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NDA 2025 (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 px=qy=rzp^x = q^y = r^z, where xx, yy and zz are in GP, then consider the following statements: I. pp, qq and rr are in AP. II. ln⁡p\ln p, ln⁡q\ln q and ln⁡r\ln r are in GP. Which of the statements given above is/are correct?

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  2. 2
    If AA and BB are non-empty subsets of a set, and AcA^c and BcB^c represent their complements, then which of the following is/are correct? I. A−B=Bc−AcA - B = B^c - A^c II. A−Bc=Ac−BA - B^c = A^c - B. Select the answer using the code given below.

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  3. 3
    Let y=x!y = x! and z=(2x)!z = (2x)!. If (z/y)=120(z/y) = 120, then what is the value of (3x)!(3x)!?

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  4. 4
    Let nn be a natural number. The number of consecutive zeros at the end of the expansion of n!n! is exactly 2. How many values of nn are possible?

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  5. For the following two (02) items: Let α\alpha and β\beta be the roots of the quadratic equation x2+(log⁡0.5(a2))x+(log⁡0.5(a2))4=0x^2 + (\log_{0.5}(a^2))x + (\log_{0.5}(a^2))^4 = 0 where a2≠1a^2 \neq 1 and log⁡0.5(a2)>0\log_{0.5}(a^2) > 0. Further, β2=α(log⁡a2(0.5))\beta^2 = \alpha(\log_{a^2}(0.5)).
    5
    If (10+log⁡10x)(10 + \log_{10} x), (10+log⁡10y)(10 + \log_{10} y) and (10+log⁡10z)(10 + \log_{10} z) are in AP, then consider the following statements: I. The GM of xx and zz is y2y^2. II. The AM of log⁡10x\log_{10} x and log⁡10z\log_{10} z is log⁡10y\log_{10} y. Which of the statements given above is/are correct?

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  6. 6
    How many terms of the series 1+3+5+7+…1+3+5+7+\ldots amount to a sum equal to 1234567898765432112345678987654321?

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  7. 7
    How many terms are identical in the two APs 19,21,23,…19, 21, 23, \ldots up to 110 terms and 19,22,25,28,…19, 22, 25, 28, \ldots up to 75 terms?

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  8. 8
    If α=−1+−32\alpha = \dfrac{-1+\sqrt{-3}}{2}, then what is the value of (1+α19−α35)100−(1−3α25+α38)50(1+\alpha^{19}-\alpha^{35})^{100}-(1-3\alpha^{25}+\alpha^{38})^{50}?

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  9. 9
    What is the remainder when 5995^{99} is divided by 13?

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  10. 10
    What is the value of the determinant of the inverse of the matrix (−4−522)\begin{pmatrix}-4 & -5 \\ 2 & 2\end{pmatrix}?

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  11. 11
    In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play at least one of the two games. How many students like to play exactly one game?

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  12. 12
    The system of equations 2x−3y−5=02x-3y-5=0, 15y−10x+50=015y-10x+50=0:

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  13. 13
    If (1−i1+i)2m(1+i1−i)2n=1\left(\dfrac{1-i}{1+i}\right)^{2m}\left(\dfrac{1+i}{1-i}\right)^{2n}=1 where i=−1i=\sqrt{-1}, then what is the smallest positive value of (m−n)(m-n)?

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  14. 14
    In obtaining the solution of the system of equations x+y+z=7x+y+z=7, x+2y+3z=16x+2y+3z=16 and x+3y+4z=22x+3y+4z=22 by Cramer's rule, the value of yy is obtained by dividing DD by D2D_2, where D=∣111123134∣D=\begin{vmatrix}1&1&1\\1&2&3\\1&3&4\end{vmatrix}. What is the value of the determinant D2D_2?

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  15. 15
    Consider the following in respect of non-singular matrices AA and BB: I. (AB)−1=A−1B−1(AB)^{-1}=A^{-1}B^{-1} II. (BA)(AB)−1=I(BA)(AB)^{-1}=I, where II is the identity matrix III. (AB)T=ATBT(AB)^T = A^T B^T. How many of the above are correct?

