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NDA II 2017 Mathematics

This test contains 120 question. Each question comprises four responses (answers). You need to select only ONE response for each question.

All questions carry equal marks.

Each question for which a wrong answer has been marked, one-third of the marks assigned to that question will be deducted as penalty.

If a candidate gives more than one answer, it will be treated as a wrong answer even if one of the given answers happens to be correct and there will be same penalty as above to
that question.

If a question is left blank, i.e., no answer is given by the candidate, there will be no penalty for that question.
  • Question 1
    If x + log10 (1 + 2x) = xlog105 + log106 then x is equal to
    Option A: 2, –3
    Option B: 2 only
    Option C: 1
    Option D: 3
    VIEW SOLUTION
  • Question 2
    The remainder and the quotient of the binary division (101110)2 ÷ (110)2 are respectively
    Option A: (111)2 and (100)2
    Option B: (100)2 and (111)2
    Option C: (101)2 and (101)2
    Option D: (100)2 and (100)2
    VIEW SOLUTION
  • Question 3
    The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 – y columns. Both AB and BA exist. What are the values of x and y respectively?
    Option A: 8 and 3
    Option B: 3 and 4
    Option C: 3 and 8
    Option D: 8 and 8
    VIEW SOLUTION
  • Question 4
    If Sn=nP+n(n1)Q2, where Sn denotes the sum of the first n terms of an AP, then the common difference is
    Option A: P + Q
    Option B: 2P + 3Q
    Option C: 2Q
    Option D: Q
    VIEW SOLUTION
  • Question 5
    The roots of the equation
    (qr)x2 + (rp) x + (pq) = 0 are
    Option A: (rp)/ (qr), 1/2
    Option B: (pq) / (qr), 1
    Option C: (q – r) / (pq), 1
    Option D: (rp) / (pq), 1/2
    VIEW SOLUTION
  • Question 6
    If E is the universal set and A = BC, then the set E – (E – (E – (E – (E – A)))) is the same as the set
    Option A: B’∪ C
    Option B: BC
    Option C: B C
    Option D: B C
    VIEW SOLUTION
  • Question 7
    If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then A (BC) is equal to
    Option A: A
    Option B: B
    Option C: C
    Option D: {x : x is a multiple of 100}
    VIEW SOLUTION
  • Question 8
    If α and β are the roots of equation 1 + x + x2 = 0, then the matrix product 1βαα αβ1β is equal to
    Option A: 1112
    Option B: 1112
    Option C: 1112
    Option D: 111-2
    VIEW SOLUTION
  • Question 9
    If |a| denotes the absolute value of an integer, then which of the following are correct?
    1. |ab| = |a| |b|
    2. |a + b| ≤ |a| + |b|
    3. |a – b| ≥ ||a| – |b||
    Select the correct answer using the code given below.
    Option A: 1 and 2 only
    Option B: 2 and 3 only
    Option C: 1 and 3 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 10
    How many different permutations can be made out of the letters of the word 'PERMUTATION'?
    Option A: 19958400
    Option B: 19954800
    Option C: 19952400
    Option D: 39916800
    VIEW SOLUTION
  • Question 11
    If  A=4i610i14i6+4i and k=12i, where i=-1,  then kA is equal to
    Option A: 2+3i5723i
    Option B: 23i572+3i
    Option C: 23i752+3i
    Option D: 2+3i572+3i
    VIEW SOLUTION
  • Question 12
    The sum of all real roots of equation x-32+x-3-2=0 is
    Option A: 2
    Option B: 3
    Option C: 4
    Option D: 6
    VIEW SOLUTION
  • Question 13
    It is given that the roots of equation x2 – 4x – log3 P = 0 are real. For this, the minimum value of P is
    Option A: 127
    Option B: 164
    Option C: 181
    Option D: 1
    VIEW SOLUTION
  • Question 14
    If A is a square matrix, then the value of adjAT – (adj A)T is equal to
    Option A: A
    Option B: 2|A|I, where I is the identity matrix
    Option C: null matrix whose order is the same as that of A
    Option D: unit matrix whose order is the same as that of A
    VIEW SOLUTION
  • Question 15
    The value of the product 612×614×618×6116×... up to infinite terms is
    Option A: 6
    Option B: 36
    Option C: 216
    Option D: 512
    VIEW SOLUTION
  • Question 16
    The value of determinant
    cos2θ2sin2θ2sin2θ2cos2θ2

