PYQ Vault

NDA 2017 (II), Paper I, Mathematics question paper

120 questions · 300 marks · 150 minutes · +2.5 per correct answer, -0.83 per wrong one

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  1. 1
    If x+log⁡10(1+2x)=xlog⁡105+log⁡106x + \log_{10}(1 + 2^x) = x\log_{10} 5 + \log_{10} 6, then xx is equal to

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  2. 2
    The remainder and the quotient of the binary division (101110)2÷(110)2(101110)_2 \div (110)_2 are respectively

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  3. 3
    The matrix AA has xx rows and x+5x+5 columns. The matrix BB has yy rows and 11−y11-y columns. Both ABAB and BABA exist. What are the values of xx and yy respectively?

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  4. 4
    If Sn=nP+n(n−1)Q2S_n = nP + \dfrac{n(n-1)Q}{2}, where SnS_n denotes the sum of the first nn terms of an AP, then the common difference is

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  5. 5
    The roots of the equation (q−r)x2+(r−p)x+(p−q)=0(q-r)x^2 + (r-p)x + (p-q) = 0 are

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  6. 6
    If EE is the universal set and A=B∪CA = B \cup C, then the set E−(E−(E−(E−(E−A))))E-(E-(E-(E-(E-A)))) is the same as the set

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  7. 7
    If A={x:x is a multiple of 2}A = \{x : x \text{ is a multiple of } 2\}, B={x:x is a multiple of 5}B = \{x : x \text{ is a multiple of } 5\} and C={x:x is a multiple of 10}C = \{x : x \text{ is a multiple of } 10\}, then A∩(B∩C)A \cap (B \cap C) is equal to

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  8. 8
    If α\alpha and β\beta are the roots of the equation 1+x+x2=01 + x + x^2 = 0, then the matrix product (1βαα)(αβ1β)\begin{pmatrix}1 & \beta \\ \alpha & \alpha\end{pmatrix}\begin{pmatrix}\alpha & \beta \\ 1 & \beta\end{pmatrix} is equal to

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  9. 9
    If ∣a∣|a| denotes the absolute value of an integer, then which of the following are correct? 1. ∣ab∣=∣a∣∣b∣|ab|=|a||b| 2. ∣a+b∣≤∣a∣+∣b∣|a+b|\leq|a|+|b| 3. ∣a−b∣≥∣∣a∣−∣b∣∣|a-b|\geq||a|-|b|| Select the correct answer using the code given below.

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  10. 10
    How many different permutations can be made out of the letters of the word 'PERMUTATION'?

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  11. 11
    If A=(4i−610i14i6+4i)A = \begin{pmatrix}4i-6 & 10i \\ 14i & 6+4i\end{pmatrix} and k=12ik = \dfrac{1}{2i}, where i=−1i = \sqrt{-1}, then kAkA is equal to

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  12. 12
    The sum of all real roots of the equation ∣x−3∣2+∣x−3∣−2=0|x-3|^2 + |x-3| - 2 = 0 is

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  13. 13
    It is given that the roots of the equation x2−4x−log⁡3P=0x^2 - 4x - \log_3 P = 0 are real. For this, the minimum value of PP is

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  14. 14
    If AA is a square matrix, then the value of adj AT−(adj A)T\text{adj}\, A^T - (\text{adj}\, A)^T is equal to

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  15. 15
    The value of the product 612×614×618×6116×…6^{\frac{1}{2}} \times 6^{\frac{1}{4}} \times 6^{\frac{1}{8}} \times 6^{\frac{1}{16}} \times \ldots up to infinite terms is

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  16. 16
    The value of the determinant ∣cos⁡2θ2sin⁡2θ2sin⁡2θ2cos⁡2θ2∣\begin{vmatrix}\cos^2\dfrac{\theta}{2} & \sin^2\dfrac{\theta}{2} \\ \sin^2\dfrac{\theta}{2} & \cos^2\dfrac{\theta}{2}\end{vmatrix} for all values of θ\theta is

