance

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If $a{\lt}b$ then $\int ^b_a\Bigg{(}|x-a|+|x-b|\Bigg{)}dx$ is equal to

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The domain of the function $f(x)=\frac{{\cos }^{-1}x}{[x]}$ is

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If the volume of the parallelepiped whose adjacent edges are $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\alpha \hat{j}+2\hat{k}$ and $\vec{c}=\hat{i}+2\hat{j}+\alpha \hat{k}$ is 15, then $\alpha$ is equal to

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Let $a$ be the distance between the lines $−2x + y = 2$ and $2x − y = 2$, and $b$ be the distance between the lines $4x − 3y= 5$ and
$6y − 8x = 1$, then

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If $cosec\theta-\cot \theta=2$, then the value of $cosec\theta$ is

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The solution of the equation ${4\cos }^2x+6{\sin }^2x=5$ are

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The function $f(x)=\begin{cases}{{(1+2x)}^{1/x}} & {,x\ne0} \\ {{e}^2} & {,x=0}\end{cases}$, is

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Let $\vec{a}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}$ be another vector such that $\vec{a}.\vec{b}=14$ and $\vec{a} \times \vec{b}=3\hat{i}+\hat{j}-8\hat{k}$ the vector $\vec{b}$ =

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Which term of the series $\frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ...$ is $\frac{\sqrt{5}}{13}$ ?

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The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distribution are

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A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the pop lation like tea and 72% of the population like coffee. Let $x$ be the number of people who like both tea & coffee. Let $m{\leq x\leq n}$, then choose the correct option.

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The value of $\cot \Bigg{(}{cosec}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\Bigg{)}$ is

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If $0{\lt}P(A){\lt}1$ and $0{\lt}P(B){\lt}1$ and $P(A\cap B)=P(A)P(B)$, then

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Which of the following is NOT true?

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$f(x)=x+|x|$ is continuous for

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If ${{a}}_1,{{a}}_2,\ldots,{{a}}_n$ are any real numbers and $n$ is
any positive integer, then

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If $D={\begin{vmatrix}{1} & 1 & {1} \\ 1 & {2+x} & {1} \\ {1} & {1} & {2+y}\end{vmatrix}}\, for\, x\ne0,\, y\ne0$ then D is

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Area of the parallelogram formed by the
lines y=4x, y=4x+1, x+y=0 and x+y=1

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A four-digit number is formed using the
digits 1, 2, 3, 4, 5 without repetition. The
probability that is divisible by 3 is

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For $a\in R$ (the set of al real numbers), $a \ne 1$, $\lim _{{n}\rightarrow\infty}\frac{({1}^a+{2}^a+{\ldots+{n}^a})}{{(n+1)}^{a-1}\lbrack(na+1)(na+b)\ldots(na+n)\rbrack}=\frac{1}{60}$ . Then one of the value of $a$ is

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If $\vec{a}=\lambda \hat{i}+\hat{j}-2\hat{k}$ , $\vec{b}=\hat{i}+\lambda \hat{j}-2\hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ and $\begin{bmatrix}{\vec{a}} & {\vec{b}} & {\vec{c}} \end{bmatrix}=7$, then the values of the $\lambda$ are

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The function $f(x)=\log (x+\sqrt[]{{x}^2+1})$ is

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The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is

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The area enclosed within the curve |x|+|y|=2 is

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If ${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$, $(a{\gt}b)$ and ${x}^2-{y}^2={c}^2$ cut at right angles, then

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Then

$a^2-b^2=c^2-d^2$

Similarly

If $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $x^2-y^2=c^2$ are orthogonal.

It means

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{c^2}+\frac{y^2}{-c^2}=1$ are orthogonal

Then

$a^2-b^2=c^2-(-c^2)$

$a^2-b^2=2c^2$

If $\alpha , \beta$ are the roots of $x^2-x-1=0$ and $A_n=\alpha^n+\beta^n$, the Arithmetic mean of $A_{n-1}$ and $A_n$ is

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If $a_1, a_2, a_3,...a_n$, are in Arithmetic Progression
with common difference d, then the sum $(sind) (cosec a_1 . cosec a_2+cosec a_2.cosec a_2+...+cosec a_{n-1}.cosec a_n)$ is equal to

