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NDA I 2015 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
    Let X be the set of all the persons living in a city.  Persons x, y in X are said to be related as x<y if y is at least 5 years older than x. Which of the following is correct?
    Option A: The relation is an an equivalence relation on X
    Option B: The relation is transitive but neither reflexive nor symmetric
    Option C: The relation is reflexive but neither transitive nor symmetric
    Option D: The relation is symmetric but neither transitive nor reflexive
    VIEW SOLUTION
  • Question 2
    Which one of the following matrices is an elementary matrix?
    Option A: 100100001
    Option B: 150010001
    Option C: 020100001
    Option D: 100010052
    VIEW SOLUTION
  • Question 3
    Consider the following statements in respect to the given equation :
    (x2+2)2+8x2=6x(x2+2)
    1. All the roots of the equation are complex.
    2. The sum of all the roots of the equation is 6.

    Which of the above statements 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 4
    In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains 8 and 2 for roots. Another student makes a mistake only in the coefficient of first-degree term and finds – 9 and –1 for roots. The correct equation is
    Option A: x210x+9=0
    Option B: x2+10x+9=0
    Option C: x210x+16=0
    Option D: x28x9=0
    VIEW SOLUTION
  • Question 5
    If A=2715 then what is A + 3A–1 equal to?
    Option A: 3I
    Option B: 5I
    Option C: 7I
    Option D: None of the above
    VIEW SOLUTION
  • Question 6
    In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is
    Option A: 35
    Option B: 40
    Option C: 50
    Option D: 55
    VIEW SOLUTION
  • Question 7
    If log10 2, log10 (2x – 1) and log10 (2x + 3) are three consecutive terms of an AP, then the value of x is
    Option A: 1
    Option B: Log5 2
    Option C: Log2 5
    Option D: Log10 5
    VIEW SOLUTION
  • Question 8
    The matrix 04+i4+i0  is
    Option A: Symmetric
    Option B: Skew-Symmetric
    Option C: Hermitian
    Option D: Skew-Hermitian
    VIEW SOLUTION
  • Question 9
    Let Z be the set of integers and aRb, where a, bZ if and only if (ab) is divisible by 5.
    Consider the following statements:
    1. The relation R partitions Z into five equivalent classes.
    2. Any two equivalent classes are either equal or disjoint.