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  17. 17
    The number of terms in the expansion of (x+a)100+(x−a)100(x+a)^{100} + (x-a)^{100} after simplification is

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  18. 18
    In the expansion of (1+x)50(1+x)^{50}, the sum of the coefficients of odd powers of xx is

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  19. 19
    If a,b,ca, b, c are non-zero real numbers, then the inverse of the matrix A=(a000b000c)A = \begin{pmatrix}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{pmatrix} is equal to

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  20. 20
    A person is to count 4500 notes. Let ana_n denote the number of notes he counts in the nnth minute. If a1=a2=a3=…=a10=150a_1 = a_2 = a_3 = \ldots = a_{10} = 150, and a10,a11,a12,…a_{10}, a_{11}, a_{12}, \ldots are in AP with the common difference −2-2, then the time taken by him to count all the notes is

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  21. 21
    The smallest positive integer nn for which (1+i1−i)n=1\left(\dfrac{1+i}{1-i}\right)^n = 1, is

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  22. 22
    If we define a relation RR on the set N×NN \times N as (a,b) R (c,d)⇔a+d=b+c(a,b)\,R\,(c,d) \Leftrightarrow a+d=b+c for all (a,b),(c,d)∈N×N(a,b),(c,d) \in N \times N, then the relation is

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  23. 23
    If y=x+x2+x3+…y = x + x^2 + x^3 + \ldots up to infinite terms, where x<1x < 1, then which one of the following is correct?

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  24. 24
    If α\alpha and β\beta are the roots of the equation 3x2+2x+1=03x^2 + 2x + 1 = 0, then the equation whose roots are α+β−1\alpha + \beta^{-1} and β+α−1\beta + \alpha^{-1} is

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  25. 25
    The value of 1log⁡3e+1log⁡3e2+1log⁡3e4+…\dfrac{1}{\log_3 e} + \dfrac{1}{\log_3 e^2} + \dfrac{1}{\log_3 e^4} + \ldots up to infinite terms is

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  26. 26
    A tea party is arranged for 16 people along 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

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  27. 27
    The system of equations kx+y+z=1kx + y + z = 1, x+ky+z=kx + ky + z = k and x+y+kz=k2x + y + kz = k^2 has no solution if kk equals

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  28. 28
    If 1⋅3+2⋅32+3⋅33+…+n⋅3n=(2n−1)3a+b41\cdot 3 + 2\cdot 3^2 + 3\cdot 3^3 + \ldots + n\cdot 3^n = \dfrac{(2n-1)3^a + b}{4}, then aa and bb are respectively

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  29. 29
    In △PQR\triangle PQR, ∠R=π2\angle R = \dfrac{\pi}{2}. If tan⁡ ⁣(P2)\tan\!\left(\dfrac{P}{2}\right) and tan⁡ ⁣(Q2)\tan\!\left(\dfrac{Q}{2}\right) are the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0, then which one of the following is correct?

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  30. 30
    If ∣z−4z∣=2\left|z - \dfrac{4}{z}\right| = 2, then the maximum value of ∣z∣|z| is equal to

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  31. 31
    The angle of elevation of a stationary cloud from a 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

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  32. 32
    The value of tan⁡9°−tan⁡27°−tan⁡63°+tan⁡81°\tan 9° - \tan 27° - \tan 63° + \tan 81° is equal to

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  33. 33
    The value of 3 cosec 20°−sec⁡20°\sqrt{3}\,\text{cosec}\,20° - \sec 20° is equal to

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  34. 34
    Angle α\alpha is divided into two parts AA and BB such that A−B=xA - B = x and tan⁡A:tan⁡B=p:q\tan A : \tan B = p : q. The value of sin⁡x\sin x is equal to

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  35. 35
    The value of sin⁡−1 ⁣(35)+tan⁡−1 ⁣(17)\sin^{-1}\!\left(\dfrac{3}{5}\right) + \tan^{-1}\!\left(\dfrac{1}{7}\right) is equal to

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  36. 36
    The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30° and 45°. If hTh_T is the height of the tower and hPh_P is the height of the pole, then which of the following are correct? 1. 2hPhT3+3=hP2\dfrac{2h_P h_T}{3+\sqrt{3}} = h_P^2 2. hT−hP3+1=hP2\dfrac{h_T - h_P}{\sqrt{3}+1} = \dfrac{h_P}{2} 3. 2(hP+hT)hP=4+3\dfrac{2(h_P + h_T)}{h_P} = 4+\sqrt{3} Select the correct answer using the code given below.