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  16. 16
    The value of the determinant ∣abclmnpqr∣\begin{vmatrix}a&b&c\\l&m&n\\p&q&r\end{vmatrix} is equal to

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  17. 17
    Let 1,ω,ω21,\omega,\omega^2 be three cube roots of unity. If x=a+bx=a+b, y=aω+bω2y=a\omega+b\omega^2, z=aω2+bωz=a\omega^2+b\omega, then what is x2+y2+z2x^2+y^2+z^2 equal to?

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  18. 18
    How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?

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  19. 19
    If aa, bb, cc are the sides of a triangle ABCABC and pp is the perimeter of the triangle, then what is ∣p+cabcp+abcap+b∣\begin{vmatrix}p+c & a & b\\c & p+a & b\\c & a & p+b\end{vmatrix} equal to?

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  20. 20
    Which one of the following is the greatest coefficient in the expansion of (1+x)100(1+x)^{100}?

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  21. For the following two (02) items: Let α\alpha and β\beta be the roots of the quadratic equation x2+(log⁡0.5(a2))x+(log⁡0.5(a2))4=0x^2+(\log_{0.5}(a^2))x+(\log_{0.5}(a^2))^4=0 where a2≠1a^2\neq 1 and log⁡0.5(a2)>0\log_{0.5}(a^2)>0. Further, β2=α(log⁡a2(0.5))\beta^2=\alpha(\log_{a^2}(0.5)).
    21
    What is β\beta equal to?

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  22. 22
    What is the relation between α\alpha and β\beta?

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  23. For the following two (02) items: Let p=∑j=1nlog⁡102jp=\sum_{j=1}^{n}\log_{10}2^j and q=∑j=1nlog⁡105jq=\sum_{j=1}^{n}\log_{10}5^j.
    23
    If p+q=66p+q=66, then which one of the following is correct?

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  24. 24
    If p+q=15p+q=15, then what is q−pq-p equal to?

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  25. For the following two (02) items: Let sin⁡A+sin⁡B=p\sin A + \sin B = p and cos⁡A+cos⁡B=q\cos A + \cos B = q.
    25
    What is pq\dfrac{p}{q} equal to?

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  26. 26
    What is p2−q2p2+q2\dfrac{p^2-q^2}{p^2+q^2} equal to?

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  27. For the following two (02) items: Let p=csc⁡20°p = \csc 20° and q=csc⁡70°q = \csc 70°.
    27
    What is (3p4−q4)\left(\dfrac{\sqrt{3}p}{4}-\dfrac{q}{4}\right) equal to?

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  28. 28
    What is p2+q2p2q2\dfrac{p^2+q^2}{p^2 q^2} equal to?

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  29. For the following two (02) items: Let cos⁡(2x+3y)=12\cos(2x+3y)=\frac{1}{2} and cos⁡(3x+2y)=32\cos(3x+2y)=\frac{\sqrt{3}}{2}, where −π<(2x+3y)<π-\pi<(2x+3y)<\pi and −π<(3x+2y)<π-\pi<(3x+2y)<\pi.
    29
    How many values does (x+y)(x+y) have?

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  30. 30
    How many values does (y−x)(y-x) have?

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  31. For the following two (02) items: Consider the equation abx2+bcx+ca=cax2+abx+bcabx^2+bcx+ca = cax^2+abx+bc.
    31
    If the roots of the equation are equal, then which one of the following is correct?

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  32. 32
    If the roots of the equation are equal, then aa, bb, cc are in

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  33. For the following two (02) items: Let (6+10+14+…(6+10+14+\ldots up to mm terms)=(1+3+5+7+…) = (1+3+5+7+\ldots up to nn terms)) where m<25m<25 and n<25n<25.
    33
    What is the relation between mm and nn?

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  34. 34
    How many values of mm are possible?

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  35. For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear.
    35
    How many triangles can be formed by joining these points?

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  36. 36
    How many quadrilaterals can be formed by joining these points?

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  37. For the following two (02) items: Let f(x)=ax2+bx+cf(x)=ax^2+bx+c be a quadratic polynomial such that f(1)=f(4)=2f(1)=f(4)=2. Further, 2 is a root of f(x)=0f(x)=0.
    37
    What is the other root of f(x)=0f(x)=0?

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  38. 38
    What is (a+b+c)(a+b+c) equal to?

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  39. For the following two (02) items: Let A=(cos⁡θsin⁡θ−sin⁡θcos⁡θ)A=\begin{pmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{pmatrix}.
    39
    What is the value of the determinant of the matrix A4A^4?

