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NDA I 2017 Mathematic

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 S be the set of all persons living in Delhi. We say that x, y in S are related if the y were born in Delhi on the same day. Which one of the following is correct?
    Option A: The relation is an equivalent relation
    Option B: The relation is not reflective but it is symmetric and transitive
    Option C: The relation is not symmetric bout it is reflexive and transitive
    Option D: The relation is not transitive but it is reflexive ands ymmetric
    VIEW SOLUTION
  • Question 2
    Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing two or three elements is
    Option A: 45
    Option B: 120
    Option C: 165
    Option D: 330
    VIEW SOLUTION
  • Question 3
    3. The value of  i2n+i2n+1+i2n+2+i2n+3, where ,is i=1
    Option A: 0
    Option B: 1
    Option C: i
    Option D: i
    VIEW SOLUTION
  • Question 4
    If the difference between the roots of the equation x2+kx+1=0 is strictly less than 5, where |k| ≥ 2, then k can be any element of the interval
    Option A: (3,2][2,3)
    Option B: (–3, 3)
    Option C: [3,2][2,3]
    Option D: None of these
    VIEW SOLUTION
  • Question 5
    If the roots of the equation x2+px+q=0 are in the same ratio as those of the equation x2+lx+m=0, then which one of the following is correct?
    Option A: p2m=l2q
    Option B: m2p=l2q
    Option C: m2p=q2l
    Option D: m2p2=l2q
    VIEW SOLUTION
  • Question 6
    The value of (1+i32)n+(1i32)nwhere n is not a multiple of 3 and i=1 is
    Option A: 1
    Option B: –1
    Option C: i
    Option D: i
    VIEW SOLUTION
  • Question 7
    Three-digit numbers are formed from the digits 1, 2 and 3 in such a way that the digits are not repeated. What is the sum of such 3 digit numbers?
    Option A: 1233
    Option B: 1322
    Option C: 1323
    Option D: 1332
    VIEW SOLUTION
  • Question 8
    What is the sum of the series 0.3 + 0.33 + 0.333 +….n terms?
    Option A: 13n191110n
    Option B: 13n291110n
    Option C: 13n131110n
    Option D: 13n191+110n
    VIEW SOLUTION
  • Question 9
    If 1, ω, ω2 are the cube roots of unity, then (1+ω)(1+ω2)1+ω3(1+ω+ω2) is equal to
    Option A: –2
    Option B: –1
    Option D: 2
    VIEW SOLUTION
  • Question 10
    If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) term is
    Option A: mn
    Option B: m + n
    Option C: 2(m + n)
    Option D: – (m + n)
    VIEW SOLUTION
  • Question 11
    The modulus and the principal argument of the complex numbers 1+2i1-(1i)2 are respectively
    Option A: 1, 0
    Option B: 1, 1
    Option C: 2, 0
    Option D: 2, 1
    VIEW SOLUTION
  • Question 12
    If the graph of a quadratic polynomial lies entirely above the x-axis, then which one of the following is correct?
