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Mathematics

Attempt all questions. Each carries 1 mark.

40 questions·1 marks each
1mcq1 marks

The number which is not rational is

  • a

    1

  • b

    π\pi

  • c

    22/7

  • d

    -1

number-systemrational-numbers
2mcq1 marks

If A and B are the nonempty sets and ABUA \subset B \subset U then AB=A \cup B =

  • a

    B

  • b

    A

  • c

    U

  • d

    A+BA + B

set-theoryunion
3mcq1 marks

If x1=5|x - 1| = 5 then x=x =

  • a

    {6,4}\{-6, 4\}

  • b

    [6,4][6, -4]

  • c

    {6,4}\{6, -4\}

  • d

    {6,4}\{-6, -4\}

absolute-valueequations
4mcq1 marks

If log3x=2\log_3 x = 2 then x=x =

  • a

    2x

  • b

    2

  • c

    9

  • d

    8

logarithmsequations
5mcq1 marks

If f(x)=2x+5f(x) = 2x + 5 for xRx \in \mathbb{R}, then f1(x)=f^{-1}(x) =

  • a

    2x52x-5

  • b

    f(x)+5f(x) + 5

  • c

    y2xy-2x

  • d

    (x5)/2(x - 5)/2

functionsinverse-function
6mcq1 marks

If sin1x=cos1x\sin^{-1} x = \cos^{-1} x then x=x =

  • a

    2-\sqrt{2}

  • b

    1/2-1/\sqrt{2}

  • c

    1/21/\sqrt{2}

  • d

    2\sqrt{2}

inverse-trigonometry
7mcq1 marks

The solution of cosx=1/2\cos x = 1/2 is

  • a

    2nπ±π/32n\pi \pm \pi/3

  • b

    nπ±π/3n\pi \pm \pi/3

  • c

    2nπ±π/22n\pi \pm \pi/2

  • d

    nππ/3n\pi - \pi/3

trigonometric-equations
8mcq1 marks

If p, q, r are in A.P. then

  • a

    q=p+rq = p + r

  • b

    p+r=2qp + r = 2q

  • c

    pr=q2pr = q^2

  • d

    p+q+r=0p + q + r = 0

sequence-seriesarithmetic-progression
9mcq1 marks

The fifth term of the sequence: 6, 12, 24, 48, … is

  • a

    56

  • b

    70

  • c

    192

  • d

    96

sequence-seriesgeometric-progression
10mcq1 marks

If A=[aij]A = [a_{ij}], where aij=i+2ja_{ij} = i + 2j, then 2×22 \times 2 matrix A is

  • a

    [3546]\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix}

  • b

    [3654]\begin{bmatrix} 3 & 6 \\ 5 & 4 \end{bmatrix}

  • c

    [3635]\begin{bmatrix} 3 & 6 \\ 3 & 5 \end{bmatrix}

  • d

    [3465]\begin{bmatrix} 3 & 4 \\ 6 & 5 \end{bmatrix}

matrices
11mcq1 marks

The value of x for the determinant x+5301=0\begin{vmatrix} x+5 & 3 \\ 0 & 1 \end{vmatrix} = 0 is

  • a

    0

  • b

    5

  • c

    -5

  • d

    3

determinants
12mcq1 marks

The system of equations: x+y=5x + y = 5, x+y=7x + y = 7 has

  • a

    one solution

  • b

    two solutions

  • c

    many solutions

  • d

    no solution

linear-equationsconsistency
13mcq1 marks

If ω\omega is the cube root of unity of a complex number then ω(1+ω)(1+ω2)=\omega(1 + \omega)(1 + \omega^2) =