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Solutions of the equation ${\tan }^{-1}\sqrt[]{{x}^2+x}+{\sin }^{-1}\sqrt[]{{x}^2+x+1}=\frac{\pi}{2}$ are

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In a Harmonic Progression, $p^{th}$ term is $q$ and
the $q^{th}$ term is $p$. Then $pq^{th}$ term is

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If the roots of the quadratic equation $x^2+px+q=0$ are tan 30° and tan 15°
respectively, then the value of 2 + p - q is

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A straight line through the point (4, 5) is
such that its intercept between the axes is
bisected at A, then its equation is

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The value of $\int \frac{({x}^2-1)}{{x}^3\sqrt[]{2{x}^4-2{x}^2+1}}dx$

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Coordinate of the focus of the parabola $4y^2+12x-20y+67=0$ is

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There are two circles in xy −plane whose
equations are $x^2+y^2-2y=0$ and $x^2+y^2-2y-3=0$. A point $(x,y)$ is
chosen at random inside the larger circle.
Then the probability that the point has been
taken from smaller circle is

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In a triangle ABC, if the tangent of half the difference of two angles is equal to one third of the tangent of half the sum of the angles, then the ratio of the sides opposite to the angles is

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If $x^my^n$=$(x+y)^{m+n}$, then $\frac{dy}{dx}$ is

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If $cos^{-1} \frac{x}{2}+cos^{-1} \frac{y}{3}=\phi$, then $9x^2-12xy cos\phi+4y^2$ is

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The value of ${3}^{3-\log _35}$ is

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There are two sets A and B with |A| = m and
|B| = n. If |P(A)| − |P(B)| = 112 then
choose the wrong option (where |A| denotes
the cardinality of A, and P(A) denotes the
power set of A)

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The eccentricity of an ellipse, with its center
at the origin is $\frac{1}{3}$
. If one of the directrices is
$x=9$, then the equation of ellipse is:

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If the angle of elevation of the top of a hill
from each of the vertices A, B and C of a
horizontal triangle is $\alpha$, then the height of
the hill is

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If $(\vec{a} \times \vec{b}) \times \vec{c}= \vec{a} \times (\vec{b} \times \vec{c})$, then

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Today is Wednesday. What would be the day
after 61 days?

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Identify the fifth number in the series:
122, 144, 166, 188, ?

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Which of the following is the odd one from
the given alternatives?

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Fill in the blank:

HEC, JGE, LIG, NKI, ______

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Choose the word opposite in meaning to the
given word: **MITIGATE**

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DNN, FQQ, HTT, ______, LZZ

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Select the pair of words, which are related in
the same way as the capitalized words are
related to each other.**BUTTERFLY : FREEDOM **

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Select the pair of words, which are related in
the same way as the capitalized words are
related to each other. **FRUGAL : EXTRAVAGANT**

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In the following figure, find the total number
of squares.

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Deepak, Rahul, Manoj, and Vinod are
brothers. Who is the heaviest?

- Rahul is heavier than Deepak and Vinod, but lighter than Manoj.
- Deepak is lighter than Rahul and Manoj, but heavier than Vinod.

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Which of the following diagrams correctly represents lions, elephants, and animals?

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Lions, Elephants, and Animals

Lions and Elephants are different animals.

Replace the question mark with an appropriate image to complete the analogous pair.

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Fill in the blank:

JAK, KBL, LCM, MDN, _____

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Find the synonym that is most nearly similar in meaning to the word:

DEBACLE

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If in a certain language, KOLKOTA is coded as LPMLPUB, how is MUMBAI coded in that

code?

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Select the related word from the given alternatives.

MELT : LIQUID : : FREEZE : ?

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Looking at the portrait of a man, Manu said, "Her mother is the wife of my father's son and I have no brother and sister." Whose portrait was Manu looking at?

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Identify the sixth number in the series:

6, 11, 21, 36, 56, ?

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U, V, W, X and T are sitting on a bench. T is sitting next to U, V is sitting next to W, W is not sitting with X who is on the left end of the bench. V is in the second position from the right. T is to the right of U and X. T and V are sitting together. In which position T is sitting?

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No women teacher can play.

Some women teachers are athletes.

I. Male athletes can play.

II. Some athletes can play.

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All mangoes are golden in colour.

No golden-coloured things are cheap.