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  37. 37
    In a triangle ABCABC, a−2b+c=0a - 2b + c = 0. The value of cot⁡ ⁣(A2)cot⁡ ⁣(C2)\cot\!\left(\dfrac{A}{2}\right)\cot\!\left(\dfrac{C}{2}\right) is

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  38. 38
    1+sin⁡A=− ⁣(sin⁡A2+cos⁡A2)\sqrt{1+\sin A} = -\!\left(\sin\dfrac{A}{2} + \cos\dfrac{A}{2}\right) is true if

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  39. 39
    In triangle ABCABC, if sin⁡2A+sin⁡2B+sin⁡2Ccos⁡2A+cos⁡2B+cos⁡2C=2\dfrac{\sin^2 A + \sin^2 B + \sin^2 C}{\cos^2 A + \cos^2 B + \cos^2 C} = 2, then the triangle is

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  40. 40
    The principal value of sin⁡−1x\sin^{-1} x lies in the interval

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  41. 41
    The points (a,b)(a, b), (0,0)(0, 0), (−a,−b)(-a, -b) and (ab,b2)(ab, b^2) are

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  42. 42
    The length of the normal from origin to the plane x+2y−2z=9x + 2y - 2z = 9 is equal to

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  43. 43
    If α\alpha, β\beta and γ\gamma are the angles which the vector OP→\overrightarrow{OP} (OO being the origin) makes with the positive direction of the coordinate axes, then which of the following are correct? 1. cos⁡2α+cos⁡2β=sin⁡2γ\cos^2\alpha + \cos^2\beta = \sin^2\gamma 2. sin⁡2α+sin⁡2β=cos⁡2γ\sin^2\alpha + \sin^2\beta = \cos^2\gamma 3. sin⁡2α+sin⁡2β+sin⁡2γ=2\sin^2\alpha + \sin^2\beta + \sin^2\gamma = 2 Select the correct answer using the code given below.

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  44. 44
    The angle between the lines x+y−3=0x + y - 3 = 0 and x−y+3=0x - y + 3 = 0 is α\alpha and the acute angle between the lines x−3y+23=0x - \sqrt{3}y + 2\sqrt{3} = 0 and 3x−y+1=0\sqrt{3}x - y + 1 = 0 is β\beta. Which one of the following is correct?

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  45. 45
    Let α⃗=i^+2j^−k^\vec{\alpha} = \hat{i}+2\hat{j}-\hat{k}, β⃗=2i^−j^+3k^\vec{\beta} = 2\hat{i}-\hat{j}+3\hat{k} and γ⃗=2i^+j^+6k^\vec{\gamma} = 2\hat{i}+\hat{j}+6\hat{k} be three vectors. If α⃗\vec{\alpha} and β⃗\vec{\beta} are both perpendicular to the vector δ⃗\vec{\delta} and δ⃗⋅γ⃗=10\vec{\delta}\cdot\vec{\gamma} = 10, then what is the magnitude of δ⃗\vec{\delta}?