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  40. 40
    What is [adj A]−1[\text{adj}\,A]^{-1} equal to?

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  41. 41
    What is the sum of the binary numbers (101101101)2(101101101)_2 and (100011)2(100011)_2?

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  42. 42
    Set XX contains 3n3n elements and set YY contains 2n2n elements, and they have nn elements in common. How many elements does (X−Y)×(Y−X)(X-Y)\times(Y-X) have?

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  43. 43
    Let A={−3,−2,−1,0,1,2,3}A=\{-3,-2,-1,0,1,2,3\} and B={0,1,4,9}B=\{0,1,4,9\}. How many elements does the subset of A×BA\times B corresponding to the relation R={(x,y):∣x∣<y}R=\{(x,y):|x|<y\} have, where x∈Ax\in A and y∈By\in B?

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  44. 44
    Consider the following statements: Statement-I: If XX is an n×nn\times n matrix, then det⁡(mX)=mndet⁡(X)\det(mX)=m^n\det(X), where mm is a scalar. Statement-II: If YY is a matrix obtained from XX by multiplying any row or column by a scalar mm, then det⁡(Y)=mdet⁡(X)\det(Y)=m\det(X). Which one of the following is correct in respect of the above statements?

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  45. 45
    Consider the following statements about the matrix M=(712348572829651748)M=\begin{pmatrix}71&23&48\\57&28&29\\65&17&48\end{pmatrix}: Statement-I: The inverse of MM does not exist. Statement-II: MM is non-singular. Which one of the following is correct?

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  46. 46
    What is cot⁡−19+cosec−1 ⁣(414)\cot^{-1}9+\text{cosec}^{-1}\!\left(\dfrac{\sqrt{41}}{4}\right) equal to?

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  47. 47
    How many values of θ\theta, where −π<θ<π-\pi<\theta<\pi, satisfy both the equations cot⁡θ=−3\cot\theta=-\sqrt{3} and csc⁡θ=−2\csc\theta=-2 simultaneously?

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  48. 48
    If x+1x=2cos⁡θx+\dfrac{1}{x}=2\cos\theta, then what is x3+1x3x^3+\dfrac{1}{x^3} equal to?

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  49. 49
    If 0≤x≤π20\leq x\leq\dfrac{\pi}{2}, then what is the number of values of xx satisfying the equation tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2\cos x?

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  50. 50
    What is the value of tan⁡ ⁣[12sec⁡−1 ⁣(23)]\tan\!\left[\dfrac{1}{2}\sec^{-1}\!\left(\dfrac{2}{\sqrt{3}}\right)\right]?

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  51. For the following two (02) items: A plane PP is parallel to the line having direction ratios ⟨1,3,2⟩\langle1,3,2\rangle and contains the line of intersection of the planes 6x+4y−5z=26x+4y-5z=2 and x−2y+3z=0x-2y+3z=0.
    51
    Which of the following are the direction ratios of the line of intersection of the given planes?

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  52. 52
    What is the equation of the plane PP?

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  53. For the following two (02) items: Suppose SS is the sphere with the smallest radius that passes through the points A(1,0,0)A(1,0,0), B(0,1,0)B(0,1,0) and C(0,0,1)C(0,0,1).
    53
    What is the radius of SS?

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  54. 54
    On which one of the following planes does the centre of SS lie?

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  55. For the following two (02) items: Let A(1,−1,0)A(1,-1,0), B(−2,1,8)B(-2,1,8) and C(−1,2,7)C(-1,2,7) are three consecutive vertices of a parallelogram ABCDABCD.
    55
    What is the fourth vertex DD?

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  56. 56
    If angle BCDBCD is θ\theta, then what is cos⁡2θ\cos^2\theta equal to?

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  57. 57
    For different values of mm, the equation 4y=mx−m+24y=mx-m+2 represents

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  58. 58
    The equation of the locus of a point equidistant from the points (a,b)(a,b) and (c,d)(c,d) is (a−c)x+(b−d)y+k=0(a-c)x+(b-d)y+k=0. What is the value of kk?

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  59. 59
    Consider the following statements in respect of the equation x2+3y=0x^2+3y=0: I. The equation represents the equation to parabola that opens upwards. II. The axis of the parabola is x=0x=0. III. The equation of the latus rectum is 4y−3=04y-3=0. How many of the statements given above are correct?

