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NDA 2026 (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 p, q and r be three unequal numbers such that p, q and r are in AP. If (q−p)(q-p), (r−q)(r-q) and pp are in GP, then (p+q):(q+r):(r+p)(p+q):(q+r):(r+p) equals

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  2. 2
    If p, g1g_1, g2g_2 and q are in GP and m is the arithmetic mean of p and q, then g12g2+g22g1\dfrac{g_1^2}{g_2}+\dfrac{g_2^2}{g_1} is equal to

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  3. 3
    Consider the following inequalities: I. 1+4i>3+2i1+4i>3+2i II. 2+3i<3+4i2+3i<3+4i III. 4+3i>3+4i4+3i>3+4i where i=−1i=\sqrt{-1}. How many of the above are valid?

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  4. 4
    Let Z1Z_1 and Z2Z_2 be complex numbers such that 3Z14Z2\dfrac{3Z_1}{4Z_2} is purely imaginary. What is ∣Z1+Z2Z1−Z2∣\left|\dfrac{Z_1+Z_2}{Z_1-Z_2}\right| equal to?

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  5. 5
    If α\alpha, β\beta, γ\gamma are cube roots of −8-8, then what is α2p2+β2q2+γ2r2β2p2+γ2q2+α2r2\dfrac{\alpha^2p^2+\beta^2q^2+\gamma^2r^2}{\beta^2p^2+\gamma^2q^2+\alpha^2r^2} equal to?

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  6. 6
    The sum of the first nn terms of an AP is 3n2+5n3n^2+5n. If the mthm^{\text{th}} term of the AP is 68, then what is the value of mm?

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  7. 7
    A set S contains (2n+1)(2n+1) elements. If the number of subsets of S which contain at most nn elements is 1024, then what is the value of nn?

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  8. 8
    What is the maximum number of points of intersection of 5 circles?

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  9. 9
    What is the greatest value of rr satisfying the inequality 15Cr+1>2× 15Cr^{15}C_{r+1}>2\times\,^{15}C_r?

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  10. 10
    If n= mC2n=\,^mC_2 then what is nC2^nC_2 equal to?

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  11. 11
    If the highest degree coefficient is equal to 1, then what is the total number of quadratic equations which are unchanged on squaring their roots?

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  12. 12
    Let α\alpha and β\beta be the roots of the quadratic equation x2−2bx+c2=0x^2-2bx+c^2=0 where bb, cc are positive real numbers. Let A be the arithmetic mean of α\alpha and β\beta; and G be the geometric mean of α\alpha and β\beta. What are the roots of the quadratic equation x2−(b+c)x+bc=0x^2-(b+c)x+bc=0?

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  13. 13
    If 1−log⁡102=log⁡10(5x+4x+3x+2x+1)1-\log_{10}2=\log_{10}(5^x+4^x+3^x+2^x+1), then what is a value of xx?

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  14. 14
    Let f(x)=∣3x2cos⁡x−sin⁡x6−10qq2q3∣f(x)=\begin{vmatrix}3x^2 & \cos x & -\sin x\\ 6 & -1 & 0\\ q & q^2 & q^3\end{vmatrix} where qq is any constant, then what is d2dx2(f(x))\dfrac{d^2}{dx^2}(f(x)) at x=0x=0 equal to?

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  15. 15
    If ∣a−bp−qx−yb−cq−ry−zc−ar−pz−x∣=k∣abcpqrxyz∣\begin{vmatrix}a-b & p-q & x-y\\b-c & q-r & y-z\\c-a & r-p & z-x\end{vmatrix}=k\begin{vmatrix}a & b & c\\p & q & r\\x & y & z\end{vmatrix}, then what is the value of kk?

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  16. 16
    If pp, qq, rr are the cube roots of unity, then what is ∣p2+q2r2r2p2q2+r2p2q2q2r2+p2∣\begin{vmatrix}p^2+q^2 & r^2 & r^2\\p^2 & q^2+r^2 & p^2\\q^2 & q^2 & r^2+p^2\end{vmatrix} equal to?