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  46. 46
    If a^\hat{a} and b^\hat{b} are two unit vectors, then the vector (a^+b^)×(a^×b^)(\hat{a}+\hat{b})\times(\hat{a}\times\hat{b}) is parallel to

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  47. 47
    A force F⃗=i^+3j^+2k^\vec{F} = \hat{i}+3\hat{j}+2\hat{k} acts on a particle to displace it from the point A(i^+2j^−3k^)A(\hat{i}+2\hat{j}-3\hat{k}) to the point B(3i^−j^+5k^)B(3\hat{i}-\hat{j}+5\hat{k}). The work done by the force will be

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  48. 48
    For any vector a⃗\vec{a}, ∣a⃗×i^∣2+∣a⃗×j^∣2+∣a⃗×k^∣2|\vec{a}\times\hat{i}|^2 + |\vec{a}\times\hat{j}|^2 + |\vec{a}\times\hat{k}|^2 is equal to

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  49. 49
    A man running round a racecourse notes that the sum of the distances 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 he encloses is

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  50. 50
    The distance of the point (1,3)(1, 3) from the line 2x+3y=62x + 3y = 6, measured parallel to the line 4x+y=44x + y = 4, is

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  51. 51
    If the vectors ai^+j^+k^a\hat{i}+\hat{j}+\hat{k}, i^+bj^+k^\hat{i}+b\hat{j}+\hat{k} and i^+j^+ck^\hat{i}+\hat{j}+c\hat{k} (a,b,c≠1a, b, c \neq 1) are coplanar, then the value of 11−a+11−b+11−c\dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c} is

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  52. 52
    The point of intersection of the line joining the points (−3,4,−8)(-3, 4, -8) and (5,−6,4)(5, -6, 4) with the XYXY-plane is

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  53. 53
    If the angle between the lines whose direction ratios are ⟨2,−1,2⟩\langle 2, -1, 2\rangle and ⟨x,3,5⟩\langle x, 3, 5\rangle is π4\dfrac{\pi}{4}, then the smaller value of xx is

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  54. 54
    The position of the point (1,2)(1, 2) relative to the ellipse 2x2+7y2=202x^2 + 7y^2 = 20 is

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  55. 55
    The equation of a straight line which cuts off an intercept of 5 units on negative direction of yy-axis and makes an angle 120° with positive direction of xx-axis is

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  56. 56
    The equation of the line passing through the point (2,3)(2, 3) and the point of intersection of lines 2x−3y+7=02x - 3y + 7 = 0 and 7x+4y+2=07x + 4y + 2 = 0 is

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  57. 57
    The equation of the ellipse whose centre is at origin, major axis is along xx-axis with eccentricity 34\dfrac{3}{4} and latus rectum 4 units is

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  58. 58
    The equation of the circle which passes through the points (1,0)(1, 0), (0,−6)(0, -6) and (3,4)(3, 4) is

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  59. 59
    A variable plane passes through a fixed point (a,b,c)(a, b, c) and cuts the axes in AA, BB and CC respectively. The locus of the centre of the sphere OABCOABC, OO being the origin, is

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  60. 60
    The equation of the plane passing through the line of intersection of the planes x+y+z=1x + y + z = 1, 2x+3y+4z=72x + 3y + 4z = 7 and perpendicular to the plane x−5y+3z=5x - 5y + 3z = 5 is given by

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  61. 61
    The inverse of the function y=5ln⁡xy = 5^{\ln x} is

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  62. 62
    A function is defined as follows: f(x)={−xx2,x≠00,x=0f(x) = \begin{cases} -\dfrac{x}{\sqrt{x^2}}, & x \neq 0 \\ 0, & x = 0 \end{cases}. Which one of the following is correct in respect of the above function?

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  63. 63
    If y=(cos⁡x)(cos⁡x)(cos⁡x)⋯∞y = (\cos x)^{(\cos x)^{(\cos x)^{\cdots\infty}}}, then dydx\dfrac{dy}{dx} is equal to

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  64. 64
    Consider the following: 1. x+x2x + x^2 is continuous at x=0x = 0. 2. x+cos⁡1xx + \cos\dfrac{1}{x} is discontinuous at x=0x = 0. 3. x2+cos⁡1xx^2 + \cos\dfrac{1}{x} is continuous at x=0x = 0. Which of the above are correct?