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  60. 60
    What is the sum of the intercepts of the line xa2+yb2=2a2+b2\dfrac{x}{a^2}+\dfrac{y}{b^2}=\dfrac{2}{a^2+b^2} on the coordinate axes?

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  61. 61
    Which one of the following is the perpendicular form of the straight line 3x+2y=7\sqrt{3}x+2y=7?

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  62. 62
    If the vertices BB and DD of a square ABCDABCD are (2,3)(2,3) and (4,1)(4,1) respectively, then what is the area of the square?

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  63. 63
    What is the value of sin⁡θ\sin\theta if θ\theta is the acute angle between the lines whose equations are px+qy=p+qpx+qy=p+q and p(x−y)+q(x+y)=2qp(x-y)+q(x+y)=2q?

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  64. 64
    The circle x2+y2−2kx−2ky+k2=0x^2+y^2-2kx-2ky+k^2=0 touches the xx-axis at PP and yy-axis at QQ. What is PQPQ equal to?

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  65. 65
    What is the distance between the foci of the hyperbola x2−4y2=1x^2-4y^2=1?

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  66. 66
    Let p⃗=a⃗−b⃗\vec{p}=\vec{a}-\vec{b}, q⃗=a⃗+b⃗\vec{q}=\vec{a}+\vec{b}. If ∣a⃗∣=∣b⃗∣=2|\vec{a}|=|\vec{b}|=2 and a⃗⋅b⃗=2\vec{a}\cdot\vec{b}=2, then what is the value of ∣p⃗×q⃗∣|\vec{p}\times\vec{q}|?

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  67. 67
    How many of the following can be a vector perpendicular to both the vectors 2i^−j^+k^2\hat{i}-\hat{j}+\hat{k} and i^+j^+3k^\hat{i}+\hat{j}+3\hat{k}? I. 4i^+5j^−3k^4\hat{i}+5\hat{j}-3\hat{k} II. −8i^−10j^+6k^-8\hat{i}-10\hat{j}+6\hat{k} III. 150(−4i^−5j^+3k^)\frac{1}{50}(-4\hat{i}-5\hat{j}+3\hat{k}). Select the correct answer.

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  68. 68
    What is the area of the parallelogram whose sides are represented by the vectors i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k} and 2i^+j^+2k^2\hat{i}+\hat{j}+2\hat{k}?

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  69. 69
    The position vectors of the vertices AA, BB, CC and DD of a quadrilateral ABCDABCD are given by 3i^+4j^−2k^3\hat{i}+4\hat{j}-2\hat{k}, 4i^−4j^−3k^4\hat{i}-4\hat{j}-3\hat{k}, 2i^−3j^+2k^2\hat{i}-3\hat{j}+2\hat{k} and 6i^−2j^+k^6\hat{i}-2\hat{j}+\hat{k} respectively. What is the angle between the diagonals ACAC and BDBD of the quadrilateral?

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  70. 70
    A force F⃗=2i^−λj^+5k^\vec{F}=2\hat{i}-\lambda\hat{j}+5\hat{k} is applied at the point A(1,2,5)A(1,2,5). If its moment about the point B(−1,−2,3)B(-1,-2,3) is 16i^−6j^+2λk^16\hat{i}-6\hat{j}+2\lambda\hat{k}, then what is the value of λ\lambda?

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  71. For the following two (02) items: Let f(x)={1−cos⁡2xx2,x<09,x=0x(16+x)−4,x>0f(x)=\begin{cases}\dfrac{1-\cos2x}{x^2}, & x<0\\ 9, & x=0\\ \dfrac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & x>0\end{cases}
    71
    What is lim⁡x→0−f(x)\displaystyle\lim_{x\to 0^-}f(x) equal to?

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  72. 72
    What is lim⁡x→0+f(x)\displaystyle\lim_{x\to 0^+}f(x) equal to?

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  73. For the following three (03) items: Consider the function f(x)=x∣x∣f(x)=x|x|.
    73
    What is lim⁡x→−1f(x)\displaystyle\lim_{x\to-1}f(x) equal to?

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  74. 74
    What is the area bounded by the curve f(x)f(x), the xx-axis and the lines x=−2x=-2 and x=1x=1?