     Which of the above statements 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 10
    If z=-21+2i3+i where i=1, then the argument θ (–π < θ ≤ π) of z is
    Option A: 3π4
    Option B: π4
    Option C: 5π6
    Option D: 3π4
    VIEW SOLUTION
  • Question 11
    If m and n are the roots of the equation (x + p) (x + q) – k = 0, then the roots of equation  (xm) (xn) + k = 0 are
    Option A: p and q
    Option B: 1p and 1q
    Option C: p and –q
    Option D: p + q and pq
    VIEW SOLUTION
  • Question 12
    What is the sum of the series 0.5 + 0.55 + 0.555 + ... to n terms?
    Option A: 59n291110n
    Option B: 195291110n
    Option C: 19n591110n
    Option D: 59n191110n
    VIEW SOLUTION
  • Question 13
    If 1, ω, ω2 are the cube roots of unity, then the value of  (1+ω)(1+ω2)(1+ω4)(1+ω8)
    Option A: –1
    Option C: 1
    Option D: 2
    VIEW SOLUTION
  • Question 14
    Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing exactly two elements is
    Option A: 20
    Option B: 40
    Option C: 45
    Option D: 90
    VIEW SOLUTION
  • Question 15
    What is the square root of i, where i=1?
    Option A: 1+i2
    Option B: 1i2
    Option C: 1+i2
    Option D: None of the above
    VIEW SOLUTION
  • Question 16
    The decimal number (127.25)10, when converted to binary number, takes the form
    Option A: (1111111.11)2
    Option B: (1111110.01)2
    Option C: (1110111.11)2
    Option D: (1111111.01)2
    VIEW SOLUTION
  • Question 17
    Consider the following in respect of two non-singular matrices A and B of same order:
    1. det (A + B) = det A + det B
    2. (A + B)–1 = A–1 + B–1
    Which of the above statements 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 18
    If X=3411, B=5221 and A=pqrs satisfies the equation AX = B, then the matrix A is equal to
    Option A: 72615
    Option B: 726623
    Option C: 742613
    Option D: 726623
    VIEW SOLUTION
  • Question 19
    What is r=01Cnn+r equal to?
    Option A: n+2C1
    Option B: n+2Cn
    Option C: n+3Cn
    Option D: n+2Cn+1
    VIEW SOLUTION
  • Question 20
    How many words can be formed using all the letters of the word ‘NATION’ so that all the three vowels should never come together?
    Option A: 354
    Option B: 348
    Option C: 288
    Option D: None of the above
    VIEW SOLUTION
  • Question 21
    (x3 – 1) can be factorised as
    where ω is one of the cube roots of unity.
    Option A: (x1)(xω)(x+ω2)
    Option B: (x1)(xω)(xω2)
    Option C: (x1)(x+ω)(x+ω2)
    Option D: (x1)(x+ω)(xω2)
    VIEW SOLUTION
  • Question 22
    What is sinπ6+i1cosπ6sinπ6i1cosπ63 where i=1, equal to?
    Option A: 1
    Option B: –1
    Option C: i
    Option D: i
    VIEW SOLUTION
  • Question 23
    Let A=x+yy2xxy, B=  21 and C=32
     If AB = C, then what is A2 equal to?
    Option A: 6104  26
    Option B: 105 424
    Option C: 56420
    Option D: 57520
    VIEW SOLUTION
  • Question 24
    The value of 1111 1+x1111+y  is
    Option A: x + y
    Option B: xy
    Option C: xy
    Option D: 1 + x + y
    VIEW SOLUTION
  • Question 25
    If A = {x  :x is a multiple of 3} and B = {x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set?
    Option A: (A \ B) ⋃ C
    Option B: (A \ B) \ C
    Option C: (A B) ⋂ C
    Option D: (A B) \ C
    VIEW SOLUTION
  • Question 26
    If (11101011)2 is converted to the decimal system, then the resulting number is
    Option A:  235
    Option B: 175
    Option C: 160
    Option D: 126
    VIEW SOLUTION
  • Question 27
    What is the real part of (sin x + i cos x)3 where i=1 ?
    Option A: – cos 3x
    Option B: – sin 3x
    Option C: sin 3x
    Option D: cos 3x
    VIEW SOLUTION
  • Question 28
    If  E(θ)=cos θsin θsin θcos θ then Eα Eβ is equal to
    Option A: E(αβ)
    Option B: E(α – β)
    Option C: E(α + β)
    Option D: –E(α + β)
    VIEW SOLUTION
  • Question 29
    If A = {x, y, z) and B = {p, q, r, s). What is the number of distinct relations from B to A?
    Option A: 4096
    Option B: 4094
    Option C: 128
    Option D: 126
    VIEW SOLUTION
  • Question 30
    If 2p + 3q = 18 and 4p2 + 4pq – 3q2 – 36 = 0, then what is (2p + q) equal to?
    Option A: 6
    Option B: 7
    Option C: 10
    Option D: 20
    VIEW SOLUTION
  • Question 31
    Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180/ π results. If the number of degrees in θ is multiplied by the number of radians in θ, then an irrational number 125π/9 results. The angle θ must be equal to
    Option A: 30º
    Option B: 45º
    Option C: 50º
    Option D: 60º
    VIEW SOLUTION
  • Question 32
    In a triangle ABC,  a=(1+3) cm, b = 2 cm and angle C = 60º. Then the other two angles are
    Option A: 45º and 75º
    Option B: 30º and 90º
    Option C: 105º and 15º
    Option D: 100º and 20º
    VIEW SOLUTION
  • Question 33
    Let α be the root of the equation 25cos2θ + 5cosθ – 12 = 0, where  π2<α<π.
    What is tanα equal to?
    Option A: 34
    Option B: 34
    Option C: 43
    Option D: 45
    VIEW SOLUTION
  • Question 34
    Let α be the root of the equation 25cos2θ + 5 cosθ – 12 = 0, where  π2<α<π.
    What is sin 2α equal to?
    Option A: 2425
    Option B: -2425
    Option C: -512
    Option D: -2125
    VIEW SOLUTION
  • Question 35
    The angle of elevation of the top of a tower from a point 20 m away from its base is 45º. What is the height of the tower?
    Option A: 10 m
    Option B: 20 m
    Option C: 30 m
    Option D: 40 m
    VIEW SOLUTION
  • Question 36
    The equation tan1(1+x)+tan1(1x)=π2 is satisfied by
    Option A: x = 1
    Option B: x = – 1
    Option C: x = 0
    Option D: x=12
    VIEW SOLUTION
  • Question 37
    The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43º and 47º, respectively. What is the height of the tower?
    Option A:  40 m
    Option B: 42 m
    Option C: 45 m
    Option D: 47 m
    VIEW SOLUTION
  • Question 38
    (1 – sin A + cos A)2 is equal to
    Option A: 2(1 – cos A) (1 + sin A)
    Option B: 2(1 – sin A) (1 + cos A)
    Option C: 2(1 – cos A) (1 – sin A)
    Option D: None of the above
    VIEW SOLUTION
  • Question 39
    What is cos θ1tan θ+sin θ1cot θ equal to?
    Option A: sin θ – cos θ
    Option B: sinθ + cosθ
    Option C: 2sin θ
    Option D: 2cos θ
    VIEW SOLUTION
  • Question 40
    Consider x=4 tan115, y=tan1170 and z=tan1199.
    What is x equal to?
    Option A: tan160119
    Option B: tan1120119
    Option C: tan190169
    Option D: tan1170169
    VIEW SOLUTION
  • Question 41
    Consider x=4 tan115, y=tan1170 and z=tan1199.
    What is xy equal to?
    Option A: tan1828845
    Option B: tan182878450
    Option C: tan182818450
    Option D: tan182878471
    VIEW SOLUTION
  • Question 42
    Consider x=4 tan115, y=tan1170 and z=tan1199.
    What is xy + z equal to?
    Option A: π2
    Option B: π3
    Option C: π6
    Option D: π4
    VIEW SOLUTION
  • Question 43
    Consider the triangle ABC with vertices A(–2, 3), B(2, 1) and C(1, 2).
    What is the circumcentre of triangle ABC?
    Option A: (–2, –2)
    Option B: (2, 2)
    Option C: (–2, 2)
    Option D: (2, –2)
    VIEW SOLUTION
  • Question 44
    Consider the triangle ABC with vertices A(–2, 3), B(2, 1) and C(1, 2).
    What is the centroid of triangle ABC?
    Option A: 13, 1
    Option B: 13, 2
    Option C: 1, 23
    Option D: 12, 3
    VIEW SOLUTION
  • Question 45
    Consider the triangle ABC with vertices A(–2, 3), B(2, 1) and C(1, 2).
    What is the foot of the altitude from the vertex A of triangle ABC?
    Option A: (1, 4)
    Option B: (–1, 3)
    Option C: (–2, 4)
    Option D: (–1, 4)
    VIEW SOLUTION
  • Question 46
    The point on the parabola y2 = 4ax nearest to the focus has its abscissa.
    Option A: x = 0
    Option B: x = a
    Option C: x=a2
    Option D: x = 2a
    VIEW SOLUTION
  • Question 47
    A line passes through (2, 2) and is perpendicular to line 3x + y = 3. Its y-intercept is
    Option A: 34
    Option B: 43
    Option C: 13
    Option D: 3
    VIEW SOLUTION
  • Question 48
    The hyperbola x2a2y2b2=1  passes through the point (35,1) and the length of its latus rectum is 43 units.
    The length of the conjugate axis is
    Option A: 2 units
    Option B: 3 units
    Option C: 4 units
    Option D: 5 units
    VIEW SOLUTION
  • Question 49
    The perpendicular distances between the straight lines 6x + 8y + 15 = 0 and 3x + 4y + 9 = 0 is
    Option A: 32 units
    Option B: 310 unit
    Option C: 34 unit
    Option D: 27 unit
    VIEW SOLUTION
  • Question 50
    The area of a triangle, whose vertices are (3, 4), (5, 2) and the point of intersection of the lines x = a and y = 5, is 3 square units. What is the value of a?