    Option A: Both the roots are real
    Option B: One root is real and the other is complex
    Option C: Both the roots are complex
    Option D: Cannot say
    VIEW SOLUTION
  • Question 13
    If |z+4|3, then the maximum value of |z + 1| is
    Option B: 4
    Option C: 6
    Option D: 10
    VIEW SOLUTION
  • Question 14
    The number of roots of the equation z2=2z¯ is
    Option A: 2
    Option B: 3
    Option C: 4
    VIEW SOLUTION
  • Question 15
    If cot α and cot β are the roots of the equation x2+bx+c=0 with b ≠ 0 then the value of cot (α + β) is
    Option A: c1b
    Option B: 1cb
    Option C: bc1
    Option D: b1c
    VIEW SOLUTION
  • Question 16
    The sum of the roots of the equation x2+bx+c=0 (where b and c are non-zero) is equal to the sum of the reciprocals of their square. Then 1c, b,cb are in
    Option A: AP
    Option B: GP
    Option C: HP
    Option D: None of the above
    VIEW SOLUTION
  • Question 17
    The sum of the roots of the equation ax2+x+c=0 (where a and c are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca2, c2 are in
    Option A: AP
    Option B: GP
    Option C: HP
    Option D: None of the above
    VIEW SOLUTION
  • Question 18
    The value of  [C(7, 0) + C(7, 1)] + [C(7, 1) + C(7, 2) ] + ……+ [C(7, 6) + C(7, 7)] is
    Option A: 254
    Option B: 255
    Option C: 256
    Option D: 257
    VIEW SOLUTION
  • Question 19
    The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word ‘EQUATION’ is
    Option A: 5200
    Option B: 4320
    Option C: 3000
    Option D: 2160
    VIEW SOLUTION
  • Question 20
    The fifth term of an AP of n terms, whose sum is n2 – 2n, is
    Option A: 5
    Option B: 7
    Option C: 8
    Option D: 15
    VIEW SOLUTION
  • Question 21
    The sum of all the two-digit odd numbers is
    Option A: 2475
    Option B: 2530
    Option C: 4905
    Option D: 5049
    VIEW SOLUTION
  • Question 22
    The sum of the first n terms of the series  12+34+78+1516+.... is equal to
    Option A: 2nn1
    Option B: 1 – 2–n
    Option C: 2-n+n1
    Option D: 2n1
    VIEW SOLUTION
  • Question 23
    Consider the following in respect of sets A and B:
    1. (AB)B=A
    2. (AB)A=A
    3. (AB)B=ϕ
    4. ABAB=B
    Which of the above are correct?
    Option A: 1, 2 and 3
    Option B: 2, 3 and 4
    Option C: 1, 3 and 4
    Option D: 1, 2 and 4
    VIEW SOLUTION
  • Question 24
    In the binary equation (1p101)2+(10q1)2=(100r00)2 where p, q and r are binary digits, what are the possible value of p, q and r, respectively?
    Option A: 0, 1, 0
    Option B: 1, 1, 0
    Option C: 0, 0, 1
    Option D: 1, 0, 1
    VIEW SOLUTION
  • Question 25
    If S={x :x2+1=0, x is real}, then S is
    Option A: {– 1}
    Option B: {0}
    Option C: {1}
    Option D: An empty set
    VIEW SOLUTION
  • Question 26
    The expansion of x-yn, n5 is done in the descending powers of x. If the sum of the fifth and sixth terms is zero, then xy is equal to
    Option A: n56
    Option B: n45
    Option C: 5n4
    Option D: 6n5
    VIEW SOLUTION
  • Question 27
    If  A=α22α and det(A3)=125 then α is equal to
    Option A: ± 1
    Option B: ± 2
    Option C: ± 3
    Option D: ± 5
    VIEW SOLUTION
  • Question 28
    If B is a non-singular matrix and A is a square matrix, then the value of det(B1AB) is equal to
    Option A: det(B)
    Option B: det(A)
    Option C: det(B–1)
    Option D: det(A–1)
    VIEW SOLUTION
  • Question 29
    If a ≠ b ≠ c, then one value of x which satisfies the equation 0xaxbx+a0xcx+bx+c0=0 is given by  ;
    Option A: a
    Option B: b
    Option C: c
    VIEW SOLUTION
  • Question 30
    A=cosαsinαsinαcosα then what is AAT equal to (where AT is the transpose of A)?
    Option A: Null matrix
    Option B: Identity matrix
    Option C: A
    Option D: –A
    VIEW SOLUTION
  • Question 31
    The equations
    x + 2y + 3z = 1
    2x + y + 3z = 2
    5x + 5y + 9z = 4
    Option A: have the unique solution
    Option B: have Infinitely many solutions
    Option C: are in inconsistent
    Option D: None of these
    VIEW SOLUTION
  • Question 32
    A=x+yyxx-y, B=3-2 and C=4-2.