I. All mangoes are cheap.

II. Golden-coloured mangoes are not cheap.

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All young scientists are open-minded.

No open-minded men are superstitious.

I. No scientist is superstitious.

II. No young people are superstitious.

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Six books are labelled A, B, C, D, E and F and
are placed side by side. Books B, C, E and F
have green covers while others have yellow
covers. Books A, B and D are new while the
rest are old volumes. Books A, B and C are
law reports while the rest are medical
extracts. Which two books are old medical
extracts and have green covers?

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Find out the wrong number in the FOLLOWING series.

2, 5, 10, 17, 26, 38, 50, 65

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Find out the wrong number in the FOLLOWING series.

30, −5, −45, −90, −145, −195, −255

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The following questions are based on the pie charts given below.

Percentage-wise distribution of students studying in Arts and Commerce in seven

different institutions – A, B, C, D, E, F, and G.

What is the total number of students studying Arts in Institutes A and G together?

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The following questions are based on the pie charts given below.

Percentage-wise distribution of students studying in Arts and Commerce in seven

different institutions – A, B, C, D, E, F, and G.

How many students from Institute B study Arts and Commerce?

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The following questions are based on the pie charts given below.

Percentage-wise distribution of students studying in Arts and Commerce in seven

different institutions – A, B, C, D, E, F, and G.

The ratio of the number of students studying Arts to that studying commerce in Institute E is

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Many shops in the local market have extended their shops and occupied most part of the footpath in front of their shops.

I. The civic authority should immediately activate a task force to clear all the footpaths encroached by the shop owners.

II. The civic authority should charge hefty penalty to the shop owners for occupying the footpath

III. The civic authority should setup a monitoring system so that encroachments do not recur in future.

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There is a significant increase in the number of patients affected by some disease in a city

I. Municipal Corporation of the city should take immediate action.

II. This problem should be raised in UNESCO.

III. Hospitals in the city should be equipped properly for the treatment of the patients

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Five Dramas A, B, C, D, and E have to be staged in 6 hours where 1 hour needs to be given per drama.

I. A break of 1 hour has to be taken in the third or four hour.

II. Drama show cannot be started with A and cannot end with C

III. D has to follow B immediately with no break in between.

IV. A cannot be done immediately after D.

V. A has to precede E immediately with no break in between.

Which hour is a break hour?

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Five Dramas A, B, C, D, and E have to be staged in 6 hours where 1 hour needs to be given per drama.

I. A break of 1 hour has to be taken in the third or four hour.

II. Drama show cannot be started with A and cannot end with C

III. D has to follow B immediately with no break in between.

IV. A cannot be done immediately after D.

V. A has to precede E immediately with no break in between.

Which is the drama to be staged first?

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Five Dramas A, B, C, D, and E have to be staged in 6 hours where 1 hour needs to be given per drama.

I. A break of 1 hour has to be taken in the third or four hour.

II. Drama show cannot be started with A and cannot end with C

III. D has to follow B immediately with no break in between.

IV. A cannot be done immediately after D.

V. A has to precede E immediately with no break in between.

Which is the drama staged immediately after the break?

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Five Dramas A, B, C, D, and E have to be staged in 6 hours where 1 hour needs to be given per drama.

I. A break of 1 hour has to be taken in the third or four hour.

II. Drama show cannot be started with A and cannot end with C

III. D has to follow B immediately with no break in between.

IV. A cannot be done immediately after D.

V. A has to precede E immediately with no break in between.

Which drama is staged immediately after D?

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Five Dramas A, B, C, D, and E have to be staged in 6 hours where 1 hour needs to be given per drama.

I. A break of 1 hour has to be taken in the third or four hour.

II. Drama show cannot be started with A and cannot end with C

III. D has to follow B immediately with no break in between.

IV. A cannot be done immediately after D.

V. A has to precede E immediately with no break in between.

Which drama is staged immediately after E?

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Running at the same constant rate, 6
identical machines can produce a total of
270 bottles per minute. At this rate, how
many bottles could 10 such machines
produce in 4 minutes?