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  65. 65
    Consider the following statements: 1. dydx\dfrac{dy}{dx} at a point on the curve gives slope of the tangent at that point. 2. If a(t)a(t) denotes acceleration of a particle, then ∫a(t) dt+c\int a(t)\,dt + c gives velocity of the particle. 3. If s(t)s(t) gives displacement of a particle at time tt, then dsdt\dfrac{ds}{dt} gives its acceleration at that instant. Which of the above statements is/are correct?

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  66. 66
    If y=sec⁡−1 ⁣(x+1x−1)+sin⁡−1 ⁣(x−1x+1)y = \sec^{-1}\!\left(\dfrac{x+1}{x-1}\right) + \sin^{-1}\!\left(\dfrac{x-1}{x+1}\right), then dydx\dfrac{dy}{dx} is equal to

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  67. 67
    What is ∫tan⁡−1(sec⁡x+tan⁡x) dx\displaystyle\int \tan^{-1}(\sec x + \tan x)\,dx equal to?

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  68. 68
    A function is defined in (0,∞)(0, \infty) by f(x)={1−x2for 0<x≤1ln⁡xfor 1<x≤2ln⁡2−1+0.5xfor 2<x<∞f(x) = \begin{cases}1 - x^2 & \text{for } 0 < x \leq 1 \\ \ln x & \text{for } 1 < x \leq 2 \\ \ln 2 - 1 + 0.5x & \text{for } 2 < x < \infty\end{cases}. Which one of the following is correct in respect of the derivative of the function, i.e., f′(x)f'(x)?

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  69. 69
    Which one of the following is correct in respect of the function f(x)=x(x−1)(x+1)f(x) = x(x-1)(x+1)?

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  70. 70
    Consider the following statements: 1. Derivative of f(x)f(x) may not exist at some point. 2. Derivative of f(x)f(x) may exist finitely at some point. 3. Derivative of f(x)f(x) may be infinite (geometrically) at some point. Which of the above statements are correct?

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  71. 71
    The maximum value of ln⁡xx\dfrac{\ln x}{x} is

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  72. 72
    The function f(x)=∣x∣−x3f(x) = |x| - x^3 is

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  73. 73
    If l1=ddx(esin⁡x)l_1 = \dfrac{d}{dx}(e^{\sin x}), l2=lim⁡h→0esin⁡(x+h)−esin⁡xhl_2 = \lim_{h \to 0}\dfrac{e^{\sin(x+h)} - e^{\sin x}}{h}, l3=∫esin⁡xcos⁡x dxl_3 = \displaystyle\int e^{\sin x}\cos x\,dx, then which one of the following is correct?

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  74. 74
    The general solution of dydx=ax+hby+k\dfrac{dy}{dx} = \dfrac{ax + h}{by + k} represents a circle only when

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  75. 75
    If lim⁡x→π2sin⁡xx=l\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\sin x}{x} = l and lim⁡x→∞cos⁡xx=m\displaystyle\lim_{x \to \infty} \frac{\cos x}{x} = m, then which one of the following is correct?

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  76. 76
    What is ∫02π1+sin⁡x2 dx\displaystyle\int_0^{2\pi} \sqrt{1 + \sin\dfrac{x}{2}}\,dx equal to?

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  77. 77
    The area bounded by the curve ∣x∣+∣y∣=1|x| + |y| = 1 is

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  78. 78
    If xx is any real number, then x21+x4\dfrac{x^2}{1+x^4} belongs to which one of the following intervals?

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  79. 79
    The left-hand derivative of f(x)=[x]sin⁡(πx)f(x) = [x]\sin(\pi x) at x=kx = k, where kk is an integer and [x][x] is the greatest integer function, is

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  80. 80
    If f(x)=x2−1f(x) = \dfrac{x}{2} - 1, then on the interval [0,π][0, \pi] which one of the following is correct?