  • a

    ω\omega

  • b

    -2

  • c

    -1

  • d

    ω\omega

complex-numberscube-root-of-unity
14mcq1 marks

A quadratic equation whose roots are 2, 3 is

  • a

    x25x+6=0x^2 - 5x + 6 = 0

  • b

    x2+5x+6=0x^2 + 5x + 6 = 0

  • c

    x2+5x6=0x^2 + 5x - 6 = 0

  • d

    x25x6=0x^2 - 5x - 6 = 0

quadratic-equationsroots
15mcq1 marks

If one root of ax2+bx+c=0ax^2 + bx + c = 0 is 2+3i2 + 3i then the other root is

  • a

    4+6i4 + 6i

  • b

    23i2 - 3i

  • c

    2i32i - 3

  • d

    2i+32i + 3

complex-numbersconjugate-roots
16mcq1 marks

Distance between the lines 2x+2y=52x + 2y = 5 and x+y=10x + y = 10 is

  • a

    15/215/2

  • b

    15/(22)15/(2\sqrt{2})

  • c

    15/(22)-15/(2\sqrt{2})

  • d

    222\sqrt{2}

coordinate-geometrydistance-between-lines
17mcq1 marks

The straight lines represented by x2+2xy+ky2=0x^2 + 2xy + ky^2 = 0 are perpendicular to each other if k=k =

  • a

    -1

  • b

    1

  • c

    0

  • d

    2

pair-of-linesperpendicularity
18mcq1 marks

limx3x535x3=\lim_{x \to 3} \dfrac{x^5 - 3^5}{x - 3} =

  • a

    0

  • b

    504

  • c

    405

  • d

    81

limitscalculus
19mcq1 marks

limx0xtanx=\lim_{x \to 0} \dfrac{x}{\tan x} =

  • a

    undefined

  • b

    0

  • c

    1

  • d

    0/0

limitsstandard-limits
20mcq1 marks

The function f(x)={x25xx5x5px=5f(x) = \begin{cases} \dfrac{x^2 - 5x}{x - 5} & x \neq 5 \\ p & x = 5 \end{cases} is continuous at x=5x = 5, for p=p =

  • a

    0

  • b

    5

  • c

    -5

  • d

    1

continuitycalculus
21mcq1 marks

If y=sin(ax2+b)y = \sin(ax^2 + b) then dy/dx=dy/dx =

  • a

    cos(ax2+b)\cos(ax^2 + b)

  • b

    cos(ax2+b)-\cos(ax^2 + b)

  • c

    2axcos(ax2+b)-2ax\cos(ax^2 + b)

  • d

    2axcos(ax2+b)2ax\cos(ax^2 + b)

differentiationchain-rule
22mcq1 marks

If x2+y2=25x^2 + y^2 = 25 then dy/dx=dy/dx =

  • a

    dydx=xy\dfrac{dy}{dx} = -\dfrac{x}{y}

  • b

    dydx=yx\dfrac{dy}{dx} = \dfrac{y}{x}

  • c

    dydx=xy\dfrac{dy}{dx} = \dfrac{x}{y}

  • d

    dydx=yx\dfrac{dy}{dx} = -\dfrac{y}{x}

implicit-differentiation
23mcq1 marks

(3x+sinx+3e3x)dx=\int (3\sqrt{x} + \sin x + 3e^{3x})\,dx =

  • a

    2x3/2cosx+e3x2x^{3/2} - \cos x + e^{3x}

  • b

    x3/2+cosx+e3xx^{3/2} + \cos x + e^{3x}

  • c

    x3/2+cosx+e3xx^{3/2} + \cos x + e^{3x}

  • d

    x3/2cosx+e3xx^{3/2} - \cos x + e^{3x}

integrationindefinite-integral
24mcq1 marks

012xex2+1dx=\int_0^1 2x e^{x^2 + 1}\,dx =

  • a

    e3e^3

  • b

    e2ee^2 - e

  • c

    e41e^4 - 1

  • d

    1

definite-integralsubstitution
25mcq1 marks

Area bounded by the x axis and the curve y=3x2y = 3x^2 and the lines x=0x = 0 and x=2x = 2 is