    for all the values of θ, is
    Option A: 1
    Option B: cos θ
    Option C: sin θ
    Option D: cos2θ
    VIEW SOLUTION
  • Question 17
    The number of terms in the expansion of (x+a)100+(xa)100 after simplification is
    Option A: 202
    Option B: 101
    Option C: 51
    Option D: 50
    VIEW SOLUTION
  • Question 18
    In the expansion of (1 + x)50, the sum of coefficients of odd powers of x is
    Option A: 226
    Option B: 249
    Option C: 250
    Option D: 251
    VIEW SOLUTION
  • Question 19
    If a, b, c are non-zero real numbers, then the inverse of matrix

    A=a000b000c

    is equal to
    Option A: a1000b1000c1
    Option B: 1abca1000b1000c1
    Option C: 1abc100010001
    Option D: 1abca000b000c
    VIEW SOLUTION
  • Question 20
    A person is to count 4500 notes. Let an denote the number of notes that he counts in the nth minute. If a1= a2 = a3 = … = a10 = 150, and a10, a11, a12, … are in AP with the common difference –2, then the time taken by him to count all the notes is
    Option A: 24 minutes
    Option B: 34 minutes
    Option C: 125 minutes
    Option D: 135 minutes
    VIEW SOLUTION
  • Question 21
    The smallest positive integer n, which 1+i1in=1, is
    Option A: 1
    Option B: 4
    Option C: 8
    Option D: 16
    VIEW SOLUTION
  • Question 22
    If we define a relation R on the set N × M as (a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) N × N, then the relation is
    Option A: symmetric only
    Option B: symmetric and transitive only
    Option C: equivalence relation
    Option D: reflexive only
    VIEW SOLUTION
  • Question 23
    If y = x + x2 + x3+ … up to infinite terms, where x < 1, then which of the following is correct?
    Option A: x=y1+y
    Option B: x=y1-y
    Option C: x=1+yy
    Option D: x=1-yy
    VIEW SOLUTION
  • Question 24
    If α and β are the roots of equation 3x2 + 2x + 1 = 0, then the equation whose roots are α + β–1 and β + α–1 is
    Option A: 3x2 + 8x + 16 = 0
    Option B: 3x2– 8x – 16 = 0
    Option C: 3x2 + 8x – 16 = 0
    Option D: x2 + 8x + 16 = 0
    VIEW SOLUTION
  • Question 25
    The value of 1log3e+1log3e2+1log3e4+... up to infinite terms is
    Option A: loge9
    Option C: 1
    Option D: loge3
    VIEW SOLUTION
  • Question 26
    A tea party is arranged for 16 people along the two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is
    Option A: 24 × 8! × 8!
    Option B: (8!)3
    Option C: 210 × 8! × 8!
    Option D: 16!
    VIEW SOLUTION
  • Question 27
    The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k2 has no solution if k equals
    Option B: 1
    Option C: –1
    Option D: –2
    VIEW SOLUTION
  • Question 28
    If 1.3+2.32+3.33++n.3n=(2n1)3a+b4 then a and b are respectively
    Option A: n, 2
    Option B: n, 3
    Option C: n + 1, 2
    Option D: n + 1, 3
    VIEW SOLUTION
  • Question 29
    In PQR, R=π2. If tanP2 and tanQ2 are the roots of equation ax2 + bx + c = 0, then which of the following is correct?
    Option A: a = b + c
    Option B: b = c + a
    Option C: c = a + b
    Option D: b = c
    VIEW SOLUTION
  • Question 30
    If z-4z=2, then the maximum value of |z| is equal to
    Option A: 1+3
    Option B: 1+5
    Option C: 1-5
    Option D: 5-1
    VIEW SOLUTION
  • Question 31
    The angle of elevation of stationary cloud from the point 25 m above a lake is 15° and the angle of depression of its image in the lake is 45°. The height of the cloud above the lake level is
    Option A: 25 m
    Option B: 253 m
    Option C: 50 m
    Option D: 503 m
    VIEW SOLUTION
  • Question 32
    The value of tan 9° – tan 27° – tan 63° + tan 81° is equals to
    Option A: –1
    Option C: 1
    Option D: 4
    VIEW SOLUTION
  • Question 33
    The value of 3 cosec 20° – sec 20° is equal to
    Option A: 4
    Option B: 2
    Option C: 1
    Option D: –4
    VIEW SOLUTION
  • Question 34
    Angle α is divided into two parts A and B such that AB = x and tan A : tan B = p : q. The value of sin x is equal to
    Option A: p+q sinαpq
    Option B: psin αp+q
    Option C: psin αp-q
    Option D: p-q sinαp+q
    VIEW SOLUTION
  • Question 35
    The value of sin-135+tan-117 is equal to
    Option B: π4
    Option C: π3
    Option D: π2
    VIEW SOLUTION
  • Question 36
    The angles of the elevation of the top of a tower from the top and the foot of a pole are respectively 30° and 45°. If hT is the height of the tower and hP is the height of the pole, then which of the following are correct?