    If AB = C, then what is A2 equal to?
    Option A:    4   8416
    Option B: 44816
    Option C: 48   412
    Option D: 48   8 12
    VIEW SOLUTION
  • Question 33
    What is the value of the determinant 11111+xyz1111+xyz?
    Option A: 1 + x + y + z
    Option B: 2xyz
    Option C: x2 y2 z2
    Option D: 2x2 y2 z2
    VIEW SOLUTION
  • Question 34
    If then xy00xyy0x = 0, then which one of the following is correct?
    Option A: xy is one of the cube root of unity
    Option B: x is one of the cube roots of Unity
    Option C: y is one of the cube roots of unity
    Option D: xy is one of the cube root of –1
    VIEW SOLUTION
  • Question 35
    Consider the set A of all matrices of order 3 × 3 with entire 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is –1. Then which one of the following is correct?
    Option A: C is empty
    Option B: B has as many elements as C
    Option C: A = BC
    Option D: B has thrice as many elements as C
    VIEW SOLUTION
  • Question 36
    If A=cos θsin θsin θcos θ ; then what is A3 equal to?
    Option A: cos 3θsin 3θsin 3θcos 3θ
    Option B: cos3 θsin3 θsin3 θcos3 θ
    Option C: cos 3θsin 3θsin 3θcos 3θ
    Option D: cos3 θsin3 θsin3 θcos3 θ
    VIEW SOLUTION
  • Question 37
    What is the order of xyzahghbfgfcxyz?
    Option A: 3 × 1
    Option B: 1 × 1
    Option C: 1 × 3
    Option D: 3 × 3
    VIEW SOLUTION
  • Question 38
    If A=0110, then the value of A4 is
    Option A: 1001
    Option B: 1100
    Option C: 0011
    Option D: 0110
    VIEW SOLUTION
  • Question 39
    If sin A=35, where 450°<A<540°, then cos A2 is equal to
    Option A: 110
    Option B: -310
    Option C: 310
    Option D: None of these
    VIEW SOLUTION
  • Question 40
    What is 1sin 10°3cos 10° equal to?
    Option B: 1
    Option C: 2
    Option D: 4
    VIEW SOLUTION
  • Question 41
    From the top of a lighthouse, 100 m high, the angle of depression of a boat is tan1512. What is the distance between the boat and the lighthouse?
    Option A: 120 m
    Option B: 180 m
    Option C: 240 m
    Option D: 360 m
    VIEW SOLUTION
  • Question 42
    The maximum value of sin x+π6+cos x+π6 in the interval 0, π2 is attained at
    Option A: π12
    Option B: π6
    Option C: π3
    Option D: π2
    VIEW SOLUTION
  • Question 43
    If K=sinπ18sin5π18sin7π18, then what is the value of K?
    Option A: 12
    Option B: 14
    Option C: 18
    Option D: 116
    VIEW SOLUTION
  • Question 44
    The expression sin α+sin βcos α+cos β  is equal to
    Option A: tanα+β2
    Option B: cotα+β2
    Option C: sinα+β2
    Option D: cosα+β2cosα+β2
    VIEW SOLUTION
  • Question 45
    If sin θ = 3sin (θ + 2α), then the value of tan(θ + α) + 2 tanα is equal to
    Option A: –1
    Option C: 1
    Option D: 2
    VIEW SOLUTION
  • Question 46
    What is the value of tan18°?
    Option A: 5110+25
    Option B: 5110+5
    Option C: 10+2551
    Option D: 10+551
    VIEW SOLUTION
  • Question 47
    Let x, y, z be positive real numbers such that x, y, z are in GP and tan-1 x, tan-1y and tan-1 z are in AP. Then which one of the following is correct?