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Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

$\begin{matrix}{\begin{matrix}{Machines} & {6\colon10}\end{matrix}} \\ {\begin{matrix}{Time} & {\, \, \, \, \, \, \, \, \, \, 1\colon4}\end{matrix}}\end{matrix}\Bigr{\}}: : 270:x$

∴$6×1×x=10×4×270$

⇒$x= \frac{(10×4×270)}{6}$

⇒$x=1800$

At what time, in minutes, between 3 o’clock
and 4 o’clock, both the needles will coincide
each other?

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0=30*3-5.5M

M=$\frac{90}{5.5}$

M=$\frac{180}{11}$

M=$16 \frac{4}{11}$

1. A is the brother of B

2. C is the father of A

3. D is the brother of E.

4. E is the daughter of B

Then, the uncle of D is?

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Clearly, D is the brother of E and E is the daughter of B.

So, D is the son of B. Also, A is the brother of B.

So, A is the uncle of D.

A person's present age is two-fifth of the age
of his mother. After 8 years, he will be one
half of the age of his mother. What is the
present age of the mother?

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then present age of his som = $\frac{2x}{5}$

After 8 year
son's age$\frac{2x}{5}+8$

mother's age =$x+8$

And given that son's age is $\frac{1}{2}$ time of mother's

$\frac{2x}{5}+8=\frac{1}{2}(x+8)$

Hence ,present age of mother is 40

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

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The first number = (1657 - 6) = 1651

Second number = (2037 - 5) = 2032

Taking the HCF of two numbers 1651, 2032 we get 127.

So, if we divide 1657 and 2037 by 127 we will get remainders 6 and 5 respectively.

The maximum and minimum value represented in signed
16 bit 2's complement representations are

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Range for 16 bits = $-2^{16-1}$ to $2^{16-1}+1$

Range for 16 bits = $-2^{15}$ to $2^{25}+1$

Range for 16 bits = $-32768$ to $32767$

The minimum number of NAND gates required for implementing the Boolean expression $AB+A\, \overline{B}C+A\, \overline{B}\, \overline{C}$

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=$AB+AB'C+AB'C'$

=$AB+AB'(C+C')$

=$AB+AB'$

=$A(B+B')$

=A

Which of the following is equivalent to the Boolean expression:

$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$

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$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$

=$(X+Y)(X+Y')(X'+Y)$

=$(XX+XY+YX+YY')(X'+Y)$

=$(X+XY)(X'+Y)$

=$X(1+Y)(X'+Y)$

=$X(X'+Y)$

=$XX'+XY$

=$XY$

Suppose the largest n bit number requires ‘d’ digits in decimal representation. Which of the following relations between ‘n’ and ‘d’ is approximately correct

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So, ${10}^d{\gt}{2}^n$

Take on both side

$\log _{10}({10}^d)\gt{\log _{10}({2}^n)}^{}$

$d{\gt}n\log _{10}(2)$

If a processor clock is rated as 2500 million cycles per second, then its clock period is:

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we know that Frequency is defined as the number of cycles in one second

Number of cycle in 1 sec = 2500 million

=> Frequency = 2500 Mhz

we know that time period is the inverse of frequency and is defined as the time taken by one cycle.

$T = \frac{1}{F}$

$T = \frac{1}{2500 \times 10^{-6}}$

$T=4 \times 10^{-10} $ sec

Write the simplified form of the Boolean expression

(A+C)(AD+AD')+AC+C

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=(A+C)A(D+D')+C(A+1)

=(A+C)+C

=A+C

FFFF will be the last memory location in a memory of size

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The Hexadecimal digits are 0-9 and A-F. The Hexadecimal system represents numbers in16 symbols, zero to nine and ten to fifteen is represented by the English alphabet A-F.

The Hexadecimal character represents 4 bits.

The last memory location in a memory of size 64K is FFFF.

64K is $2^{16}$ bytes, i.e.

$16^4$ bytes = 1000 bytes in hexadecimal code.

The last accessible address is 1000-1 = FFFF.

‘Floating point representation' is used to represent

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The Boolean expression AB+ AB' + A'C + AC is unaffected by the value of the Boolean variable

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If a signal passing through a gate is inhibited by sending a low into one of the inputs, and the output is HIGH, the gate is a(n):

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A | B | Output |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

What can you call a person who leads an unconventional style of living?

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“Bite the bullet” means

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Fill in the banks with the correct option

Technical writing demands ______ use of language

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Select correct articles

He is….M.A. with PhD and teaches in …university.