    1. 2hPhT3+3=hP2

    2. hThP3+1=hP2

    3. 2hP+hThP=4+3
    Select the correct answer using the code given below
    Option A: 1 and 3 only
    Option B: 2 and 3 only
    Option C: 1 and 2 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 37
    In a triangle ABC, a – 2b + c = 0. The value of cot A2 cot C2 is
    Option A: 92
    Option B: 3
    Option C: 32
    Option D: 1
    VIEW SOLUTION
  • Question 38
    1+sin A=sinA2+cosA2 is true if
    Option A: 3π2<A<5π2 only
    Option B: π2<A<3π2 only
    Option C: 3π2<A<7π2
    Option D: 0<A<3π2
    VIEW SOLUTION
  • Question 39
    In triangle ABC, if sin2A+sin2B+sin2Ccos2A+cos2B+cos2C=2 then the triangle is
    Option A: right-angled
    Option B: equilateral
    Option C: isosceles
    Option D: obtuse-angled
    VIEW SOLUTION
  • Question 40
    The principal value of sin–1 x lies in the interval
    Option A: π2,π2
    Option B: π2,π2
    Option C: 0,π2
    Option D: [0, π]
    VIEW SOLUTION
  • Question 41
    The points (a, b), (0, 0), (–a, –b) and (ab, b2) are
    Option A: the vertices of parallelogram
    Option B: the vertices of a rectangle
    Option C: the vertices of a square
    Option D: collinear
    VIEW SOLUTION
  • Question 42
    The length of the normal from origin to the plane x + 2y – 2z = 9 is equal to
    Option A: 2 units
    Option B: 3 units
    Option C: 4 units
    Option D: 5 units
    VIEW SOLUTION
  • Question 43
    If α, β and γ are the angles which the vector OP (O being the origin) makes with positive direction of coordinate axes, then which of the following are correct?
    1. cos2α + cos2 β = sin2 γ
    2. sin2 α + sin2 β = cos2 γ
    3. sin2 α + sin2 β + sin2 γ  = 2
    Select the correct answer using the code given below
    Option A: 1 and 2 only
    Option B: 2 and 3 only
    Option C: 1 and 3 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 44
    The angle between the lines x + y – 3 = 0 and xy + 3 = 0 is α and the acute angle between the lines x 3y+23=0 and 3xy+1=0 is β. Which one of the following is correct?
    Option A: α = β
    Option B: α > β
    Option C: α < β
    Option D: α = 2β
    VIEW SOLUTION
  • Question 45
    Let α=i^+2j^k^, β=2i^j^+3k^ and γ=2i^+j^+6k^ be three vectors. If  α and β are both perpendicular to the vector δ and δ·γ=10, then what is the magnitude of δ?
    Option A: 3 units
    Option B: 23 units
    Option C: 32 unit
    Option D: 13 unit
    VIEW SOLUTION
  • Question 46
    If a^ and b^ are two unit vectors, then the vector a^+b^×a^×b^ is parallel to
    Option A: a^-b^
    Option B: a^+b^
    Option C: 2a^-b^
    Option D: 2a^+b^
    VIEW SOLUTION
  • Question 47
    A force F=i^+3j^+2k^ acts on a particle to displace it from the point Ai^+2j^3k^ to the point B3i^-j^+5k^. The work done by the force will be
    Option A: 5 units
    Option B: 7 units
    Option C: 9 units
    Option D: 10 units
    VIEW SOLUTION
  • Question 48
    For any vector a a×i^2+a×j^2+a×k^2 is equal to
    Option A: a2
    Option B: 2a2
    Option C: 3a2
    Option D: 4a2
    VIEW SOLUTION
  • Question 49
    A man running around a race course notes that the sum of the distance of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path enclosed is
    Option A: 18π square metres
    Option B: 15π square metres
    Option C: 12π square metres
    Option D: 8π square metres
    VIEW SOLUTION
  • Question 50
    The distance of point (1,3) from the line 2x + 3y = 6, measured parallel to the line 4x + y = 4, is
    Option A: 513 units
    Option B: 317 units
    Option C: 17 units
    Option D: 172 units
    VIEW SOLUTION
  • Question 51
    If the vectors ai^+j^+k^, i^+bj^+k^ and i^+j^+ck^ a, b, c1 are coplanar, then the value of 11a+11b+11c is equal to
    Option B: 1
    Option C: a + b + c
    Option D: abc
    VIEW SOLUTION
  • Question 52
    The point of intersection of the line joining the points (–3, 4, –8) and (5, –6, 4) with the XY-plane is
    Option A: 73, 83, 0
    Option B: -73, 83, 0
    Option C: -73, 83, 0
    Option D: 73, 83, 0
    VIEW SOLUTION
  • Question 53
