PYQ Vault

NDA 2017 (I), 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
    Let SS be the set of all persons living in Delhi. We say that xx, yy in SS are related if they were born in Delhi on the same day. Which one of the following is correct?

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  2. 2
    Let A={1,2,3,4,5,6,7,8,9,10}A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}. Then the number of subsets of AA containing two or three elements is

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  3. 3
    The value of i2n+i2n+1+i2n+2+i2n+3i^{2n} + i^{2n+1} + i^{2n+2} + i^{2n+3}, where i=−1i = \sqrt{-1}, is

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  4. 4
    If the difference between the roots of the equation x2+kx+1=0x^2 + kx + 1 = 0 is strictly less than 5\sqrt{5}, where ∣k∣≥2|k| \geq 2, then kk can be any element of the interval

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  5. 5
    If the roots of the equation x2+px+q=0x^2 + px + q = 0 are in the same ratio as those of the equation x2+lx+m=0x^2 + lx + m = 0, then which one of the following is correct?

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  6. 6
    The value of (−1+i32)n+(−1−i32)n\left(\dfrac{-1+i\sqrt{3}}{2}\right)^n + \left(\dfrac{-1-i\sqrt{3}}{2}\right)^n, where nn is not a multiple of 3 and i=−1i = \sqrt{-1}, is

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  7. 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 three-digit numbers?

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  8. 8
    What is the sum of the series 0.3+0.33+0.333+…0.3 + 0.33 + 0.333 + \ldots to nn terms?

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  9. 9
    If 1,ω,ω21, \omega, \omega^2 are the cube roots of unity, then (1+ω)(1+ω2)(1+ω3)(1+ω+ω2)(1+\omega)(1+\omega^2)(1+\omega^3)(1+\omega+\omega^2) is equal to

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  10. 10
    If the sum of mm terms of an AP is nn and the sum of nn terms is mm, then the sum of (m+n)(m+n) terms is

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  11. 11
    The modulus and principal argument of the complex number 1+2i1−(1−i)2\dfrac{1+2i}{1-(1-i)^2} are respectively

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  12. 12
    If the graph of a quadratic polynomial lies entirely above the x-axis, then which one of the following is correct?

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  13. 13
    If ∣z+4∣≤3|z+4| \leq 3, then the maximum value of ∣z+1∣|z+1| is

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  14. 14
    The number of roots of the equation z2=2zˉz^2 = 2\bar{z} is

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  15. 15
    If cot⁡α\cot\alpha and cot⁡β\cot\beta are the roots of the equation x2+bx+c=0x^2 + bx + c = 0 with b≠0b \neq 0, then the value of cot⁡(α+β)\cot(\alpha+\beta) is

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  16. 16
    The sum of the roots of the equation x2+bx+c=0x^2 + bx + c = 0 (where bb and cc are non-zero) is equal to the sum of the reciprocals of their squares. Then 1c, b, cb\dfrac{1}{c},\, b,\, \dfrac{c}{b} are in

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  17. 17
    The sum of the roots of the equation ax2+x+c=0ax^2 + x + c = 0 (where aa and cc are non-zero) is equal to the sum of the reciprocals of their squares. Then a, ca2, c2a,\, ca^2,\, c^2 are in

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  18. 18
    The value of [C(7,0)+C(7,1)]+[C(7,1)+C(7,2)]+…+[C(7,6)+C(7,7)][C(7,0)+C(7,1)]+[C(7,1)+C(7,2)]+\ldots+[C(7,6)+C(7,7)] is

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  19. 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

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  20. 20
    The fifth term of an AP of nn terms, whose sum is n2−2nn^2 - 2n, is

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  21. 21
    The sum of all the two-digit odd numbers is

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  22. 22
    The sum of the first nn terms of the series 12+34+78+1516+…\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{7}{8}+\dfrac{15}{16}+\ldots is equal to

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  23. 23
    Consider the following in respect of sets AA and BB: 1. (A−B)∪B=A(A-B) \cup B = A 2. (A−B)∪A=A(A-B) \cup A = A 3. (A−B)∩B=ϕ(A-B) \cap B = \phi 4. A⊆B⇒A∪B=BA \subseteq B \Rightarrow A \cup B = B Which of the above are correct?