    Option A: x = y = z
    Option B: xz = 1
    Option C: x ≠ y and y = z
    Option D: x = y and y ≠ z
    VIEW SOLUTION
  • Question 48
    If tan(α + β) = 2 and tan (α – β) = 1, then tan (2α) is equal to
    Option A: –3
    Option B: –2
    Option C: -13
    Option D: 1
    VIEW SOLUTION
  • Question 49
    Consider the following of triangle ABC:
    (a) sinB+C2=cosA2
    (b) tanB+C2=cotA2
    (c) sin (B + C) = cos A
    (d) tan (B + C) = –cot A

    Which of the above are correct?
    Option A: a and c
    Option B: a and b
    Option C: a and d
    Option D: b and c
    VIEW SOLUTION
  • Question 50
    If sec θ – cosec θ = 43, then what is (sin θ – cos θ) equal to?
    Option A: –2 only
    Option B: 12 only
    Option C: Both –2 and 12
    Option D: Neither 12 nor – 2
    VIEW SOLUTION
  • Question 51
    If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (–1, 2) and (–3, 2), then the centroid of the triangle is
    Option A: 13,73
    Option B: 1,73
    Option C: 13,73
    Option D: 1,73
    VIEW SOLUTION
  • Question 52
    The incentre of a triangle with vertices A(1, 3), B(0, 0), and C(2, 0) is
    Option A: 1,32
    Option B: 23, 13
    Option C: 23, 32
    Option D: 1,13
    VIEW SOLUTION
  • Question 53
    If the three consecutive vertices of a parallelogram are (–2,  –1), (1, 0) and (4, 3), then what are the coordinates of the fourth vertex?
    Option A: (1, 2)
    Option B: (1, 0)
    Option C: (0, 0)
    Option D: (1, –1)
    VIEW SOLUTION
  • Question 54
    The two circles x2+y2=r2 and x2+y2-10x+16=0 intersect at two distinct points. Then which one of the following is correct?
    Option A: 2 < r < 8
    Option B: r = 2 or r = 8
    Option C: r < 2
    Option D: r > 2
    VIEW SOLUTION
  • Question 55
    What is the equation of the circle which passes through the points (3, –2) and (–2, 0) and having its centre on the line 2xy – 3 = 0?
    Option A: x2+y2+3x+2=0
    Option B: x2+y2+3x+12y+2=0
    Option C: x2+y2+2x=0
    Option D: x2+y2=5
    VIEW SOLUTION
  • Question 56
    What is the ratio in which the point C-27, -207 divides the line joining the points A(–2, –2) and B(2, –4)?
    Option A: 1 : 3
    Option B: 3 : 4
    Option C: 1 : 2
    Option D: 2 : 3
    VIEW SOLUTION
  • Question 57
    What is the equation of the ellipse having foci (±2, 0) and the eccentricity 14?
    Option A: x264+y260=1
    Option B: x260+y264=1
    Option C: x220+y224=1
    Option D: x224+y220=1
    VIEW SOLUTION
  • Question 58
    What is the equation of the straight line parallel to 2x + 3y + 1 = 0 and passes through the point (–1, 2)?
    Option A: 2x + 3y – 4 = 0
    Option B: 2x + 3y – 5 = 0
    Option C: x + y – 1 = 0
    Option D: 3x – 2y + 7 = 0
    VIEW SOLUTION
  • Question 59
    What is the acute angle between the pair of straight lines 2x+3y=1 and 3x+2y=2?
    Option A: tan1126
    Option B: tan112
    Option C: tan1(3)
    Option D: 4tan113
    VIEW SOLUTION
  • Question 60
    If the centroid of a triangle formed by (7, x), (y, –6) and (9, 10) is (6, 3), then the values of x and y are respectively
    Option A: 5, 2
    Option B: 2, 5
    Option C: 1, 0
    Option D: 0, 0
    VIEW SOLUTION
  • Question 61
    A straight line with direction cosines  0, 1, 0 is
    Option A: parallel to x-axis
    Option B: parallel to y-axis
    Option C: parallel to z-axis
    Option D: equally inclined to all the axes
    VIEW SOLUTION
  • Question 62
    (0, 0 , 0), (a, 0, 0), (0, b, 0) and (0, 0, c) are four distinct points. What are the coordinates of the point, which is equidistant from the four points?