    Option A: 2
    Option B: 3
    Option C: 4
    Option D: 5
    VIEW SOLUTION
  • Question 51
    The length of perpendicular from the origin to a line is 5 units and the line makes an angle 120º with the positive direction of x-axis. The equation of the line is
    Option A: x+3y=5
    Option B: 3x+y=10
    Option C: 3xy=10
    Option D: None of the above
    VIEW SOLUTION
  • Question 52
    The equation of the line joining the origin to the point of intersection of the lines  xa+yb=1 and xb+ya=1 is
    Option A: xy = 0
    Option B: x + y = 0
    Option C: x = 0
    Option D: y = 0
    VIEW SOLUTION
  • Question 53
    The projections of a directed line segment on the coordinate axes are 12, 4, 3, respectively.
    What is the length of the line segment?
    Option A: 19 units
    Option B: 17 units
    Option C: 15 units
    Option D: 13 units
    VIEW SOLUTION
  • Question 54
    The projections of a directed line segment on the coordinate axes are 12, 4, 3, respectively.
    What are the direction cosines of the line segment?
    Option A: 1213, 413, 313
    Option B: 1213, 413, 313
    Option C: 1213, 413, -313
    Option D: -1213, 413, 313
    VIEW SOLUTION
  • Question 55
    From the point P(3, –1, 11), a perpendicular is drawn on the line L given by the equation x2=y23=z34.  Let Q be the foot of the perpendicular.
    What are the direction ratios of the line segment PQ?
    Option A: 1, 6, 4
    Option B: 1, 6,4
    Option C: 1,6, 4
    Option D: 2,6, 4
    VIEW SOLUTION
  • Question 56
    From the point P(3, –1, 11), a perpendicular is drawn on the line L given by the equation x2=y23=z34.  Let Q be the foot of the perpendicular.
    What is the length of the line segment PQ?
    Option A: 47 units
    Option B: 7 units
    Option C: 53 units
    Option D: 8 units
    VIEW SOLUTION
  • Question 57
    A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C, respectively.
    What are the intercepts made by plane ABC on the axes?
    Option A: 3, 6, 9
    Option B: 1, 2, 3
    Option C: 1, 4, 9
    Option D: 2, 4, 6
    VIEW SOLUTION
  • Question 58
    A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C, respectively.
    What is the equation of plane ABC?
    Option A: x + 2y + 3z = 1
    Option B: 3x + 2y + z = 3
    Option C: 2x + 3y + 6z = 18
    Option D: 6x + 3y + 2z = 8
    VIEW SOLUTION
  • Question 59
    A point P (1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.
    What is the length of one of the diagonals of the cuboid?
    Option A: 10 units
    Option B: 14 units
    Option C: 4 units
    Option D: 5 units
    VIEW SOLUTION
  • Question 60
    A point P (1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.
    What is the equation of the plane passing through P(1, 2, 3) and parallel to xy-plane?
    Option A: x + y = 3
    Option B: xy = –1
    Option C: z = 3
    Option D: x + 2y + 3z = 14
    VIEW SOLUTION
  • Question 61
    If G(x)=25x2, then what is limx1G(x)G(1)x1 equal to?
    Option A: 126
    Option B: 15
    Option C: 16
    Option D: 16
    VIEW SOLUTION
  • Question 62
    Consider the following statements:
     1. y=ex+ex2is an increasing function on [0, ∞).
     2. y=exex2is an increasing function on (–∞, ∞).
     Which of the above statements 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 63
    For each non-zero real number x, let f(x) = x|x|. The range of f is
    Option A: a null set
    Option B: a set consisting of only one element
    Option C: a set consisting of two elements
    Option D: a set consisting of infinitely many elements
    VIEW SOLUTION
  • Question 64
    Consider the following statements:
    1. f(x) = [x], where [.] is the greatest integer function, is discontinuous at x = n, where n Z
    2. f(x) = cot x is discontinuous at x = , where n Z.
     Which of the above statements 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 65
    What is the derivative of  tan11+x21x with respect to tan–1 x?
    Option B: 12
    Option C: 1
    Option D: x
    VIEW SOLUTION
  • Question 66
    If f(x)=loge1+x1x, g(x)=3x+x31+3x2  and gf(t) = g(f(t)), then what is gfe1e+1 equal to?
    Option A: 2
    Option B: 1
    Option D: 12
    VIEW SOLUTION
  • Question 67
    Given a function f(x)=-1ifx0ax+bif0<x<11ifx1where a, b are constants, the function is continuous everywhere.