  • a

    8

  • b

    -8

  • c

    3

  • d

    0

definite-integralarea-under-curve
26mcq1 marks

If the marginal revenue function is 32xx23 - 2x - x^2, for the output x, then the total revenue function is

  • a

    xx2x3/3x - x^2 - x^3/3

  • b

    3xx2x3/33x - x^2 - x^3/3

  • c

    xx2+x3/3x - x^2 + x^3/3

  • d

    xx2x3/3x - x^2 - x^3/3

calculusmarginal-revenue
27mcq1 marks

The critical point for f(x)=x36x2+9x2f(x) = x^3 - 6x^2 + 9x - 2 are

  • a

    1, -3

  • b

    -1, 3

  • c

    1, 3

  • d

    -1, -3

calculuscritical-points
28mcq1 marks

The letter of the word 'union' can be arranged in the number of ways:

  • a

    60

  • b

    120

  • c

    5

  • d

    4

permutationscombinatorics
29mcq1 marks

If 18Cr=18Cr+2^{18}C_r = {}^{18}C_{r+2} then r=r =

  • a

    18

  • b

    9

  • c

    8

  • d

    16

combinationscombinatorics
30mcq1 marks

If the revenue function R=x3x2R = x - 3x^2 and cost function C=x2xC = x^2 - x, then the maximum profit is at x=x =

  • a

    1/4

  • b

    4

  • c

    2

  • d

    3

calculusmaxima-minimaprofit
31mcq1 marks

The probability that a card drawn from a pack of 52 cards will be a diamond or a king is

  • a

    1/52

  • b

    1/13

  • c

    2/13

  • d

    4/13

probabilitycards
32mcq1 marks

The median of the distribution: 5, 3, 2, 4, 10, 7, 12 is

  • a

    4

  • b

    6

  • c

    7

  • d

    5

statisticsmedian
33mcq1 marks

The ratio of the prices of the first and second items is 3:5. If the price of the second item is Rs125, then the price of the first item is

  • a

    375

  • b

    75

  • c

    625

  • d

    15

ratio-proportion
34mcq1 marks

If a profit of 10 percent is made by selling an article for Rs 1320, then the cost price in Rupees

  • a

    1200

  • b

    1100

  • c

    1250

  • d

    1150

profit-loss
35mcq1 marks

In an examination 25 percent of the examinee have been failed and 240 are passed, then the total number of examinees are

  • a

    300

  • b

    320

  • c

    265

  • d

    350

percentage
36mcq1 marks

A, B and C are in partnership. Towards capitals A contributed Rs 3600 and B Rs 3000. The profit amounted is Rs 3800 out of which C receives Rs 1600. The capital of C is Rs

  • a

    4800

  • b

    4000

  • c

    3000

  • d

    2000

partnershipratio
37mcq1 marks

If 1 US dollar = Rs 110 then Rs 5000 will get US dollar

  • a

    46.5

  • b

    44.5

  • c

    45.45

  • d

    50

currency-conversionarithmetic
38mcq1 marks

If P, r, A are the principal, amount and rate of interest per annum respectively, then after n years the amount A will be

  • a

    P(1+r/100)nP(1 + r/100)^n

  • b

    P(1r/100)nP(1 - r/100)^n

  • c

    (P+r/100)n(P + r/100)^n

  • d

    P(r+1/100)nP(r + 1/100)^n

compound-interest
39mcq1 marks

The amount of annuity due of Rs 25 a year for 5 yrs at 4 percent per year is

  • a

    140.0

  • b

    140.4

  • c

    125.0

  • d

    150

annuityfinancial-math
40mcq1 marks

If x+iy=(2+i3)2x + iy = (2 + i3)^2 then (x,y)=(x, y) =

  • a

    (5,12)(5, -12)

  • b

    (5,12)(-5, -12)

  • c

    (5,12)(5, 12)

  • d

    (5,12)(-5, 12)

complex-numbers
B

English

Attempt all questions. Each carries 1 mark.