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  24. 24
    In the binary equation (1p101)2+(10q1)2=(100r00)2(1p101)_2 + (10q1)_2 = (100r00)_2, where pp, qq and rr are binary digits, what are the possible values of pp, qq and rr respectively?

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  25. 25
    If S={x:x2+1=0, x is real}S = \{x : x^2 + 1 = 0,\, x \text{ is real}\}, then SS is

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  26. 26
    The expansion of (x−y)n(x-y)^n, n≥5n \geq 5 is done in descending powers of xx. If the sum of the fifth and sixth terms is zero, then xy\dfrac{x}{y} is equal to

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  27. 27
    If A=(α22α)A = \begin{pmatrix} \alpha & 2 \\ 2 & \alpha \end{pmatrix} and det⁡(A3)=125\det(A^3) = 125, then α\alpha is equal to

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  28. 28
    If BB is a non-singular matrix and AA is a square matrix, then the value of det⁡(B−1AB)\det(B^{-1}AB) is equal to

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  29. 29
    If a≠b≠ca \neq b \neq c, then one value of xx which satisfies the equation ∣0x−ax−bx+a0x−cx+bx+c0∣=0\begin{vmatrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{vmatrix} = 0 is given by

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  30. 30
    If A=(cos⁡αsin⁡α−sin⁡αcos⁡α)A = \begin{pmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{pmatrix}, then what is AATAA^T equal to (where ATA^T is the transpose of AA)?

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  31. 31
    The equations x+2y+3z=1x+2y+3z=1, 2x+y+3z=22x+y+3z=2, 5x+5y+9z=45x+5y+9z=4

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  32. 32
    If A=(x+yyxx−y)A = \begin{pmatrix} x+y & y \\ x & x-y \end{pmatrix}, B=(3−2)B = \begin{pmatrix} 3 \\ -2 \end{pmatrix} and C=(4−2)C = \begin{pmatrix} 4 \\ -2 \end{pmatrix}. If AB=CAB = C, then what is A2A^2 equal to?

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  33. 33
    What is the value of the determinant ∣11111+xyz1111+xyz∣\begin{vmatrix}1&1&1\\1&1+xyz&1\\1&1&1+xyz\end{vmatrix}?

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  34. 34
    If ∣xy00xyy0x∣=0\begin{vmatrix}x&y&0\\0&x&y\\y&0&x\end{vmatrix}=0, then which one of the following is correct?

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  35. 35
    Consider the set AA of all matrices of order 3×33\times3 with entries 0 or 1 only. Let BB be the subset of AA consisting of all matrices whose determinant is 1. Let CC be the subset of AA consisting of all matrices whose determinant is −1-1. Then which one of the following is correct?

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  36. 36
    If A=(cos⁡θsin⁡θ−sin⁡θcos⁡θ)A = \begin{pmatrix}\cos\theta & \sin\theta \\ -\sin\theta & \cos\theta\end{pmatrix}, then what is A3A^3 equal to?

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  37. 37
    What is the order of [x  y  z][ahghbfgfc][xyz][x\; y\; z]\begin{bmatrix}a&h&g\\h&b&f\\g&f&c\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}?

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  38. 38
    If A=(0110)A = \begin{pmatrix}0&1\\1&0\end{pmatrix}, then the value of A4A^4 is

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  39. 39
    If sin⁡A=35\sin A = \dfrac{3}{5}, where 450°<A<540°450° < A < 540°, then cos⁡A2\cos\dfrac{A}{2} is equal to

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  40. 40
    What is 1sin⁡10°−3cos⁡10°\dfrac{1}{\sin 10°} - \dfrac{\sqrt{3}}{\cos 10°} equal to?