    What is the value of a?
    Option A: –1
    Option C: 1
    Option D: 2
    VIEW SOLUTION
  • Question 68
    Given a function f(x)=-1ifx0ax+bif0<x<11ifx1where a, b are constants, the function is continuous everywhere.

    What is the value of b?
    Option A: –1
    Option B: 1
    Option D: 2
    VIEW SOLUTION
  • Question 69
    Consider the following functions:
    1. fx=x3, x
    2. fx=sinx, 0<x<2π
    3. fx=ex, x

    Which of the above functions have inverse defined on their ranges?
    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 70
    The integral dxa cos x+b sin x is of the form 1r lntan x+α2.

    What is r equal to?
    Option A: a2 + b2
    Option B: a2+b2
    Option C: a + b
    Option D: a2-b2
    VIEW SOLUTION
  • Question 71
    The integral dxa cos x+b sin x is of the form 1r lntan x+α2.

    What is α equal to?
    Option A: tan-1ab
    Option B: tan1ba
    Option C: tan1a+ba-b
    Option D: tan1a-ba+b
    VIEW SOLUTION
  • Question 72
    Consider the function fx=x21x2+1, where x.

    At what value of x does f(x) attain minimum value?
    Option A: –1
    Option C: 1
    Option D: 2
    VIEW SOLUTION
  • Question 73
    Consider the function fx=x21x2+1, where x.

    What is the minimum value of f(x)?
    Option B: 1/2
    Option C: –1
    Option D: 2
    VIEW SOLUTION
  • Question 74
    Consider the function fx=α cos xπ-2xifxπ23ifx=π2which is continuous at x=π2, where α is a constant.

    What is the value of α?
    Option A: 6
    Option B: 3
    Option C: 2
    Option D: 1
    VIEW SOLUTION
  • Question 75
    Consider the function fx=α cos xπ-2xifxπ23ifx=π2which is continuous at x=π2, where α is a constant.

    What is limx0 fx equal to?
    Option B: 3
    Option C: 3π
    Option D: 6π
    VIEW SOLUTION
  • Question 76
    Consider the line x=3y and the circle x2 + y2 = 4.

    What is the area of the region in the first quadrant enclosed by the x-axis, the line x=3 and the circle?
    Option A: π332
    Option B: π232
    Option C: π312
    Option D: None of the above
    VIEW SOLUTION
  • Question 77
    Consider the line x=3y and the circle x2 + y2 = 4.

    What is the area of the region in the first quadrant enclosed by the x-axis, the line x=3y and the circle?
    Option A: π3
    Option B: π6
    Option C: π332
    Option D: None of the above
    VIEW SOLUTION
  • Question 78
    Consider the curves y = sin x and y = cos x.

    What is the area of the region bounded by the above two curves and the lines x = 0 and x=π4?
    Option A: 2-1
    Option B: 2+1
    Option C: 2
    Option D: 2
    VIEW SOLUTION
  • Question 79
    Consider the curves y = sin x and y = cos x.

    What is the area of the region bounded by the above two curves and the lines x=π4 and x=π2?
    Option A: 21
    Option B: 2+1
    Option C: 22
    Option D: 2
    VIEW SOLUTION
  • Question 80
    Consider the function f(x) = 0·75x4x3 – 9x2 + 7

    What is the maximum value of the function?
    Option A: 1
    Option B: 3
    Option C: 7
    Option D: 9
    VIEW SOLUTION
  • Question 81
    Consider the function f(x) = 0·75x4x3 – 9x2 + 7

    Consider the following statements :

    1. The function attains local minima at x = – 2 and x = 3.

    2. The function increases in the interval (–2, 0).

    Which of the above statements 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 82
    Consider the parametric equation

    x=a(1t2)1+t2, y=2at1+t2

    What does the equation represent?
    Option A: It represents a circle of diameter a
    Option B: It represents a circle of radius a
    Option C: It represents a parabola
    Option D: None of the above
    VIEW SOLUTION
  • Question 83
    Consider the parametric equation

    x=a(1t2)1+t2, y=2at1+t2

    What is dydx equal to?
    Option A: yx
    Option B: -yx
    Option C: xy
    Option D: -xy
    VIEW SOLUTION
  • Question 84
    Consider the parametric equation

    x=a(1t2)1+t2, y=2at1+t2

    What is d2ydx2 equal to?
    Option A: a2y2
    Option B: a2x2
    Option C: a2x2
    Option D: -a2y3
    VIEW SOLUTION
  • Question 85
    Consider the following statements:
    1. The general solution of dydx=fx+x is of the form y = g(x) + c, where c is an arbitrary constant.
    2. The degree of dydx2=fx is 2.
    Which of the above statements 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 86
    What isdxx2+a2 equal to?

    where c is the constant of integration.
    Option A: ln x+x2+a2a+c
    Option B: ln xx2+a2a+c
    Option C: ln x2+x2+a2a+c
    Option D: None of the above
    VIEW SOLUTION
  • Question 87
    Consider the integral Im=0πsin2mxsinxdx, where m is a positive integer.
    What is I1 equal to?
    Option B: 1/2
    Option C: 1
    Option D: 2
    VIEW SOLUTION
  • Question 88
    Consider the integral Im=0πsin2mxsinxdx, where m is a positive integer.