40 questions·1 marks each
41mcq1 marks

Could you …………..these papers.

  • a

    clear out

  • b

    clear away

  • c

    clear up

  • d

    clear off

phrasal-verbsvocabulary
42mcq1 marks

I am going to ………...a house that I'm thinking of buying.

  • a

    look on

  • b

    look through

  • c

    look over

  • d

    look into

phrasal-verbsvocabulary
43mcq1 marks

You can not ride or drive safely before he has been …………....

  • a

    break down

  • b

    break out

  • c

    break off

  • d

    break in

phrasal-verbsvocabulary
44mcq1 marks

We had to ...............dried milk as fresh milk wasn't available.

  • a

    fall back on

  • b

    fall back

  • c

    fall in

  • d

    fall off

phrasal-verbsvocabulary
45mcq1 marks

He is a pleasant friendly man who …………....well with nearly everybody.

  • a

    get over

  • b

    get round

  • c

    get off

  • d

    get on

phrasal-verbsvocabulary
46mcq1 marks

A scientific method of photostating is ………….......

  • a

    Zeroxography

  • b

    photography

  • c

    orthography

  • d

    lithography

vocabularyone-word
47mcq1 marks

Morbid fear of everything in general is .....................

  • a

    pathophobia

  • b

    panophobia

  • c

    podophobia

  • d

    xenophobia

vocabularyphobia
48mcq1 marks

Lover of trees is called ......................

  • a

    podophile

  • b

    hippophile

  • c

    dendrophile

  • d

    paedophile

vocabularyone-word
49mcq1 marks

Hater of knowledge ...................

  • a

    pacifist

  • b

    iconoclast

  • c

    misogynist

  • d

    misologist

vocabularyone-word
50mcq1 marks

Choose the right synonym of the word "magniloquent"

  • a

    boastful

  • b

    sentimental

  • c

    mournful

  • d

    venal

vocabularysynonym
51mcq1 marks

Choose the right synonym of "pellucid"

  • a

    dark

  • b

    transparent

  • c

    dim light

  • d

    vague

vocabularysynonym
52mcq1 marks

Give right synonym of "overwhelm"

  • a

    over joy

  • b

    over lap

  • c

    overpower

  • d

    over stretch

vocabularysynonym
53mcq1 marks

The antonym of "alienate" is.......................

  • a

    social

  • b

    alleviate

  • c

    transfer

  • d

    reconcile

vocabularyantonym
54mcq1 marks

Choose the right antonym of "wanton"

  • a

    restrained

  • b

    reckless

  • c

    unruly

  • d

    vagabond

vocabularyantonym
55mcq1 marks

One who plays for pleasure is..............

  • a

    fanatic

  • b

    amateur

  • c

    egoist

  • d

    feminist

vocabularyone-word
56mcq1 marks

Fill in the words in right order: The…….. of these roses is sweet. The...of burning rubber is unbearable.

  • a

    scent, perfume

  • b

    perfume, scent

  • c

    smell, stink

  • d

    stink, smell

vocabularyword-usage
57mcq1 marks

One who abandons his/her religious faith:

  • a

    heuristic

  • b

    fanatic

  • c

    agnostic

  • d

    apostate

vocabularyone-word
58mcq1 marks

What do you understand by the expression "the philosopher's stone"?

  • a

    an imaginary substance that people believed could change any metal into gold, or enable people to live for ever

  • b

    scholar's step wise argument

  • c

    ground for discussion

  • d

    philosopher related land

idiomsexpressions
59mcq1 marks

A person who is hard to please is …….....

  • a

    taciturn

  • b

    fastidious

  • c

    stubborn

  • d

    hedonist

vocabularyone-word
60mcq1 marks

John is born………... highly educated parents.

  • a

    of

  • b

    by

  • c

    for

  • d

    from

prepositionsgrammar
61mcq1 marks

We can travel ……..car or walk ….....feet or go…....horseback.