    Option A: a+b+c3, a+b+c3, a+b+c3
    Option B: (a, b, c )
    Option C: a2, b2, c2
    Option D: a3, b3, c3
    VIEW SOLUTION
  • Question 63
    The point P(3, 2, 4), Q(4, 5, 2), R(5, 8, 0) and S(2, –1, 6) are
    Option A: vertices of a rhombus which is not a square
    Option B: non-coplanar
    Option C: collinear
    Option D: coplanar but not collinear
    VIEW SOLUTION
  • Question 64
    The line passing through the points (1, 2, –1) and (3, –1, 2) meets the yz-plane at which one of the following points?
    Option A: 0,72,52
    Option B: 0,72,12
    Option C: 0,72,52
    Option D: 0,72,52
    VIEW SOLUTION
  • Question 65
    Under which one of the following conditions, are the lines x = ay + b; z = cy + d and x = ey + f; z = gy + h perpendicular?
    Option A: ae + cg – 1 = 0
    Option B: ae + bf – 1 = 0
    Option C: ae + cg + 1 = 0
    Option D: ag + ce – 1 = 0
    VIEW SOLUTION
  • Question 66
    If a=i^j^+k^,   b=2i^+3j^+2k^   and   c=i^+mj^+nk^, are three coplanar vectors and |c|=6, then which one of the following is correct?
    Option A: m = 2 and n = ±1
    Option B: m = ±2 and n = –1
    Option C: m = 2 and n = –1
    Option D: m = ±2 and n = 1
    VIEW SOLUTION
  • Question 67

    Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin. What is OA+OB+OC+OD equal to?

    Option A: 2OP
    Option B: 4OP
    Option C: 6OP
    Option D: 8OP
    VIEW SOLUTION
  • Question 68
    ABCD is a quadrilateral whose diagonals are AC and BD. Which one of the following is correct?
    Option A: BA+CD=AC+DB
    Option B: BA+CD=BD+CA
    Option C: BA+CD=AC+BD
    Option D: BA+CD=BC+AD
    VIEW SOLUTION
  • Question 69
    If a×b=c and b×c=a, then which one of the following is correct?
    Option A: a,b,c are orthogonal in pairs and |a|=|c|and|b|=1
    Option B: a,b,c are non-orthogonal to each other
    Option C: a,b,c are orthogonal in pairs but |a||c|
    Option D: a,b,c are orthogonal in pairs but |b|1
    VIEW SOLUTION
  • Question 70
    If a=2i^+3j^+4k^ and b=3i^+2j^-λk^ are perpendicular, then what is the value of  λ?
    Option A: 2
    Option B: 3
    Option C: 4
    Option D: 5
    VIEW SOLUTION
  • Question 71
    What is limx0ex(1+x)x2 equal to?
    Option B: 12
    Option C: 1
    Option D: 2
    VIEW SOLUTION
  • Question 72
    What is 0π2dθ1+cosθ equal to?
    Option A: 12
    Option B: 1
    Option C: 3
    Option D: None of these
    VIEW SOLUTION
  • Question 73
    What is dxxx7+1 equal to?
    Option A: 12Inx71x7+1+c
    Option B: 17Inx7+1x7+c
    Option C: Inx717x+c
    Option D: 17Inx7x7+1+c
    VIEW SOLUTION
  • Question 74
    The function f : X → Y defined by f(x) = cos x, where xX, is one-one and onto if X and Y are respectively equal to
    Option A: [0, π] and [–1, 1]
    Option B: π2,π2 and [–1, 1]
    Option C: [0, π] and [–1, 1]
    Option D: [0, π] and [0, 1]
    VIEW SOLUTION
  • Question 75
    If (x) = xx1, then what is f(a)f(a+1) equal to?