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  41. 41
    From the top of a lighthouse, 100 m high, the angle of depression of a boat is tan⁡−1 ⁣(512)\tan^{-1}\!\left(\dfrac{5}{12}\right). What is the distance between the boat and the lighthouse?

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  42. 42
    The maximum value of sin⁡ ⁣(x+π6)+cos⁡ ⁣(x+π6)\sin\!\left(x+\dfrac{\pi}{6}\right)+\cos\!\left(x+\dfrac{\pi}{6}\right) in the interval (0,π2)\left(0,\dfrac{\pi}{2}\right) is attained at

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  43. 43
    If K=sin⁡ ⁣(π18)sin⁡ ⁣(5π18)sin⁡ ⁣(7π18)K = \sin\!\left(\dfrac{\pi}{18}\right)\sin\!\left(\dfrac{5\pi}{18}\right)\sin\!\left(\dfrac{7\pi}{18}\right), then what is the value of KK?

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  44. 44
    The expression sin⁡α+sin⁡βcos⁡α+cos⁡β\dfrac{\sin\alpha+\sin\beta}{\cos\alpha+\cos\beta} is equal to

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  45. 45
    If sin⁡θ=3sin⁡(θ+2α)\sin\theta = 3\sin(\theta+2\alpha), then the value of tan⁡(θ+α)+2tan⁡α\tan(\theta+\alpha)+2\tan\alpha is equal to

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  46. 46
    What is the value of tan⁡18°\tan 18°?

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  47. 47
    Let xx, yy, zz be positive real numbers such that xx, yy, zz are in GP and tan⁡−1x\tan^{-1}x, tan⁡−1y\tan^{-1}y and tan⁡−1z\tan^{-1}z are in AP. Then which one of the following is correct?

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  48. 48
    If tan⁡(α+β)=2\tan(\alpha+\beta)=2 and tan⁡(α−β)=1\tan(\alpha-\beta)=1, then tan⁡(2α)\tan(2\alpha) is equal to

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  49. 49
    Consider the following for triangle ABCABC: 1. sin⁡ ⁣(B+C2)=cos⁡ ⁣(A2)\sin\!\left(\dfrac{B+C}{2}\right) = \cos\!\left(\dfrac{A}{2}\right) 2. tan⁡ ⁣(B+C2)=cot⁡ ⁣(A2)\tan\!\left(\dfrac{B+C}{2}\right) = \cot\!\left(\dfrac{A}{2}\right) 3. sin⁡(B+C)=cos⁡A\sin(B+C) = \cos A 4. tan⁡(B+C)=−cot⁡A\tan(B+C) = -\cot A Which of the above are correct?

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  50. 50
    If sec⁡θ−cosec θ=43\sec\theta - \text{cosec}\,\theta = \dfrac{4}{3}, then what is (sin⁡θ−cos⁡θ)(\sin\theta - \cos\theta) equal to?

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  51. 51
    If a vertex of a triangle is (1,1)(1, 1) and the midpoints of two sides of the triangle through this vertex are (−1,2)(-1, 2) and (3,2)(3, 2), then the centroid of the triangle is

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  52. 52
    The incentre of the triangle with vertices A(1,3)A(1, \sqrt{3}), B(0,0)B(0, 0) and C(2,0)C(2, 0) is

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  53. 53
    If the three consecutive vertices of a parallelogram are (−2,−1)(-2, -1), (1,0)(1, 0) and (4,3)(4, 3), then what are the coordinates of the fourth vertex?

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  54. 54
    The two circles x2+y2=r2x^2+y^2=r^2 and x2+y2−10x+16=0x^2+y^2-10x+16=0 intersect at two distinct points. Then which one of the following is correct?

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  55. 55
    What is the equation of the circle which passes through the points (3,−2)(3, -2) and (−2,0)(-2, 0) and having its centre on the line 2x−y−3=02x - y - 3 = 0?

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  56. 56
    What is the ratio in which the point C ⁣(−27,−207)C\!\left(-\dfrac{2}{7}, -\dfrac{20}{7}\right) divides the line joining the points A(−2,−2)A(-2, -2) and B(2,−4)B(2, -4)?