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  17. 17
    If A is a square matrix such that ∣A∣=−2|A|=-2, then ∣AAT∣|AA^T|, where ATA^T is the transpose of A, is equal to

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  18. 18
    Consider the following statements: I. If n×nn\times n (n>1n>1) matrix is symmetric, then its inverse is also a symmetric matrix. II. If n×nn\times n (n>1n>1) matrix is singular, then its adjoint is also a singular matrix. Which of the statements given above is/are correct?

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  19. 19
    If M=(200020002)M=\begin{pmatrix}2&0&0\\0&2&0\\0&0&2\end{pmatrix}, then what is the value of ∣M∣⋅∣adjM∣|M|\cdot|\text{adj}M|?

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  20. 20
    If Mk=(kk−1k−1k)M_k=\begin{pmatrix}k & k-1\\k-1 & k\end{pmatrix} where kk is a natural number, then what is ∣M1∣+∣M2∣+∣M3∣+…+∣M50∣|M_1|+|M_2|+|M_3|+\ldots+|M_{50}| equal to?

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  21. 21
    If MTM^T is the transpose of a 2×22\times2 matrix M, then which of the following is/are correct? I. ∣M+MT∣=∣M∣+∣MT∣|M+M^T|=|M|+|M^T| if M is symmetric. II. ∣M+MT∣=0|M+M^T|=0 if M is anti-symmetric. Select the answer using the code given below.

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  22. 22
    If M is a square matrix such that M3=MM^3=M, then how many values of ∣M∣|M| are possible?

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  23. 23
    Let p=(x+y+z)p=(x+y+z) and q=xyzq=xyz. If ∣x111y111z∣\begin{vmatrix}x&1&1\\1&y&1\\1&1&z\end{vmatrix} is positive, then which one of the following is correct?

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  24. 24
    What is (((A∩B)∪(A−B))−((A∩B)∪(B−A)))∪A(((A\cap B)\cup(A-B))-((A\cap B)\cup(B-A)))\cup A equal to?

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  25. 25
    Let A and B be two sets. For some set C, both A∩CA\cap C and B∩CB\cap C are empty sets and A∪C=B∪CA\cup C=B\cup C. Which of the following is/are true? I. C=φC=\varphi II. A=BA=B III. A∪B=CA\cup B=C. Select the answer using the code given below.

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  26. 26
    If 2sec⁡4β=tan⁡2α+cot⁡2α2\sec4\beta=\tan2\alpha+\cot2\alpha, then which one of the following is a possible value of (α+β)(\alpha+\beta)?

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  27. 27
    If α\alpha and β\beta are complementary angles such that α−β=π6\alpha-\beta=\dfrac{\pi}{6} and mtan⁡β=ntan⁡αm\tan\beta=n\tan\alpha, then what is (m+nm−n)\left(\dfrac{m+n}{m-n}\right) equal to?

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  28. 28
    If x=sec⁡θ−tan⁡θx=\sec\theta-\tan\theta and y=csc⁡θ+cot⁡θy=\csc\theta+\cot\theta, then which one of the following is correct?

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  29. 29
    If cos⁡θ=13\cos\theta=\dfrac{1}{3}, then what is the value of sin⁡ ⁣(θ2)sin⁡ ⁣(3θ2)\sin\!\left(\dfrac{\theta}{2}\right)\sin\!\left(\dfrac{3\theta}{2}\right)?

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  30. 30
    cos⁡x+3sin⁡x\cos x+\sqrt{3}\sin x is maximum when xx is equal to

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  31. 31
    If θ\theta lies in the fourth quadrant and 3cot⁡θ+4=03\cot\theta+4=0, then what is the value of sin⁡2θ+cos⁡2θ\sin2\theta+\cos2\theta?

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  32. 32
    If cos⁡α+cos⁡β=0=sin⁡α+sin⁡β\cos\alpha+\cos\beta=0=\sin\alpha+\sin\beta, α≠β\alpha\neq\beta, then what is a value of cos⁡2α+cos⁡2β+2cos⁡(α+β)\cos2\alpha+\cos2\beta+2\cos(\alpha+\beta)?

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  33. 33
    In a triangle ABC, sin⁡A=cos⁡B+cos⁡C\sin A=\cos B+\cos C, then what is tan⁡ ⁣(B2)+cot⁡ ⁣(B2)\tan\!\left(\dfrac{B}{2}\right)+\cot\!\left(\dfrac{B}{2}\right) equal to?