    If the angle between the lines whose direction ratios are (2, –1, 2) and (x, 3, 5) is π4, then the smaller value of x is
    Option A: 52
    Option B: 4
    Option C: 2
    Option D: 1
    VIEW SOLUTION
  • Question 54
    The position of the point (1, 2) relative to the ellipse 2x2+7y2=20 is
    Option A: outside the ellipse
    Option B: inside the ellipse but not at the focus
    Option C: on the ellipse
    Option D: at the focus
    VIEW SOLUTION
  • Question 55
    The equation of a straight line which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle 120° with positive direction of x-axis is
    Option A: y+3x+5=0
    Option B: y-3x+5=0
    Option C: y+3x-5=0
    Option D: y-3x-5=0
    VIEW SOLUTION
  • Question 56
    The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x – 3y + 7 = 0 and 7x + 4y + 2 = 0 is
    Option A: 21x + 46y – 180 = 0
    Option B: 21x – 46y + 96 = 0
    Option C: 46x + 21y – 155 = 0
    Option D: 46x – 21y – 29 = 0
    VIEW SOLUTION
  • Question 57
    The equation of the ellipse whose centre is at the origin, major axis is along x-axis with eccentricity 34 and latus rectum 4 units is
    Option A: x21024+7y264=1
    Option B: 49x21024+7y264=1
    Option C: 7x21024+49y264=1
    Option D: x21024+y264=1
    VIEW SOLUTION
  • Question 58
    The equation of the circle which passes through the points (1, 0), (0, –6) and (3, 4) is
    Option A: 4x2+4y2+142x+47y+140=0
    Option B: 24x2+4y2142x47y+138=0
    Option C: 4x2+4y2142x+47y+138=0
    Option D: 4x2+4y2+150x49y+138=0
    VIEW SOLUTION
  • Question 59
    A variable plane passes through a fixed point (a, b, c) and cuts the axes in A, B and C respectively. The locus of the centre of the sphere OABC, O being the origin, is
    Option A: xa+yb+zc=1
    Option B: ax+by+cz=1
    Option C: ax+by+cz=2
    Option D: xa+yb+zc=2
    VIEW SOLUTION
  • Question 60
    The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7, and perpendicular to the plane x – 5y + 3z = 5 is given by
    Option A: x + 2y + 3z – 6 = 0
    Option B: x + 2y + 3z + 6 = 0
    Option C: 3x + 4y + 5z – 8 = 0
    Option D: 3x + 4y + 5z + 8 = 0
    VIEW SOLUTION
  • Question 61
    The inverse of the function y = 5ln x is
    Option A: x=y1ln 5, y>0
    Option B: x=yln 5, y>0
    Option C: x=y1ln 5, y<0
    Option D: x=5 ln y, y>0
    VIEW SOLUTION
  • Question 62
    A function is defined as follows:
    fx=xx2,x00,x=0
    Which one of the following is correct in respect of the above function?
    Option A: f(x) is continuous at x = 0 but not differentiable at x = 0
    Option B: f(x) is continuous as well as differentiable at x = 0
    Option C: f(x) is discontinuous at x = 0
    Option D: None of the above
    VIEW SOLUTION
  • Question 63
    If y=(cos x)(cos x)(cos x)..., then dydx is equal to
    Option A: y2 tan x1y ln (cos x)
    Option B: y2 tan x1+y ln (cos x)
    Option C: y2 tan x1y ln (sin x)
    Option D: y2 sin x1+y ln (sin x)
    VIEW SOLUTION
  • Question 64
    Consider the following:
    1. x + x2 is continuous at x = 0
    2. x + cos 1x is discontinuous at x = 0
    3. x2 + cos 1x is continuous at x = 0
    Which of the above are correct?
    Option A: 1 and 2 only
    Option B: 2 and 3 only
    Option C: 1 and 3 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 65
    Consider the following statements:
    1. dy/dx at a point on the curve gives slope of the tangent at that point.
    2. If a(t) denotes acceleration of a particle, then a(t)dt+c gives velocity of the particle.
    3. If s(t) gives displacement of a particle at time t, then ds/dt gives its acceleration at that instant.
    Which of the above statements is/are correct?
    Option A: 1 and 2 only
    Option B: 2 only
    Option C: 1 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 66
    If y=sec1x+1x1+sin1x1x+1, then dydx is equal to
    Option B: 1
    Option C: x1x+1
    Option D: x+1x1
    VIEW SOLUTION
  • Question 67
    What istan1(secx+tanx)dx equal to?
    Option A: πx4+x24+c
    Option B: πx2+x24+c
    Option C: πx4+πx24+c
    Option D: πx4x24+c
    VIEW SOLUTION
  • Question 68
    A function is defined in (0, ∞) by