     
    Option A: faa+1
    Option B: fa2
    Option C: f1a
    Option D:  f(–a)
    VIEW SOLUTION
  • Question 76
    What is (xe1+ex1)dxxe+ex equal to?
    Option A: x22+c
    Option B: In (x + e) + c
    Option C: ln xe+ex+c
    Option D: 1e ln xe+ex+c
    VIEW SOLUTION
  • Question 77
    Let f:[6,6] be defined by fx=x2-3. Consider the following:

    1. (fff) -1=(fff) 12. (fff) -1-4 (fff) 1=(ff) 0

    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 78
    Let f(x) = px + q and g(x) = mx + n. Then f(g(x)) = g(f(x)) is equivalent to
    Option A: f(p)  = g(m)
    Option B: f(q)  = g(n)
    Option C: f(n)  = g(q)
    Option D: f(m) = g(p)
    VIEW SOLUTION
  • Question 79
    If Fx=9x2 = then what is limx1F(x)F(1)x1 equal to?
    Option A: 142
    Option B: 18
    Option C: 122
    Option D: 122
    VIEW SOLUTION
  • Question 80
    What is d2xdy2 equal to?
    Option A: d2ydx21dydx3
    Option B: d2ydx21dydx2
    Option C: -d2ydx2dydx-3
    Option D: d2ydx21
    VIEW SOLUTION
  • Question 81
    Let Fx :x, x is rational0, x is irrational and  gx :0, x is rationalx, x is irrational
    If f : and g :, then f-g is
     
    Option A: one-one and into
    Option B: neither one-one nor onto
    Option C: many one and onto
    Option D: one-one and onto
    VIEW SOLUTION
  • Question 82
    What is the length of the longest interval in which the function fx=3 sin x4 sin3 x is increasing?
    Option A: π3
    Option B: π2
    Option C: 3π2
    Option D: π
    VIEW SOLUTION
  • Question 83
    If x dy = y(dx + y dy); y(1) = 1 and y(x) > 0, then what is y(–3) equal to?
    Option A: 3
    Option B: 2
    Option C: 1
    VIEW SOLUTION
  • Question 84
    What is the maximum value of the function f(x) = 4 sin2 x + 1?
    Option A: 5
    Option B: 3
    Option C: 2
    Option D: 1
    VIEW SOLUTION
  • Question 85
    Let f(x) be an indefinite integral of sin2 x.
    Consider the following statements:

    Statement 1: The function f(x) satisfies f(x + π) = f(x) for all real x.
    Statement 2: sin2(x+π)=sin2x for all real x.

    Which one of the following is correct with respect to the above statements?
    Option A: Both the statements are true and Statement 2 is the correct explanation of Statement 1
    Option B: Both the statements are true but Statement 2 is not the correct explanation of Statement 1
    Option C: Statement 1 is true but Statement 2 is false
    Option D: Statement 1 is false but Statement 2 is true
    VIEW SOLUTION
  • Question 86
    What are the degree and order respectively of the differential equation y=xdydx2+dxdy2?
    Option A: 1, 2
    Option B: 2, 1
    Option C: 1, 4
    Option D: 4, 1
    VIEW SOLUTION
  • Question 87
    What is the differential equation corresponding to y22ay+x2=a2 by eliminating a?
    Option A: (x22y2)p24 pxyx2=0
    Option B: (x22y2)p2+4 pxyx2=0
    Option C: (x2+2y2)p24 pxyx2=0
    Option D: (x2+2y2)p24 pxy+x2=0
    Where p=dydx
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  • Question 88
    What is the general solution of the differential equation ydx(x+2y2)dy=0?
    Option A: x=y2+cy
    Option B: x=2cy2
    Option C: x=2y2+cy
    Option D: None of these
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  • Question 89
    Let f(x + y) = f(x) f(y) for all x and y. Then what is f ’(5) equal to [where f ’(x) is the derivative of f(x)]?