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  81. 81
    The order and degree of the differential equation [1+(dydx)2]3=ρ2[d2ydx2]2\left[1+\left(\dfrac{dy}{dx}\right)^2\right]^3 = \rho^2\left[\dfrac{d^2y}{dx^2}\right]^2 are respectively

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  82. 82
    If y=cos⁡−1 ⁣(2x1+x2)y = \cos^{-1}\!\left(\dfrac{2x}{1+x^2}\right), then dydx\dfrac{dy}{dx} is equal to

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  83. 83
    The set of all points, where the function f(x)=1−e−x2f(x) = \sqrt{1 - e^{-x^2}} is differentiable, is

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  84. 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\sin x + \cos x1. 10\sqrt{10}
    B. 3sin⁡x+4cos⁡x3\sin x + 4\cos x2. 2\sqrt{2}
    C. 2sin⁡x+cos⁡x2\sin x + \cos x3. 5
    D. sin⁡x+3cos⁡x\sin x + 3\cos x4. 5\sqrt{5}
    Code:

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  85. 85
    If f(x)=x(x−x+1)f(x) = x(\sqrt{x} - \sqrt{x+1}), then f(x)f(x) is

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  86. 86
    Which one of the following graphs represents the function f(x)=xx, x≠0f(x) = \dfrac{x}{x},\ x \neq 0?

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  87. 87
    Let f(n)=[14+n1000]f(n) = \left[\dfrac{1}{4} + \dfrac{n}{1000}\right], where [x][x] denotes the integral part of xx. Then the value of ∑n=11000f(n)\displaystyle\sum_{n=1}^{1000} f(n) is

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  88. 88
    ∫(ln⁡x)−1 dx−∫(ln⁡x)−2 dx\displaystyle\int (\ln x)^{-1}\,dx - \int (\ln x)^{-2}\,dx is equal to

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  89. 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 kk times the height of the jar. The value of kk is

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  90. 90
    The value of ∫0π/4tan⁡x dx+∫0π/4cot⁡x dx\displaystyle\int_0^{\pi/4}\sqrt{\tan x}\,dx + \int_0^{\pi/4}\sqrt{\cot x}\,dx is equal to

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  91. 91
    Let gg be the greatest integer function. Then the function f(x)=(g(x))2−g(x2)f(x) = (g(x))^2 - g(x^2) is discontinuous at

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  92. 92
    The differential equation of minimum order by eliminating the arbitrary constants AA and CC in the equation y=A[sin⁡(x+C)+cos⁡(x+C)]y = A[\sin(x+C) + \cos(x+C)] is

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  93. 93
    Consider the following statements: Statement I: x>sin⁡xx > \sin x for all x>0x > 0. Statement II: f(x)=x−sin⁡xf(x) = x - \sin x is an increasing function for all x>0x > 0. Which one of the following is correct in respect of the above statements?

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  94. 94
    The solution of the differential equation dydx=yϕ′(x)−y2ϕ(x)\dfrac{dy}{dx} = \dfrac{y\phi'(x) - y^2}{\phi(x)} is

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  95. 95
    If f(x)=4x+x41+4x3f(x) = \dfrac{4x+x^4}{1+4x^3} and g(x)=ln⁡ ⁣(1+x1−x)g(x) = \ln\!\left(\dfrac{1+x}{1-x}\right), then what is the value of f∘g ⁣(e−1e+1)f \circ g\!\left(\dfrac{e-1}{e+1}\right) equal to?

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  96. 96
    The value of the determinant ∣1−αα−α2α21−ββ−β2β21−γγ−γ2γ2∣\begin{vmatrix}1-\alpha & \alpha-\alpha^2 & \alpha^2 \\ 1-\beta & \beta-\beta^2 & \beta^2 \\ 1-\gamma & \gamma-\gamma^2 & \gamma^2\end{vmatrix} is equal to

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  97. 97
    The adjoint of the matrix A=(102210031)A = \begin{pmatrix}1 & 0 & 2 \\ 2 & 1 & 0 \\ 0 & 3 & 1\end{pmatrix} is

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  98. 98
    If A=(−222−2)A = \begin{pmatrix}-2 & 2 \\ 2 & -2\end{pmatrix}, then which one of the following is correct?