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  57. 57
    What is the equation of the ellipse having foci (±2,0)(\pm 2, 0) and the eccentricity 14\dfrac{1}{4}?

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  58. 58
    What is the equation of the straight line parallel to 2x+3y+1=02x+3y+1=0 and passes through the point (−1,2)(-1, 2)?

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  59. 59
    What is the acute angle between the pair of straight lines 2x+3y=1\sqrt{2}x+\sqrt{3}y=1 and 3x+2y=2\sqrt{3}x+\sqrt{2}y=2?

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  60. 60
    If the centroid of a triangle formed by (7,x)(7, x), (y,−6)(y, -6) and (9,10)(9, 10) is (6,3)(6, 3), then the values of xx and yy are respectively

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  61. 61
    A straight line with direction cosines ⟨0,1,0⟩\langle 0, 1, 0\rangle is

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  62. 62
    (0,0,0)(0, 0, 0), (a,0,0)(a, 0, 0), (0,b,0)(0, b, 0) and (0,0,c)(0, 0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points?

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  63. 63
    The points P(3,2,4)P(3, 2, 4), Q(4,5,2)Q(4, 5, 2), R(5,8,0)R(5, 8, 0) and S(2,−1,6)S(2, -1, 6) are

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  64. 64
    The line passing through the points (1,2,−1)(1, 2, -1) and (3,−1,2)(3, -1, 2) meets the yzyz-plane at which one of the following points?

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  65. 65
    Under which one of the following conditions are the lines x=ay+b;  z=cy+dx=ay+b;\; z=cy+d and x=ey+f;  z=gy+hx=ey+f;\; z=gy+h perpendicular?

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  66. 66
    If a⃗=i^−j^+k^\vec{a}=\hat{i}-\hat{j}+\hat{k}, b⃗=2i^+3j^+2k^\vec{b}=2\hat{i}+3\hat{j}+2\hat{k} and c⃗=i^+mj^+nk^\vec{c}=\hat{i}+m\hat{j}+n\hat{k} are three coplanar vectors and ∣c⃗∣=6|\vec{c}|=\sqrt{6}, then which one of the following is correct?

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  67. 67
    Let ABCDABCD be a parallelogram whose diagonals intersect at PP and let OO be the origin. What is OA→+OB→+OC→+OD→\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD} equal to?

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  68. 68
    ABCDABCD is a quadrilateral whose diagonals are ACAC and BDBD. Which one of the following is correct?

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  69. 69
    If a⃗×b⃗=c⃗\vec{a}\times\vec{b}=\vec{c} and b⃗×c⃗=a⃗\vec{b}\times\vec{c}=\vec{a}, then which one of the following is correct?

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  70. 70
    If a⃗=2i^+3j^+4k^\vec{a}=2\hat{i}+3\hat{j}+4\hat{k} and b⃗=3i^+2j^−λk^\vec{b}=3\hat{i}+2\hat{j}-\lambda\hat{k} are perpendicular, then what is the value of λ\lambda?

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  71. 71
    What is lim⁡x→0ex−(1+x)x2\lim_{x\to 0}\dfrac{e^x-(1+x)}{x^2} equal to?

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  72. 72
    What is ∫0π/2dθ1+cos⁡θ\int_0^{\pi/2}\dfrac{d\theta}{1+\cos\theta} equal to?

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  73. 73
    What is ∫dxx(x7+1)\int\dfrac{dx}{x(x^7+1)} equal to?

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  74. 74
    The function f:X→Yf:X\to Y defined by f(x)=cos⁡xf(x)=\cos x, where x∈Xx\in X, is one-one and onto if XX and YY are respectively equal to

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  75. 75
    If f(x)=xx−1f(x)=\dfrac{x}{x-1}, then what is f(a)f(a+1)\dfrac{f(a)}{f(a+1)} equal to?

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  76. 76
    What is ∫(xe−1+ex−1) dxxe+ex\int\dfrac{(x^{e-1}+e^{x-1})\,dx}{x^e+e^x} equal to?