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  75. 75
    Consider the following statements: I. The function is increasing in the interval (−∞,∞)(-\infty,\infty). II. The function is differentiable at x=0x=0. Which of the statements given above is/are correct?

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  76. For the following two (02) items: Consider the function f(x)=x1−xf(x)=\dfrac{x}{1-x} (x>0, x≠1)(x>0,\,x\neq1).
    76
    What is f(x)f(x+1)\dfrac{f(x)}{f(x+1)} equal to?

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  77. 77
    What is (1−x)f(x)+xf(x+1)(1-x)f(\sqrt{x})+xf(\sqrt{x}+1) equal to?

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  78. For the following three (03) items: Let y=f(x)=xsin⁡−1x1−x2+ln⁡1−x2y=f(x)=\dfrac{x\sin^{-1}x}{\sqrt{1-x^2}}+\ln\sqrt{1-x^2}.
    78
    What is the slope of the tangent to the curve y=f(x)y=f(x) at x=0.5x=0.5?

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  79. 79
    What is d2ydx2\dfrac{d^2y}{dx^2} at x=0x=0 equal to?

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  80. 80
    If x=sin⁡θx=\sin\theta, then what is dydx\dfrac{dy}{dx} equal to?

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  81. For the following two (02) items: Consider the function f(x)=1−(x−1)23f(x)=1-\sqrt[3]{(x-1)^2}.
    81
    What is the domain of the function?

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  82. 82
    The function has

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  83. For the following two (02) items: Consider the function f(x)={4(5x),x<08k+x,x≥0f(x)=\begin{cases}4(5^x), & x<0\\ 8k+x, & x\geq0\end{cases}.
    83
    If the function is continuous, then what is the value of kk?

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  84. 84
    What is f′(−1)f'(-1) equal to?

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  85. For the following two (02) items: Let u=∫excos⁡x dxu=\int e^x\cos x\,dx and v=∫exsin⁡x dxv=\int e^x\sin x\,dx.
    85
    What is u+vu+v equal to?

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  86. 86
    Consider the following: I. dudx=−v\dfrac{du}{dx}=-v II. dvdx=−u\dfrac{dv}{dx}=-u. Which of the above is/are correct?

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  87. For the following two (02) items: Let the function f(x)=∣x−3∣+∣x−4∣f(x)=|x-3|+|x-4| be defined on the interval [0,5][0,5].
    87
    What is dydx\dfrac{dy}{dx} at x=3.5x=3.5 equal to?

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  88. 88
    Consider the following statements: I. The function is differentiable at x=3x=3. II. The function is differentiable at x=4x=4. Which of the statements given above is/are correct?

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  89. For the following two (02) items: Consider the function f(x)=10x−10−x10x+10−xf(x)=\dfrac{10^x-10^{-x}}{10^x+10^{-x}}.
    89
    What is f∘f∘f∘f∘f(0)f\circ f\circ f\circ f\circ f(0) equal to?

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  90. 90
    What is the inverse of the function?

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  91. 91
    What is the degree of the differential equation (d2ydx2)3/2=(dydx)5/2\left(\dfrac{d^2y}{dx^2}\right)^{3/2}=\left(\dfrac{dy}{dx}\right)^{5/2}?

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  92. 92
    What is ∫nn+1(x−[x]) dx\int_n^{n+1}(x-[x])\,dx, where [⋅][\cdot] is the greatest integer function and nn is natural number?

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  93. 93
    Consider the following statements: I. y=xe2xy=xe^{2x} is the solution of dydx=y ⁣(2+1x)\dfrac{dy}{dx}=y\!\left(2+\dfrac{1}{x}\right). II. y=xln⁡∣x∣+cxy=x\ln|x|+cx is the solution of dydx=x+yx\dfrac{dy}{dx}=\dfrac{x+y}{x}. Which of the statements given above is/are correct?

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  94. 94
    If kk is an arbitrary constant, then what is the general solution of the equation (x+y)2dydx=k2(x+y)^2\dfrac{dy}{dx}=k^2?

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  95. 95
    What is ∫dx10x+10−x\displaystyle\int\dfrac{dx}{10^x+10^{-x}} equal to?

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  96. 96
    A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct? I. The rectangle of the largest area is the square. II. It is possible to form a rectangle of an area of 27 cm2^2. Select the answer using the code given below.