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  34. 34
    Consider the following in respect of inverse circular functions: I. sin⁡−1(−x)=−sin⁡−1x\sin^{-1}(-x)=-\sin^{-1}x II. cos⁡−1(−x)=cos⁡−1x\cos^{-1}(-x)=\cos^{-1}x III. tan⁡−1(−x)=π−tan⁡−1x\tan^{-1}(-x)=\pi-\tan^{-1}x IV. cot⁡−1(−x)=π−cot⁡−1x\cot^{-1}(-x)=\pi-\cot^{-1}x. How many of the above are correct?

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  35. 35
    What is tan⁡ ⁣[2tan⁡−112−π4]\tan\!\left[2\tan^{-1}\dfrac{1}{2}-\dfrac{\pi}{4}\right] equal to?

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  36. 36
    The angles A, B and C of a triangle are in the ratio 1:1:4. If the longest side of the triangle is 3 units, then what is the perimeter of the triangle?

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  37. 37
    In a triangle ABC, if aa, bb and cc are the lengths of the sides opposite to the angles A, B and C respectively, then what is sin⁡(A−B)sin⁡(A+B)\dfrac{\sin(A-B)}{\sin(A+B)} equal to?

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  38. 38
    What is the smallest positive xx satisfying log⁡sin⁡xcos⁡x+log⁡cos⁡xsin⁡x=2\log_{\sin x}\cos x+\log_{\cos x}\sin x=2?

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  39. 39
    A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67.5°. What is the height of the plane above the ground?

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  40. 40
    What is the length of the chord of a unit circle which subtends at the centre of the circle an angle of 45°?

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  41. 41
    Let R be a relation on the set N of natural numbers defined by R={(x,y):x,y∈N and x=y3}R=\{(x,y):x,y\in N\text{ and }x=y^3\}. Which of the following statements is/are correct? I. R is symmetric relation. II. R is transitive relation. Select the answer using the code given below.

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  42. 42
    For a given kk, what is the minimum value of x2+kx+k2x^2+kx+k^2?

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  43. 43
    Consider the following statements: I. x+x+1=0\sqrt{x}+x+1=0 has two irrational roots. II. 5x−x−4=05\sqrt{x}-x-4=0 has two rational roots. Which of the statements given above is/are correct?

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  44. 44
    How many numbers greater than 1000 can be formed using the digits 0, 1, 2 and 3 (repetition of digits is not allowed)?

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  45. 45
    If pthp^{\text{th}} term of an AP is kk, then what is the sum of pthp^{\text{th}} term, (p+q)th(p+q)^{\text{th}} term and (p−q)th(p-q)^{\text{th}} term of the AP?

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  46. For the next five (05) items that follow: Let u be a positive integer and f be a real number lying between 0 and 1. Further, (2+1)10=u+f(\sqrt{2}+1)^{10}=u+f and (2−1)10=v(\sqrt{2}-1)^{10}=v.
    46
    Consider the following statements: I. (u+v+f)(u+v+f) is an integer. II. (f+v)(f+v) is an integer. Which of the statements given above is/are correct?

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  47. 47
    What is the multiplicative inverse of (2+1)20(\sqrt{2}+1)^{20}?

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  48. 48
    What is the value of (v+f)(v+f)?

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  49. 49
    What is the value of u?

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  50. 50
    What is the value of uv?

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  51. For the next two (02) items that follow: The equation of a straight line which passes through the origin and makes an angle α\alpha (0≤α≤90°0\leq\alpha\leq90°) with the line L: x+3y+33=0x+\sqrt{3}y+3\sqrt{3}=0 is x−3y=0x-\sqrt{3}y=0.
    51
    What is the value of α\alpha?

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  52. 52
    What is the angle made by the line L with positive direction of y-axis?

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  53. For the next two (02) items that follow: P(-2,-3,5), Q(4,-1,5), R(6,-4,8) and S(2,-6,10) are four points.
    53
    Consider the following statements: I. PQ is parallel to RS. II. PR is perpendicular to QS. Which of the statements given above is/are correct?

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  54. 54
    What is (PQ2+2QS2−2PR2)(PQ^2+2QS^2-2PR^2) equal to?