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  77. 77
    Let f:[−6,6]→Rf:[-6,6]\to\mathbb{R} be defined by f(x)=x2−3f(x)=x^2-3. Consider the following: 1. (f∘f∘f)(−1)=(f∘f∘f)(1)(f\circ f\circ f)(-1) = (f\circ f\circ f)(1) 2. (f∘f∘f)(−1)−4(f∘f∘f)(1)=(f∘f)(0)(f\circ f\circ f)(-1) - 4(f\circ f\circ f)(1) = (f\circ f)(0) Which of the above is/are correct?

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  78. 78
    Let f(x)=px+qf(x)=px+q and g(x)=mx+ng(x)=mx+n. Then f(g(x))=g(f(x))f(g(x))=g(f(x)) is equivalent to

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  79. 79
    If F(x)=9−x2F(x)=\sqrt{9-x^2}, then what is lim⁡x→1F(x)−F(1)x−1\lim_{x\to1}\dfrac{F(x)-F(1)}{x-1} equal to?

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  80. 80
    What is d2xdy2\dfrac{d^2x}{dy^2} equal to?

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  81. 81
    Let f(x)={x,x is rational0,x is irrationalf(x)=\begin{cases}x, & x\text{ is rational}\\0, & x\text{ is irrational}\end{cases} and g(x)={0,x is rationalx,x is irrationalg(x)=\begin{cases}0, & x\text{ is rational}\\x, & x\text{ is irrational}\end{cases}. If f:R→Rf:\mathbb{R}\to\mathbb{R} and g:R→Rg:\mathbb{R}\to\mathbb{R}, then (f−g)(f-g) is

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  82. 82
    What is the length of the longest interval in which the function f(x)=3sin⁡x−4sin⁡3xf(x)=3\sin x - 4\sin^3 x is increasing?

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  83. 83
    If x dy=y(dx+y dy)x\,dy = y(dx + y\,dy); y(1)=1y(1) = 1 and y(x)>0y(x) > 0, then what is y(−3)y(-3) equal to?

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  84. 84
    What is the maximum value of the function f(x)=4sin⁡2x+1f(x)=4\sin^2 x+1?

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  85. 85
    Let f(x)f(x) be an indefinite integral of sin⁡2x\sin^2 x. Consider the following statements: Statement 1: The function f(x)f(x) satisfies f(x+π)=f(x)f(x+\pi)=f(x) for all real xx. Statement 2: sin⁡2(x+π)=sin⁡2x\sin^2(x+\pi)=\sin^2 x for all real xx. Which one of the following is correct in respect of the above statements?

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  86. 86
    What are the degree and order respectively of the differential equation y=x(dydx)2+(dxdy)2y=x\left(\dfrac{dy}{dx}\right)^2+\left(\dfrac{dx}{dy}\right)^2?

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  87. 87
    What is the differential equation corresponding to y2−2ay+x2=a2y^2-2ay+x^2=a^2 by eliminating aa?

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  88. 88
    What is the general solution of the differential equation y dx−(x+2y2) dy=0y\,dx-(x+2y^2)\,dy=0?

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  89. 89
    Let f(x+y)=f(x)f(y)f(x+y)=f(x)f(y) for all xx and yy. Then what is f′(5)f'(5) equal to [where f′(x)f'(x) is the derivative of f(x)f(x)]?

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  90. 90
    If f(x)f(x) and g(x)g(x) are continuous functions satisfying f(x)=f(a−x)f(x)=f(a-x) and g(x)+g(a−x)=2g(x)+g(a-x)=2, then what is ∫0af(x)g(x) dx\int_0^a f(x)g(x)\,dx equal to?

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  91. 91
    What is the solution of the differential equation ln⁡ ⁣(dydx)−a=0\ln\!\left(\dfrac{dy}{dx}\right)-a=0?