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  97. 97
    If I1=∫ee2dxln⁡xI_1=\int_e^{e^2}\dfrac{dx}{\ln x} and I2=∫12exx dxI_2=\int_1^2\dfrac{e^x}{x}\,dx, then which one of the following is correct?

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  98. 98
    What is the area of the region bounded by ∣x∣≤2k|x|\leq2k and ∣y∣≤k|y|\leq k, where kk is a positive real number?

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  99. 99
    Consider the following statements regarding the function f(x)=1x−5f(x)=\dfrac{1}{x-5}: Statement-I: f(x)f(x) is decreasing on the intervals x<5x<5 and x>5x>5. Statement-II: f′(x)>0f'(x)>0 for all x≠5x\neq5. Which one of the following is correct?

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  100. 100
    Consider the following statements: Statement-I: The function f(x)=x3+128xf(x)=\dfrac{x^3+128}{x} has a minimum value 48 at x=4x=4. Statement-II: As xx increases through 4, f′(x)f'(x) changes sign from positive to negative. Which one of the following is correct?

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  101. 101
    What is the harmonic mean of the numbers C(10,3)C(10,3), C(10,4)C(10,4), C(10,5)C(10,5), C(10,6)C(10,6) and C(10,7)C(10,7)?

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  102. 102
    In a sample survey of a village, the probability that a farmer is in debt is 0.60. What is the probability that three randomly selected farmers are all in debt (assume independence of events)?

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  103. 103
    The probability that a family owns a laptop is 0.68; that it also owns a desktop is 0.56. If the probability that it owns both is 0.48, then what is the probability that a randomly selected family owns a laptop or a desktop?

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  104. 104
    An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?

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  105. 105
    An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is the probability that a white ball, a red ball and a blue ball are drawn?

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  106. 106
    Under which of the following conditions may binomial distribution be used? I. The number of trials is infinite and not fixed. II. The trials are independent. III. Each trial has two possible outcomes. Select the correct answer using the code given below.

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  107. 107
    A person XX speaks the truth 4 out of 5 times and person YY speaks the truth 5 out of 6 times. What is the probability that they will contradict each other in stating the fact?

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  108. 108
    The probability that a student passes Physics test is 2/3 and the probability that he passes both Physics test and English test is 11/15. The probability that he passes at least one test is 4/5. What is the probability that he passes English test?

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  109. 109
    An event XX can happen with probability pp and event YY can happen with probability qq. Further, XX and YY are independent events. Which of the following statements is/are correct? I. The probability that exactly one of the events happens is p+q−pqp+q-pq. II. The probability that at least one of the events happens is p+q−2pqp+q-2pq. Select the answer using the code given below.

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  110. 110
    Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the colours black, white and red appear in the first, second and third tosses respectively?

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  111. 111
    A fair coin is tossed 4 times. What is the probability that two heads do not occur consecutively?

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  112. 112
    In a throw of three dice, what is the probability of getting one prime number, one composite number and one number which is neither prime nor composite?

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  113. 113
    An integer is chosen at random from the first 50 integers. What is the probability that the integer is neither divisible by 5 nor 9?

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  114. 114
    Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

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  115. 115
    The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard deviation?

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  116. 116
    Let XX be a random variable following binomial distribution with parameters n=5n=5 and p=kp=k. Further, P(X=1)=0.4096P(X=1)=0.4096 and P(X=2)=0.2048P(X=2)=0.2048. What is the value of kk?

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  117. 117
    The frequency distribution of the marks obtained by students in a Science examination is given below: Marks: 5–15, 15–25, 25–35, 35–45; Number of students: 20, 30, 30, 20. What is the arithmetic mean?

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  118. 118
    If P(A)=0.3P(A)=0.3, P(B)=0.4P(B)=0.4 and P(A∣B)=0.5P(A|B)=0.5, then what is the value of P(B∣A)P(B|A)?

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  119. 119
    If P(A)=1/3P(A)=1/3, P(B)=1/2P(B)=1/2 and P(A∩B)=1/4P(A\cap B)=1/4, then what is the value of P(Aˉ∪B)P(\bar{A}\cup B)?

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  120. 120
    Consider the following statements: I. Mean and variance have the same unit of measurement. II. Mean deviation and standard deviation have the same unit of measurement. Which of the statements given above is/are correct?

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