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  99. 99
    Geometrically Re(z2−i)=2\text{Re}(z^2-i)=2, where i=−1i=\sqrt{-1} and Re is the real part, represents

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  100. 100
    If p+q+r=a+b+c=0p+q+r = a+b+c = 0, then the determinant ∣paqbrcqcrapbrbpcqa∣\begin{vmatrix}pa & qb & rc \\ qc & ra & pb \\ rb & pc & qa\end{vmatrix} equals

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  101. 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

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  102. 102
    Let a die be loaded in such a way that even faces are twice as likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed?

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  103. 103
    Let the sample space consist of non-negative integers up to 50, XX denote the numbers which are multiples of 3 and YY denote the odd numbers. Which of the following is/are correct? 1. P(X)=825P(X) = \dfrac{8}{25} 2. P(Y)=12P(Y) = \dfrac{1}{2} Select the correct answer using the code given below.

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  104. 104
    For two events AA and BB, let P(A)=12P(A) = \dfrac{1}{2}, P(A∪B)=23P(A \cup B) = \dfrac{2}{3} and P(A∩B)=16P(A \cap B) = \dfrac{1}{6}. What is P(Aˉ∩B)P(\bar{A} \cap B) equal to?

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  105. 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 least when measured about median. Which of the above statements are correct?

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  106. 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?

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  107. 107
    Which one of the following can be considered as appropriate pair of values of regression coefficient of yy on xx and regression coefficient of xx on yy?

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  108. 108
    Let AA and BB be two events with P(A)=13P(A) = \dfrac{1}{3}, P(B)=16P(B) = \dfrac{1}{6} and P(A∩B)=112P(A \cap B) = \dfrac{1}{12}. What is P(B∣Aˉ)P(B|\bar{A}) equal to?

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  109. 109
    In a binomial distribution, the mean is 23\dfrac{2}{3} and the variance is 59\dfrac{5}{9}. What is the probability that X=2X = 2?

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  110. 110
    The probability that a ship safely reaches a port is 13\dfrac{1}{3}. The probability that out of 5 ships, at least 4 ships would arrive safely is

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  111. 111
    What is the probability that at least two persons out of a group of three persons were born in the same month (disregard year)?

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  112. 112
    It is given that Xˉ=10\bar{X}=10, Yˉ=90\bar{Y}=90, σX=3\sigma_X=3, σY=12\sigma_Y=12 and rXY=0.8r_{XY}=0.8. The regression equation of XX on YY is

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  113. 113
    If P(B)=34P(B) = \dfrac{3}{4}, P(A∩B∩Cˉ)=13P(A \cap B \cap \bar{C}) = \dfrac{1}{3} and P(Aˉ∩B∩Cˉ)=13P(\bar{A} \cap B \cap \bar{C}) = \dfrac{1}{3}, then what is P(B∩C)P(B \cap C) equal to?

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  114. 114
    The following table gives the monthly expenditure of two families:
    ItemsFamily A (in ₹)Family B (in ₹)
    Food3,5002,700
    Clothing500800
    Rent1,5001,000
    Education2,0001,800
    Miscellaneous2,5001,800
    In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the following ratios?

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  115. 115
    If a variable takes values 0,1,2,3,…,n0, 1, 2, 3, \ldots, n with frequencies 1,C(n,1),C(n,2),C(n,3),…,C(n,n)1, C(n,1), C(n,2), C(n,3), \ldots, C(n,n) respectively, then the arithmetic mean is

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  116. 116
    In a multiple-choice test, an examinee either knows the correct answer with probability pp, or guesses with probability 1−p1-p. The probability of answering a question correctly is 1m\dfrac{1}{m}, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

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  117. 117
    If x1x_1 and x2x_2 are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

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  118. 118
    Consider the following statements: 1. Variance is unaffected by 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?

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  119. 119
    Five sticks of length 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?

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  120. 120
    The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

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