    What is I2 + I3 equal to?
    Option A: 4
    Option B: 2
    Option C: 1
    VIEW SOLUTION
  • Question 89
    Consider the integral Im=0πsin2mxsinxdx, where m is a positive integer.

    What is Im equal to?
    Option B: 1
    Option C: m
    Option D: 2m
    VIEW SOLUTION
  • Question 90
    Consider the integral Im=0πsin2mxsinxdx, where m is a positive integer.

    Consider the following:

    1. ImIm – 1 is equal to 0.

    2. I2m > Im

    Which of the 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 91
    Given that ddx1+x2+x41+x+x2=Ax+B.

    What is the value of A?
    Option A: –1
    Option B: 1
    Option C: 2
    Option D: 4
    VIEW SOLUTION
  • Question 92
    Given that ddx1+x2+x41+x+x2=Ax+B.

    What is the value of B?
    Option A: –1
    Option B: 1
    Option C: 2
    Option D: 4
    VIEW SOLUTION
  • Question 93
    Given thatlimx 2+x21+x-Ax-B=3.

    What is the value of A?
    Option A: –1
    Option B: 1
    Option C: 2
    Option D: 3
    VIEW SOLUTION
  • Question 94
    Given thatlimx 2+x21+x-Ax-B=3.

    What is the value of B?
    Option A: –1
    Option B: 3
    Option C: –4
    Option D: –3
    VIEW SOLUTION
  • Question 95
    What is the solution of the differential equation

    ydx-xdyy2=0?

    Where c is an arbitrary constant.
    Option A: xy = c
    Option B: y = cx
    Option C: x + y = c
    Option D: xy = c
    VIEW SOLUTION
  • Question 96
    What is the solution of the differential equation

    sin dydxa=0

    Where c is an arbitrary constant.
    Option A: y=xsin1a+c
    Option B: x=ysin1a+c
    Option C: y=x+xsin1a+c
    Option D: y=sin1a+c
    VIEW SOLUTION
  • Question 97
    What is the solution of the differential equation

    dxdy+xy-y2=0?

    Where c is the arbitrary constant.
    Option A: xy = x4 + c
    Option B: xy = y4 + c
    Option C: 4xy = y4 + c
    Option D: 3xy = y3 + c
    VIEW SOLUTION
  • Question 98
    What is xexdxx+12 equal to?

    Where c is the constant of integration.
    Option A: (x + 1)2ex + c
    Option B: (x + 1) ex + c
    Option C: exx+1+c
    Option D: ex(x+1)2+c
    VIEW SOLUTION
  • Question 99
    The adjacent sides AB and AC of a triangle ABC are represented by the vectors 2i^+3j^+2k^ and 4i^+5j^+2k^ respectively. The area of triangle ABC is
    Option A: 6 square units
    Option B: 5 square units
    Option C: 4 square units
    Option D: 3 square units
    VIEW SOLUTION
  • Question 100
    A force F=3i^+4j^3k^ is applied at the point P, whose position vector is r=2i^2j^3k^. What is the magnitude of the moment of the force about the origin?
    Option A: 23 units
    Option B: 19 units
    Option C: 18 units
    Option D: 21 units
    VIEW SOLUTION
  • Question 101
    Given that the vectors α and β are non-collinear. The values of x and y for which uv=w holds true if u=2xα+yβ, v=2yα+3xβ and w=2α5β, are
    Option A: x = 2, y = 1
    Option B: x = 1, y = 2
    Option C: x = –2, y = 1
    Option D: x = –2, y = –1
    VIEW SOLUTION
  • Question 102
    If a=7,b=11anda+b=103, then ab is equal to
    Option A: 40
    Option B: 10
    Option C: 410
    Option D: 210
    VIEW SOLUTION
  • Question 103
    Let α, β, γ be distinct real numbers. The points with position vectors αi^+βj^+γk^,βi^+γj^+αk^    and   γi^+αj^+βk^
    Option A: are collinear
    Option B: form an equilateral triangle
    Option C: form a scalene triangle
    Option D: form a right-angled triangle
    VIEW SOLUTION
  • Question 104
    If a+b+c=0, then which of the following is/are correct?