    Option A: f(5) f ’(0)
    Option B: f(5) – f ’(0)
    Option C: f(5) f(0)
    Option D: f(5) + f ’(0)
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  • Question 90
    If f(x) and g(x) are continuous functions satisfying f(x) = f(a – x) and g(x) + g(a – x) = 2, then what is 0af(x)g(x)dx equal to?
    Option A: 0ag(x)dx
    Option B: 0af(x)dx
    Option C: 20af(x)dx
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  • Question 91
    What is the solution of the differential equation lndydxa=0?
    Option A: y=xea+c
    Option B: x=yea+c
    Option C: y = ln x + c
    Option D: x = ln y + c
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  • Question 92
    Let f(x) be defined as follows:
    fx=2x+1, 3<x<2x1,   2x<0x+2,       0x<1
    Which one of the following statements is correct with respect to the above function?
    Option A: It is discontinuous at x = –2 but continuous at every other point.
    Option B: It is continuous only in the interval (–3, –2).
    Option C: It is discontinuous at x = 0 but continuous at every other point.
    Option D: It is discontinuous at every point
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  • Question 93
    Consider the following statements
    1. If limxaf(x) and limxag(x) both exist, then limxa{f(x)g(x)} exists.
    2. If limxa{f(x)g(x)} exists, then both limxaf(x) and limxag(x) and  must exist.

    Which of the above statement is/are correct?
    Option A: 1 only
    Option B: 2 only
    Option C: Both 1 and 2
    Option D: Neither 1 nor 2
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  • Question 94
    Which one of the following functions is neither even nor odd?
    Option A: x21
    Option B: x+3x
    Option C: |x|
    Option D: x2(x3)
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  • Question 95
    What is the derivative of log10(5x2+3) with respect to x?
    Option A: xlog10e5x2+3
    Option B: 2xlog10e5x2+3
    Option C: 10xlog10e5x2+3
    Option D: 10xlog10105x2+3
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  • Question 96
    Let fa=a1a+1.
    Consider the following:
    1. f(2a) = f(a) + 1
    2. f1a=f(a)
    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
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  • Question 97
    What is the maximum area of a triangle that can be inscribed in a circle of radius a?
    Option A: 3a24
    Option B: a22
    Option C: 33a24
    Option D: 3a24
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  • Question 98
    Let fx=x+1x, where x 0, 1. Which one of the following is correct?
    Option A: f(x) fluctuates in the interval
    Option B: f(x) increases in the interval
    Option C: f(x) decreases in the interval
    Option D: None of these
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  • Question 99
    Suppose the function f(x)=xn, n0 is differentiable for all x. Then n can be any element of the interval
    Option A: [1, ∞)
    Option B: (0, ∞)
    Option C: 12, 
    Option D: None of these
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  • Question 100
    What is e1e2ln xxdx equal to?
    Option A: 32
    Option B: 52
    Option C: 3
    Option D: 4
    VIEW SOLUTION
  • Question 101
    The variance of 20 observations is 5. If each observation is multiplied by 3, then what is the new variance of the resulting observations?
    Option A: 5
    Option B: 10
    Option C: 15
    Option D: 45
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  • Question 102
    The mean of a group of 100 observations was found to be 20. Later it was found that four observations were incorrect, which were recorded as 21, 21, 18 and 20. What is the mean if the incorrect observations are omitted?
    Option A: 18
    Option B: 20
    Option C: 21
    Option D: 22
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  • Question 103
    A committee of two persons is constituted from two men and two women. What is the probability that the committee will have only women?
    Option A: 16
    Option B: 13
    Option C: 12
    Option D: 23
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  • Question 104
    A question is given to three students A, B and C whose chance of solving it are 12, 13 and 14 respectively. What is the probability that the question will be solved?