    f(x)=1x2 for 0<x1ln x for 1<x2ln 21+0.5x for 2<x<

    Which of the following is correct in respect of the derivation of the function, i.e., f’(x)?
    Option A: f’(x) = 2x for 0 < x ≤ 1
    Option B:  f’(x) = –2x for 0 < x ≤ 1
    Option C:  f’(x) = –2x for 0 < x < 1
    Option D: f’(x) = 0 for 0 < x < ∞
    VIEW SOLUTION
  • Question 69
    Which of the following is correct in respect of the function f(x) = x(x – 1)(x+1)?
    Option A: The local maximum value is larger than local minimum value
    Option B: The local maximum value is smaller than local minimum value
    Option C: The function has no local maximum
    Option D: The function has no local minimum
    VIEW SOLUTION
  • Question 70
    Consider the following statements:
    1. Derivative of f(x) may not exist at some point.
    2. Derivative of f(x) may exist finitely at some point.
    3. Derivative of f(x) may be infinite (geometrically) at some point.
    Which of the above statements are correct?
    Option A: 1 and 2 only
    Option B: 2 and 3 only
    Option C: 1 and 3 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 71
    The maximum value of ln xx is
    Option A: e
    Option B: 1e
    Option C: 2e
    Option D: 1
    VIEW SOLUTION
  • Question 72
    The function f(x)=|x|x3 is
    Option A: odd
    Option B: even
    Option C: both even and odd
    Option D: neither even nor odd
    VIEW SOLUTION
  • Question 73
    If
    l1=ddxesin xl2=limh0esin (x+h)esin xhl3=esin xcosx dx