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  55. For the next two (02) items that follow: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0.
    55
    What is the equation of the line L?

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  56. 56
    What are the direction ratios of a line M parallel to the plane P?

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  57. For the next two (02) items that follow: Let X(a,p), Y(b,q) and Z(c,r) be the points such that a, b and c are in AP.
    57
    If p, q and r are in AP, then the points X, Y and Z are

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  58. 58
    If p, q and r are not in AP and b=cb=c, then the line joining the points X, Y and Z is parallel to

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  59. For the next two (02) items that follow: Consider the points A(0,2), B(2,3), C(4,5) and D(0,k).
    59
    If the points lie on a circle, then what is/are the possible value(s) of k?

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  60. 60
    If a circle is drawn through A, B and D, then what is the diameter of the circle?

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  61. For the next two (02) items that follow: The foci of the ellipse px2+16y2=16ppx^2+16y^2=16p and the foci of the hyperbola 25(81x2−144y2)=1166425(81x^2-144y^2)=11664 coincide (assume p<16p<16).
    61
    What is the value of p?

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  62. 62
    What is the difference between the eccentricities of the hyperbola and the ellipse?

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  63. For the next two (02) items that follow: The equation of the sphere S is x2+y2+z2−4x−6y−12z+k=0x^2+y^2+z^2-4x-6y-12z+k=0.
    63
    What is the radius of the sphere passing through origin and concentric with the sphere S?

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  64. 64
    If the radius of the sphere S is 8 units, what is the value of k?

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  65. For the next two (02) items that follow: Let a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c}, a⃗+b⃗\vec{a}+\vec{b}, b⃗+c⃗\vec{b}+\vec{c}, a⃗+b⃗+c⃗\vec{a}+\vec{b}+\vec{c} be unit vectors.
    65
    What is the angle between a⃗\vec{a} and b⃗\vec{b}?

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  66. 66
    What is the angle between a⃗\vec{a} and c⃗\vec{c}?

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  67. For the next two (02) items that follow: Let a⃗×b⃗=c⃗\vec{a}\times\vec{b}=\vec{c} and b⃗×c⃗=a⃗\vec{b}\times\vec{c}=\vec{a}.
    67
    Consider the following statements: I. a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} are orthogonal in pairs. II. a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} are unit vectors. Which of the statements given above is/are correct?

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  68. 68
    Consider the following statements: I. (a⃗×b⃗)⋅c⃗+(b⃗×c⃗)⋅a⃗=(c⃗×a⃗)⋅b⃗(\vec{a}\times\vec{b})\cdot\vec{c}+(\vec{b}\times\vec{c})\cdot\vec{a}=(\vec{c}\times\vec{a})\cdot\vec{b}. II. {(a⃗×b⃗)×(b⃗×c⃗)}⋅b⃗=1\{(\vec{a}\times\vec{b})\times(\vec{b}\times\vec{c})\}\cdot\vec{b}=1. Which of the statements given above is/are correct?

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  69. For the next two (02) items that follow: Let a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} be unit vectors. Further, a⃗\vec{a} is perpendicular to b⃗\vec{b}; c⃗\vec{c} makes angle π3\frac{\pi}{3} with both a⃗\vec{a} and b⃗\vec{b}; and c⃗=pa⃗+qb⃗+r(a⃗×b⃗)\vec{c}=p\vec{a}+q\vec{b}+r(\vec{a}\times\vec{b}).
    69
    What is the value of (p+q)(p+q)?

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  70. 70
    What is the value of r2r^2?

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  71. 71
    If f(x)f(x) is differentiable at x=ax=a, then consider the following statements: I. f(x)f(x) is continuous at x=ax=a. II. lim⁡x→af(x)=f(a)\lim_{x\to a}f(x)=f(a). Which of the statements given above is/are correct?

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  72. 72
    What is lim⁡x→1x(n2−1)−1x(n+1)−1\lim_{x\to1}\dfrac{x^{(n^2-1)}-1}{x^{(n+1)}-1} equal to, where n>1n>1 is a natural number?

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  73. 73
    What is lim⁡x→010sin⁡x−1tan⁡x\lim_{x\to0}\dfrac{10^{\sin x}-1}{\tan x} equal to?