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  92. 92
    Let f(x)={2x+1,−3<x<−2x−1,−2≤x<0x+2,0≤x<1f(x)=\begin{cases}2x+1, & -3<x<-2\\x-1, & -2\leq x<0\\x+2, & 0\leq x<1\end{cases}. Which one of the following statements is correct in respect of the above function?

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  93. 93
    Consider the following statements: 1. If lim⁡x→af(x)\lim_{x\to a}f(x) and lim⁡x→ag(x)\lim_{x\to a}g(x) both exist, then lim⁡x→a{f(x)g(x)}\lim_{x\to a}\{f(x)g(x)\} exists. 2. If lim⁡x→a{f(x)g(x)}\lim_{x\to a}\{f(x)g(x)\} exists, then both lim⁡x→af(x)\lim_{x\to a}f(x) and lim⁡x→ag(x)\lim_{x\to a}g(x) must exist. Which of the above statements is/are correct?

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  94. 94
    Which one of the following functions is neither even nor odd?

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  95. 95
    What is the derivative of log⁡10(5x2+3)\log_{10}(5x^2+3) with respect to xx?

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  96. 96
    Let f(a)=a−1a+1f(a)=\dfrac{a-1}{a+1}. Consider the following: 1. f(2a)=f(a)+1f(2a)=f(a)+1 2. f ⁣(1a)=−f(a)f\!\left(\dfrac{1}{a}\right)=-f(a) Which of the above is/are correct?

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  97. 97
    What is the maximum area of a triangle that can be inscribed in a circle of radius aa?

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  98. 98
    Let f(x)=x+1xf(x)=x+\dfrac{1}{x}, where x∈(0,1)x\in(0,1). Then which one of the following is correct?

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  99. 99
    Suppose the function f(x)=xnf(x)=x^n, n≠0n\neq0 is differentiable for all xx. Then nn can be any element of the interval

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  100. 100
    What is ∫e−1e2∣ln⁡xx∣ dx\int_{e^{-1}}^{e^2}\left|\dfrac{\ln x}{x}\right|\,dx equal to?

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  101. 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?

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  102. 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?

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  103. 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?

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  104. 104
    A question is given to three students AA, BB and CC whose chances of solving it are 12\dfrac{1}{2}, 13\dfrac{1}{3} and 14\dfrac{1}{4} respectively. What is the probability that the question will be solved?

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  105. 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?

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  106. 106
    For two dependent events AA and BB, it is given that P(A)=0.2P(A)=0.2 and P(B)=0.5P(B)=0.5. If A⊆BA\subseteq B, then the values of conditional probabilities P(A∣B)P(A|B) and P(B∣A)P(B|A) are respectively

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  107. 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 than to its boundary?

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  108. 108
    If two regression lines between height (x)(x) and weight (y)(y) are 4y−15x+410=04y-15x+410=0 and 30x−2y−825=030x-2y-825=0, then what will be the correlation coefficient between height and weight?

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  109. 109
    In an examination, 40% of candidates got second class. When the data are represented by a pie chart, what is the angle corresponding to second class?

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  110. 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?

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  111. 111
    A card is drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that it is an ace?

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  112. 112
    If the data are moderately non-symmetrical, then which one of the following empirical relationships is correct?

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  113. 113
    Data can be represented in which of the following forms? 1. Textual form 2. Tabular form 3. Graphical form Select the correct answer using the code given below.

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  114. 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 PP, then abscissa of point PP gives the value of which one of the following measures of central tendency?

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  115. 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?

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  116. 116
    If the regression coefficient of xx on yy and yy on xx are −12-\dfrac{1}{2} and −18-\dfrac{1}{8} respectively, then what is the correlation coefficient between xx and yy?

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  117. 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?

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  118. 118
    If two fair dice are thrown, then what is the probability that the sum is neither 8 nor 9?

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  119. 119
    Let AA and BB are two mutually exclusive events with P(A)=13P(A)=\dfrac{1}{3} and P(B)=14P(B)=\dfrac{1}{4}. What is the value of P(Aˉ∩Bˉ)P(\bar{A}\cap\bar{B})?

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  120. 120
    The mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trials?

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