    then which one of the following is correct?
    Option A: l1l2
    Option B: ddx(l3)=l2
    Option C: l3dx=l2
    Option D: l2=l3
    VIEW SOLUTION
  • Question 74
    The general solution of
    dydx=ax+hby+k
    represents a circle only when
    Option A: a = b = 0
    Option B: a = –b ≠ 0
    Option C: a = b ≠ 0, h = k
    Option D: a = b ≠ 0
    VIEW SOLUTION
  • Question 75
    If limxπ2sinxx=l and limxcos xx=m, then which of the following is correct?
    Option A: l = 1, m = 1
    Option B: l=2π, m=
    Option C: l=2π, m=0
    Option D: l = 1, m = ∞
    VIEW SOLUTION
  • Question 76
    What is 02π1+sinx2dx equal to?
    Option A: 8
    Option B: 4
    Option C: 2
    VIEW SOLUTION
  • Question 77
    The area bounded by the curve x+y=1 is
    Option A: 1 square unit
    Option B: 22 square units
    Option C: 2 square units
    Option D: 23 square units
    VIEW SOLUTION
  • Question 78
    If x is any real number, then x21+x4 belongs to which of the following intervals?
    Option A: (0,1)
    Option B: 0,12
    Option C: 0,12
    Option D: [0,1]
    VIEW SOLUTION
  • Question 79
    The left-hand derivative of

    f(x) = [x] sin (πx) at x = k

    where k is an integer and [x] is the greatest integer function, is
    Option A: (1)k(k1)π
    Option B: (1)k1(k1)π
    Option C: (1)kkπ
    Option D: (1)k1kπ
    VIEW SOLUTION
  • Question 80
    If f(x)=x2-1, then on the interval [0, π] which of the following is correct?
    Option A: tan [f(x)], where [·] is the greatest integer function, and 1fx are both continuous
    Option B: tan [f(x)], where [·] is the greatest integer function, and f–1(x) are both continuous
    Option C: tan [f(x)], where [·] is the greatest integer function, and 1fx are both discontinuous
    Option D: tan [f(x)], where [·] is the greatest integer function, is discontinuous but 1fx is continuous
    VIEW SOLUTION
  • Question 81
    The order and degree of the differential equation 1+dydx23=ρ2d2ydx22 are respectively
    Option A: 3 and 2
    Option B: 2 and 2
    Option C: 2 and 3
    Option D: 1 and 3
    VIEW SOLUTION
  • Question 82
    If y=cos12x1+x2, then dydx is equal to
    Option A: 21+x2for all |x|<1
    Option B: 21+x2 for all |x|>1
    Option C: 21+x2 for all |x|<1
    Option D: None of the above
    VIEW SOLUTION
  • Question 83
    The set of all points, where the function f(x)=1ex2 is differentiable, is
    Option A: (0, ∞)
    Option B: (–∞, ∞)
    Option C: (–∞, 0) ∪ (0, ∞)
    Option D: (–1, ∞)
    VIEW SOLUTION
  • Question 84
    Match List-I with List-II and select the correct answer using the code given below the lists:
     
    List–I
    (Function)
    List–II
    (Maximum value)
    A. sin x + cos x 1. 10
    B. 3 sin x + 4 cos x 2. 2
    C. 2 sin x + cos x 3. 5
    D. sin x + 3 cos x 4. 5