  • a

    by, on, on

  • b

    for, by, on

  • c

    on, by, on

  • d

    on, on, on

prepositionsgrammar
62mcq1 marks

Lucky was fined... parking his vehicle ………...a no parking area.

  • a

    in, for

  • b

    for, in

  • c

    at, for

  • d

    for, with

prepositionsgrammar
63mcq1 marks

Nobody knew the way………...except John.

  • a

    besides

  • b

    but

  • c

    except

  • d

    beside

prepositionsgrammar
64mcq1 marks

He would think it …………...him to tell a lie.

  • a

    above

  • b

    below

  • c

    under

  • d

    beneath

prepositionsgrammar
65mcq1 marks

……….....doing the cooking, I help hostel boys.

  • a

    besides

  • b

    beside

  • c

    behind

  • d

    opposite

prepositionsgrammar
66mcq1 marks

Peter hardly ever goes to parties,………....?

  • a

    doesn't he?

  • b

    does he?

  • c

    did he?

  • d

    didn't he?

question-tagsgrammar
67mcq1 marks

Ann'll lend it to you, Oh no,...............

  • a

    she'll.

  • b

    she can't.

  • c

    she won't.

  • d

    she did.

grammarresponses
68mcq1 marks

Everyone warned you,…………....

  • a

    have they?

  • b

    haven't they?

  • c

    didn't they?

  • d

    did they?

question-tagsgrammar
69mcq1 marks

They are ugly and expensive;………….people buy them.

  • a

    but

  • b

    however

  • c

    still

  • d

    yet

conjunctionsgrammar
70mcq1 marks

He had no qualification;...he got the job.

  • a

    however

  • b

    in spite of

  • c

    though

  • d

    nevertheless

conjunctionsgrammar
71mcq1 marks

Students come to a bad end if they do not mend their ways in time. It means:

  • a

    they may become criminal, go to jail and suffer disgrace

  • b

    will die soon

  • c

    marry and settle

  • d

    fight with their parents and relatives

idiomscomprehension
72mcq1 marks

What does "be neck and neck" stand for?

  • a

    equally good in competition

  • b

    be good friends

  • c

    great enmity

  • d

    ready for competition

idioms
73mcq1 marks

As a beginner in the Spanish class I could not stand the pace.

  • a

    could not learn

  • b

    maintain the level

  • c

    very weak

  • d

    not fit for the class

idioms
74mcq1 marks

He is the friend……………....I trust most in family matters.

  • a

    who

  • b

    whom

  • c

    which

  • d

    him

relative-pronounsgrammar
75mcq1 marks

Public often ………....people who are good at sport.

  • a

    attract

  • b

    appeal

  • c

    admire

  • d

    support

vocabularyword-choice
76mcq1 marks

Choose the word with correct spelling:

  • a

    forein

  • b

    foraign

  • c

    foreign

  • d

    foreigne

spelling
77mcq1 marks

In the word "transcendental" which syllable has the primary stress:

  • a

    1st syllable

  • b

    2nd syllable

  • c

    3rd syllable

  • d

    4th syllable

phoneticsword-stress
78mcq1 marks

I was invited to ………. dinner given to welcome the new ambassador.

  • a

    a

  • b

    the

  • c

    an

  • d

    none

articlesgrammar
79mcq1 marks

He goes to ………..temple sometimes to give lectures.

  • a

    a

  • b

    the

  • c

    an

  • d

    none

articlesgrammar
80mcq1 marks

He has worked for us ever ...he left school.

  • a

    from

  • b

    during

  • c

    for

  • d

    since

conjunctionsgrammar
C

General Knowledge (G.K.) & IT Related

Attempt all questions. Each carries 1 mark.

20 questions·1 marks each
81mcq1 marks

Analog computer works on the supply of

  • a

    physical strength.

  • b

    natural strength.

  • c

    magnetic strength.