    Option A: 124
    Option B: 14
    Option C: 34
    Option D: 2324
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  • Question 105
    The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the number of boys in the class?
    Option A: 50
    Option B: 55
    Option C: 60
    Option D: 100
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  • Question 106
    For two dependent events, A and E, it is given that P(A) = 0.2 and P(B) = 0.5. If AB, then the value of conditional probabilities P(A|B) and P(B|A) are respectively
    Option A: 23,35
    Option B: 25,1
    Option C: 1,25
    Option D: Information is insufficient
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  • Question 107
    A point is chosen at random inside a circle. What is the probability that the point is closer to the centre of the circle then to its boundary?
    Option A: 15
    Option B: 14
    Option C: 13
    Option D: 12
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  • Question 108
    If two regression lines between height (x) and weight (y) are 4y – 15x + 410 = 0 and 30 x – 2y – 825 = 0, then what will be the correlation coefficient between height and weight?
    Option A: 13
    Option B: 12
    Option C: 23
    Option D: 34
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  • Question 109
    In an examination, 40% of candidates get second class. When the data are represented by a pie chart, what is the angle corresponding to the second class?
    Option A: 40°
    Option B: 90°
    Option C: 144°
    Option D: 320°
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  • Question 110
    Consider the following statements:
    Statement 1: Range is not a good measure of dispersion
    Statement 2: Range is highly affected by the existence of extreme values
     
    Which one of the following is correct in respect of the above statements?
    Option A: Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
    Option B: Both Statement 1 and Statement 2 are correct but Statement 2 is not the correct explanation of Statement 1
    Option C: Statement 1 is correct but Statement 2 is not correct
    Option D: Statement 2 is correct but Statement 1 is not correct
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  • Question 111
    A card is drawn from a well shuffled ordinary deck of 52 cards. What is the probability that it is an ace?
    Option A: 113
    Option B: 213
    Option C: 313
    Option D: 152
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  • Question 112
    If the data is moderately non-symmetrical then which one of the following empirical relationships is correct?
    Option A: 2 × Standard deviation = 5 × Mean deviation
    Option B: 5 × Standard deviation = 2 × Mean deviation
    Option C: 4 × Standard deviation = 5 × Mean deviation
    Option D: 5 × Standard deviation = 4 × Mean deviation
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  • Question 113
    Data can be represented in which of the following forms
    I. Textual form
    II. Tabular form
    III Graphical form

    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
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  • Question 114
    For given statistical data, the graphs for less than ogive and more than ogive are drawn. If the point at which the two curves intersect is P, then abscissa of point P gives the value of which one of the following measures of central tendency?
    Option A: Median
    Option B: Mean
    Option C: Mode
    Option D: Geometric mean
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  • Question 115
    Consider the following statements:
    1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other.
    2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities

    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
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  • Question 116
    If the regression coefficient of x on y and y on x are -12  and -18 respectively, then what is the correlation coefficient between x and y?
    Option A: 14
    Option B: 116
    Option C: 116
    Option D: 14
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  • Question 117
    A sample of 5 observations has mean 32 and median 33. Later it is found that an observation was recorded incorrectly as 40 instead of 35. If we correct the data, then which one of the following is correct?
    Option A: The mean and median remain the same
    Option B: The median remains the same but the mean will decrease
    Option C: The mean and median both will decrease
    Option D: The mean remains the same but median will decrease
    VIEW SOLUTION
  • Question 118
    If two fair dice are thrown, then what is the probability that the sum is neither 8 nor 9?
    Option A: 16
    Option B: 14
    Option C: 34
    Option D: 56
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  • Question 119
    Let A and B are two mutually exclusive events with P(A) = 13 and P(B) = 14. What is the value of P(A¯B¯)
    Option A: 16
    Option B: 14
    Option C: 13
    Option D: 512
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  • Question 120
    The mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trials?
    Option A: 2
    Option B: 12
    Option C: 18
    Option D: 24
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