    Code:
    Option A: 
    A B C D
    2 3 1 4
    Option B: 
    A B C D
    2 3 4 1
    Option C: 
    A B C D
    3 2 1 4
    Option D: 
    A B C D
    3 2 4 1
    VIEW SOLUTION
  • Question 85
    If f(x)=x(xx+1), then f(x) is
    Option A: continuous but not differentiable at x = 0
    Option B: differentiable at x = 0
    Option C: not continuous at x = 0
    Option D: None of the above
    VIEW SOLUTION
  • Question 86
    Which of the following graphs represents the function f(x)=xx, x0?
    Option A: 
    Option B: 
    Option C: 
    Option D: None of the above
    VIEW SOLUTION
  • Question 87
    Let f(n)=14+n1000 , where [x] denotes the integral part of x. Then the value of n=11000f(n) is
    Option A: 251
    Option B: 250
    Option C: 1
    VIEW SOLUTION
  • Question 88
    (ln x)1dx(ln x)2dx is equal to
    Option A: x(ln x)–1 + c
    Option B: x(ln x)–2 + c
    Option C: x(ln x) + c
    Option D: x(ln x)2 + c
    VIEW SOLUTION
  • Question 89
    A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be k times the height of the jar. The value of k is
    Option A: 1
    Option B: 2
    Option C: 3
    Option D: 4
    VIEW SOLUTION
  • Question 90
    The value of 0π4tan xdx+0π4cot xdx is equal to
    Option A: π4
    Option B: π2
    Option C: π22
    Option D: π2
    VIEW SOLUTION
  • Question 91
    Let g be the greatest integer function. Then the function f(x) = (g(x))2g(x) is discontinuous at
    Option A: all integers
    Option B: all integers except 0 and 1
    Option C: all integers except 0
    Option D: all integers except 1
    VIEW SOLUTION
  • Question 92
    The differential equation of the minimum order by eliminating the arbitrary constants A and C in the equation y = A[sin(x + C) + cos(x + C)] is
    Option A: y'' + (sin x + cos x)y' = 1
    Option B: y'' = (sin x + cos x)y'
    Option C: y'' = (y')2 + sinxcosx
    Option D: y'' + y = 0
    VIEW SOLUTION
  • Question 93
    Consider the following statements:
    Statements I:
    x > sin x for all x > 0
    Statement II:
    f(x) = x – sin x is an increasing function for all x > 0
    Which one of the following is correct in respect of the above statements?
    Option A: Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I.
    Option B: Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I
    Option C: Statement I is true but Statement II is false
    Option D: Statement I is false but Statement II is true
    VIEW SOLUTION
  • Question 94
    The solution of the differential equation dydx=yϕ'(x)y2ϕ(x) is
    Option A: y=xϕ(x)+c
    Option B: y=ϕ(x)x+c
    Option C: y=ϕ(x)+cx
    Option D: y=ϕ(x)x+c
    VIEW SOLUTION
  • Question 95
    If f(x)=4x+x41+4x3 and gx=ln1+x1x, then what is the value of fge1e+1 equal to?
    Option A: 2
    Option B: 1
    Option D: 12
    VIEW SOLUTION
  • Question 96
    The value of the determinant 1ααα2α21βββ2β21γγγ2γ2 is equal to
    Option A: (αβ)(βγ)(αγ)
    Option B: (αβ)(βγ)(γα)
    Option C: (αβ)(βγ)(γα)(α+β+γ)
    VIEW SOLUTION
  • Question 97
    The adjoint of matrix A=102210031 is
    Option A: 162214631
    Option B: 162214631
    Option C: 612412631
    Option D: 621421316
    VIEW SOLUTION
  • Question 98
    If A=2222 , then which of following is correct?
    Option A: A2 = −2A
    Option B: A2 = −4A
    Option C: A2 = −3A
    Option D: A2 = 4A
    VIEW SOLUTION
  • Question 99
    Geometrically, Re (z2i) = 2, where i=1 and Re is the real part, represents
    Option A: circle
    Option B: ellipse
    Option C: rectangular hyperbola
    Option D: parabola
    VIEW SOLUTION
  • Question 100
    If p + q + r = a + b + c = 0, then the determinant paqbrcqcrapbrbpcqa equals
    Option B: 1
    Option C: pa + qb + rc
    Option D: pa + qb + rc + a + b + c
    VIEW SOLUTION
  • Question 101
    A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is
    Option A: 16
    Option B: 23
    Option C: 13
    Option D: 12
    VIEW SOLUTION
  • Question 102
    Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?
    Option A: 13
    Option B: 23
    Option C: 49
    Option D: 59
    VIEW SOLUTION
  • Question 103
    Let the sample space consist of non-negative integers up to 50. X denotes the numbers which are multiples of 3 and Y denotes the odd numbers. Which of the following is/are correct?
    1. P(X)=825