  • d

    continuous electrical pulses.

computer-fundamentalsanalog-computer
82mcq1 marks

We can make use of the wild card entries such as ……….. in Windows Explorer.

  • a

    #,@

  • b

    ^,*

  • c

    ?,*

  • d

    ?,#

operating-systemwildcards
83mcq1 marks

Which of the following is the second largest measurement of RAM?

  • a

    Megabyte

  • b

    Gigabyte

  • c

    Byte

  • d

    Terabyte

memory-units
84mcq1 marks

Cache memory acts between

  • a

    CPU and Hard disk.

  • b

    RAM and ROM.

  • c

    CPU and RAM.

  • d

    All of these.

cache-memorycomputer-architecture
85mcq1 marks

Which of the following is billionth of a second?

  • a

    Microsecond

  • b

    Nanosecond

  • c

    Terabyte

  • d

    Gigabyte

time-units
86mcq1 marks

The Binary Coded Decimal (BCD) uses

  • a

    6 bits

  • b

    8 bits

  • c

    16 bits

  • d

    32 bits

number-systemsbcd
87mcq1 marks

RAM is also called as

  • a

    Virtual memory.

  • b

    Volatile memory.

  • c

    Non volatile memory.

  • d

    Cache memory.

memoryram
88mcq1 marks

CPU stands for

  • a

    Central Planning Unit.

  • b

    Computer Planning Union.

  • c

    Computer Processing Unit.

  • d

    Central Processing Unit.

computer-fundamentalsabbreviations
89mcq1 marks

If you want to copy a portion of the text then you need to use

  • a

    Control & C

  • b

    Command & C

  • c

    Control & V

  • d

    Command and V

shortcutssoftware
90mcq1 marks

Which one is not an operating system?

  • a

    Windows

  • b

    Linux

  • c

    Unix

  • d

    LaTex

operating-system
91mcq1 marks

Who described his policy of unification as one of 'blood and iron'?

  • a

    Hitler

  • b

    Mazzini

  • c

    Napoleon

  • d

    Bismarck

world-historygeneral-knowledge
92mcq1 marks

Who is known as the father of Modern Medicine?

  • a

    Erastosthenes

  • b

    Euclid

  • c

    Pythagoras

  • d

    Hippocrates

general-knowledgefamous-people
93mcq1 marks

Which of the following is the place of worship for Judaism?

  • a

    Temple

  • b

    Fire Temple

  • c

    Chapel

  • d

    Synagogue

general-knowledgereligion
94mcq1 marks

The hottest planet of the solar system is

  • a

    Mercury

  • b

    Venus

  • c

    Mars

  • d

    Jupiter

general-knowledgeastronomy
95mcq1 marks

The first word pronounced at the surface of the Moon during Apollo Expedition is

  • a

    OK!

  • b

    Yes!

  • c

    Hurry!

  • d

    Fine!

general-knowledgespace
96mcq1 marks

The longest district of Nepal is

  • a

    Kavrepalunchowk

  • b

    Sindhupalunchowk

  • c

    Parsa

  • d

    Udaypur

nepal-geographydistricts
97mcq1 marks

Which person had divided Nepal into 32 districts?

  • a

    Chandra Samsher

  • b

    Ranoddip

  • c

    Bir Samsher

  • d

    Judhha Samsher

nepal-historyadministration
98mcq1 marks

The longest glacier of Nepal is

  • a

    Khumbu.

  • b

    Lamtang.

  • c

    Upper Arun.

  • d

    Kanchanjangha.

nepal-geographyglaciers
99mcq1 marks

Rawan of epic Ramayana had written two books. The name of one of those books is

  • a

    Arkapakshya.

  • b

    Rawapakshya.

  • c

    Manupakshya.

  • d

    Jiwapakshya.

general-knowledgeepics
100mcq1 marks

The founder of Tao Religion is

  • a

    Kanfusius.

  • b

    Laotse.

  • c

    Ding.

  • d

    Fung.

general-knowledgereligion

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