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Fill in the blank with the most appropriate option

Kedar__________ this project for a month and now he is about to join a new project.

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Select the correct form of verb/ Subject-verb agreement

The principal, along with his assistants, ___________ the meeting.

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Choose the correct alternative

The country cleared this __path and pavedit__ with packed gravel, so they would have a peaceful place to hike and bike

Which of the following alternatives to the underlined portion would NOT be acceptable?

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You might think you’ve experienced VR, and you might have been pretty impressed. Particularly, if you’re a gamer, there are some great experiences to be had out there (or rather, in there) today. But over the next few year, in VR as in all fields of technology, we’re going to see things that make what is cutting-edge today look like space lnvaders. And although the games will be amazing, the effects of this transformation will be far broader, touching on our work, education, and social lives.

Today’s most popular VR applications involve taking total control of user’s sense (sight and hearing, particularly) to create a totally immersive experience that places the user in a fully virtual environment that feels pretty realistic. Climb up something high and look down, and you’re likely to get a sense of vertigo. If you see an object moving quickly towards your head, you’ll feel an urge to duck out of the way.

Very soon, VR creators will extend this sensory hijacking to our other facilities – for example, touch and smell – to deepen that sense of immersion. At the same time, the devices we use to visit these virtual worlds will become cheaper and lighter, removing the friction that can currently be a barrier.

I believe extended reality (XR) – a term that covers virtual reality (VR), augmented reality (AR), and mixed reality (MR) – will be one of the most transformative tech trends of the next five years. It will be enabled and augmented by other tech trends, including super-fast networking, that will let us experience VR as a cloud service just like we currently consume music and movies. And artificial intelligence (Al) will provide us with more personalized virtual worlds to explore, even giving us realistic virtual characters to share our experiences

with.

The passage states all the following about VR applications except

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You might think you’ve experienced VR, and you might have been pretty impressed. Particularly, if you’re a gamer, there are some great experiences to be had out there (or rather, in there) today. But over the next few year, in VR as in all fields of technology, we’re going to see things that make what is cutting-edge today look like space lnvaders. And although the games will be amazing, the effects of this transformation will be far broader, touching on our work, education, and social lives.

Today’s most popular VR applications involve taking total control of user’s sense (sight and hearing, particularly) to create a totally immersive experience that places the user in a fully virtual environment that feels pretty realistic. Climb up something high and look down, and you’re likely to get a sense of vertigo. If you see an object moving quickly towards your head, you’ll feel an urge to duck out of the way.

Very soon, VR creators will extend this sensory hijacking to our other facilities – for example, touch and smell – to deepen that sense of immersion. At the same time, the devices we use to visit these virtual worlds will become cheaper and lighter, removing the friction that can currently be a barrier.

I believe extended reality (XR) – a term that covers virtual reality (VR), augmented reality (AR), and mixed reality (MR) – will be one of the most transformative tech trends of the next five years. It will be enabled and augmented by other tech trends, including super-fast networking, that will let us experience VR as a cloud service just like we currently consume music and movies. And artificial intelligence (Al) will provide us with more personalized virtual worlds to explore, even giving us realistic virtual characters to share our experiences

with.

‘Duck out of something’ means

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Select an antonym for the word ‘augment’ from the options given below:

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Select the word which means the same as the following:

To read something carefully

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Choose the correct alternative with the correct choice

given below each statement:

You are to conform ______________ the rules of the institute.

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Choose the antonym:

BOLD

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Select the one which best expresses the same sentence in indirect/direct speech:

He said, “I am glad to be here this evening.”

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Identify the word that is similar in meaning to the

underlined word.

Raghu made__ adulatory__ remarks about the waiter who served the food.

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Which of the phrase given below should replace the phrase printed in bold to make the sentence grammatically correct.

He is addicted to smoke.

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Fill in the blanks with the correct preposition

Jagdish is waiting for me_____ the campus.

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Read the following sentence to find if there is any error in any part:

(A) If I were him / (B) I would teach / (C) him a lesson /

(D) No error

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Choose the synonym

**LIBERAL**

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Fill in the blank

Neither Peter nor I ________ responsible for this blunder.

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**Online Test Series, **

Information About Examination,

Syllabus, Notification

and More.

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**Online Test Series, **

Information About Examination,

Syllabus, Notification

and More.

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