    1. a, b, c are coplanar.

    2. a×b=b×c=c×a

    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 105
    If a+b=ab, then which one of the following is correct?
    Option A: a=λb for some scalar λ
    Option B: a is parallel to b
    Option C: a is perpendicular to b
    Option D: a=b=0
    VIEW SOLUTION
  • Question 106
    The mean and variance of 10 observations are given to be 4 and 2, respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be, respectively
    Option A: 8 and 20
    Option B: 8 and 4
    Option C: 8 and 8
    Option D: 80 and 40
    VIEW SOLUTION
  • Question 107
    Which one of the following measures of central tendency is used in construction of index numbers?
    Option A: Harmonic mean
    Option B: Geometric mean
    Option C: Median
    Option D: Mode
    VIEW SOLUTION
  • Question 108
    The correlation coefficient between two variable X and Y is found to be 0·6. All the observations on X and Y are transformed using the transformation U = 2 – 3X and V = 4Y + 1. The correlation coefficient between the transformed variables U and V will be
    Option A: –0.5
    Option B: +0.5
    Option C: –0.6
    Option D: +0.6
    VIEW SOLUTION
  • Question 109
    Which of the following statements is/are correct in respect of regression coefficients?
    1. It measures the degree of linear relationship between two variables.
    2. It gives the value by which one variable changes for a unit change in the other variable.
    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 110
    A set of annual numerical data, comparable over the years, is given for the last 12 years.
    Consider the following statements:
    1. The data is best represented by a broken line graph, each corner (turning point) representing the data of one year.
    2. Such a graph depicts the chronological change and also enables one to make a short-term forecast.
    Which of the above statements 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 111
    Two men hit at a target with probabilities 1/2 and 1/3, respectively. What is the probability that exactly one of them hits the target?
    Option A: 1/2
    Option B: 1/3
    Option C: 1/6
    Option D: 2/3
    VIEW SOLUTION
  • Question 112
    Two similar boxes Bi (i = 1, 2) contain (i + 1) red and (5 – i – 1) black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours?
    Option A: 1/2
    Option B: 3/10
    Option C: 2/5
    Option D: 3/5
    VIEW SOLUTION
  • Question 113
    In an examination, the probability of a candidate solving a question is 1/2. Out of the given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?
    Option A: 1/64
    Option B: 3/16
    Option C: 1/2
    Option D: 13/16
    VIEW SOLUTION
  • Question 114
    If AB, then which one of the following is not correct?
    Option A: PAB=0
    Option B: PA|B=PAPB
    Option C: PB|A=PBPA
    Option D: PA|AB=PAPB
    VIEW SOLUTION
  • Question 115
    The mean and the variance in a binomial distribution are found to be 2 and 1, respectively. The probability P(X = 0) is
    Option A: 1/2
    Option B: 1/4
    Option C: 1/8
    Option D: 1/16
    VIEW SOLUTION
  • Question 116
    The mean of five numbers is 30. If one number is excluded, the mean becomes 28. The excluded number is
    Option A: 28
    Option B: 30
    Option C: 35
    Option D: 38
    VIEW SOLUTION
  • Question 117
    If A and B are two events such that P(AB)=34,  P(AB)=14andP(A)=23, then what is P(B) equal to?
    Option A: 1/3
    Option B: 2/3
    Option C: 1/8
    Option D: 2/9
    VIEW SOLUTION
  • Question 118
    The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at
    Option A: median
    Option B: mode
    Option C: arithmetic mean
    Option D: None of the above
    VIEW SOLUTION
  • Question 119
    In throwing of two dice, the number of exhaustive events that ‘5’ will never appear on any one of the dice is
    Option A: 5
    Option B: 18
    Option C: 25
    Option D: 36
    VIEW SOLUTION
  • Question 120
    Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is
    Option A: 1/26
    Option B: 1/221
    Option C: 4/223
    Option D: 1/13
    VIEW SOLUTION
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