    2. P(Y)=12
    Select the correct answer using the code given below.
    Option A: 1 only
    Option B: 2 only
    Option C: Both 1 and 2
    Option D: Neither 1 nor 2
    VIEW SOLUTION
  • Question 104
    For two events A and B, let PA=12, P(AB)=23 and P(AB)=16.  What is PA¯B equal to?
    Option A: 16
    Option B: 14
    Option C: 13
    Option D: 12
    VIEW SOLUTION
  • Question 105
    Consider the following statements:
    1. Coefficient of variation depends on the unit of measurement of the variable.
    2. Range is a measure of dispersion.
    3. Mean deviation is the least when measured about median.
    Which of the above statements are correct?
    Option A: 1 and 2 only
    Option B: 2 and 3 only
    Option C: 1 and 3 only
    Option D: 1, 2 and 3
    VIEW SOLUTION
  • Question 106
    Given that the arithmetic mean and standard deviation of a sample of 15 observations are 24 and 0, respectively. Then which one of the following is the arithmetic mean of the smallest five observations in the data?
    Option B: 8
    Option C: 16
    Option D: 24
    VIEW SOLUTION
  • Question 107
    Which of the following can be considered as the appropriate pair of values of regression coefficient of y on x and regression coefficient of x on y?
    Option A: (1, 1)
    Option B: (–1, 1)
    Option C: 12, 2
    Option D: 13, 103
    VIEW SOLUTION
  • Question 108
    Let A and B be two events with P(A) = 13 , P(B) = 16 and P(AB)=112. What is PB|A¯ equal to?
    Option A: 15
    Option B: 17
    Option C: 18
    Option D: 110
    VIEW SOLUTION
  • Question 109
    In a binomial distribution, the mean is 23 and the variance is 59. What is the probability that X = 2?
    Option A: 536
    Option B: 2536
    Option C: 25216
    Option D: 2554
    VIEW SOLUTION
  • Question 110
    The probability that a ship safely reaches a port is 13. The probability that out of 5 ships, at least 4 ships would arrive safely is
    Option A: 1243
    Option B: 10243
    Option C: 11243
    Option D: 13243
    VIEW SOLUTION
  • Question 111
    What is the probability that at least two persons out of a group of three persons were born in the same month (disregard the year)?
    Option A: 33144
    Option B: 1772
    Option C: 1144
    Option D: 29
    VIEW SOLUTION
  • Question 112
    It is given that X¯ = 10, Y¯ = 90, σX = 3, σY = 12 and rXY = 0.8. The regression equation of X and Y is
    Option A: Y = 3.2X + 58
    Option B: X = 3.2Y + 58
    Option C: X = −8 + 0.2Y
    Option D: Y = –8 + 0.2X
    VIEW SOLUTION
  • Question 113
    If P(B) = 34, PABC¯=13 and PA¯BC¯=13, then what is P(B ∩ C) equal to?
    Option A: 112
    Option B: 34
    Option C: 115
    Option D: 19
    VIEW SOLUTION
  • Question 114
    The following table gives the monthly expenditure of two families:
     
      Expenditure (in Rs)
    Items Family A Family B
    Food 3,500 2,700
    Clothing 500 800
    Rent 1,500 1,000
    Education 2,000 1,800
    Miscellaneous 2,500 1,800

    In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which of the following ratios?
    Option A: 1 : 1
    Option B: 10 : 9
    Option C: 100 : 91
    Option D: 5 : 4
    VIEW SOLUTION
  • Question 115
    If a variable takes values 0, 1, 2, 3, ..… , n with frequencies 1, C(n, 1), C(n, 2), C(n, 3), ….. , C(n, n) respectively, then the arithmetic mean is
    Option A: 2n
    Option B: n + 1
    Option C: n
    Option D: n2
    VIEW SOLUTION
  • Question 116
    In a multiple choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 – p. The probability of answering a question correctly is 1m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is
    Option A: mp1+mp
    Option B: mp1+m-1p
    Option C: m-1p1+m-1p
    Option D: m-1p1+mp
    VIEW SOLUTION
  • Question 117
    If xand x2 are positive quantities, then the condition for the difference between arithmetic mean and the geometric mean to be greater than 1 is
    Option A: x1+x2>2x1x2
    Option B: x1+x2>2
    Option C: x1-x2>2
    Option D: x1+x2<2x1x2+1
    VIEW SOLUTION
  • Question 118
    Consider the following statements:
    1. Variance is unaffected by the change of origin and change of scale.
    2. Coefficient of variance is independent of the unit of observations.
    Which of the statements given above is/are correct?
    Option A: 1 only
    Option B: 2 only
    Option C: Both 1 and 2
    Option D: Neither 1 nor 2
    VIEW SOLUTION
  • Question 119
    Five sticks of lengths 1, 3, 5, 7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can form a triangle?
    Option A: 0.5
    Option B: 0.4
    Option C: 0.3
    VIEW SOLUTION
  • Question 120
    The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is
    Option A: 0.36
    Option B: 0.2
    Option C: 0.6
    Option D: 0.9
    VIEW SOLUTION
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