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  74. 74
    What is the derivative of x∣x∣\dfrac{x}{|x|} with respect to xx, where x<0x<0?

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  75. 75
    Consider the following statements in respect of the function f(x)=xf(x)=x in the interval (−1,1)(-1,1): I. The function attains maximum value. II. The function attains minimum value. Which of the statements given above is/are correct?

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  76. 76
    If y4=x+x2+4\sqrt[4]{y}=x+\sqrt{x^2+4}, then what is x2+4dydx\sqrt{x^2+4}\dfrac{dy}{dx} equal to?

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  77. 77
    What is the length of the longest interval in which the function f(x)=2cos⁡2x−1f(x)=2\cos^2x-1 is decreasing?

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  78. 78
    If A and B are acute angles such that 2A+2B=π2A+2B=\pi, then what is the maximum value of sin⁡A⋅sin⁡B\sin A\cdot\sin B?

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  79. 79
    What is the solution of the differential equation cos⁡ ⁣(dydx)=p\cos\!\left(\dfrac{dy}{dx}\right)=p when y(0)=qy(0)=q?

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  80. 80
    If 2f(x)+f(1−x)=x2f(x)+f(1-x)=x, then what is f(x)f(x) equal to?

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  81. For the next two (02) items that follow: Let (ey)x−y=0(e^y)^x-y=0, where y is a function of x whose domain is (0,10].
    81
    What is dydx\dfrac{dy}{dx} equal to?

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  82. 82
    What is dydx\dfrac{dy}{dx} equal to, given that y=y0y=y_0 when x=1x=1?

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  83. For the next two (02) items that follow: Let ∫0π/2asin⁡x+bcos⁡x(a+b)(sin⁡x+cos⁡x)dx=k\int_0^{\pi/2}\dfrac{a\sin x+b\cos x}{(a+b)(\sin x+\cos x)}dx=k.
    83
    What is the value of k?

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  84. 84
    What is ∫0π/2acos⁡x+bsin⁡xsin⁡x+cos⁡xdx\int_0^{\pi/2}\dfrac{a\cos x+b\sin x}{\sin x+\cos x}dx equal to?

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  85. For the next two (02) items that follow: Let S and T be the sets where f(x)=x33−5x22+6x+7f(x)=\frac{x^3}{3}-\frac{5x^2}{2}+6x+7 decreases and increases respectively.
    85
    What is T equal to?

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  86. 86
    What is S equal to?

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  87. For the next two (02) items that follow: Let k be the area between the curve y=sinx and x-axis in the interval [0,π/4][0,\pi/4].
    87
    What is the area between the curve y=sinx and the x-axis in the interval [π/4,π/2][\pi/4,\pi/2]?

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  88. 88
    What is the area between the curve y=cosx and the x-axis in the interval [π/4,π/2][\pi/4,\pi/2]?

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  89. For the next two (02) items that follow: Consider the curves y=x^2 and y=2|x|.
    89
    What is the number of points of intersection of the curves?

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  90. 90
    What is the area bounded by the curves, the lines x=0 and x=1?

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  91. For the next two (02) items that follow: Let ∫sin⁡θ dθ(2+cos⁡θ)(3+4cos⁡θ)=Aln⁡∣2+cos⁡θ∣+Bln⁡∣3+4cos⁡θ∣\int\dfrac{\sin\theta\,d\theta}{(2+\cos\theta)(3+4\cos\theta)}=A\ln|2+\cos\theta|+B\ln|3+4\cos\theta|.
    91
    What is the value of A?

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  92. 92
    What is the value of B?

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  93. For the next two (02) items that follow: Let f(x)=sin⁡xf(x)=\sin x and g(x)−f(x)=f(4−x)g(x)-f(x)=f(4-x).
    93
    What is ∫04f(x)g(x)dx\int_0^4\dfrac{f(x)}{g(x)}dx equal to?

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  94. 94
    What is ∫04f(4−x)g(4−x)dx\int_0^4\dfrac{f(4-x)}{g(4-x)}dx equal to?

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  95. For the next two (02) items that follow: Let f(x)={ax(x−1),x<1x−1,1≤x≤3px2+qx+2,x>3f(x)=\begin{cases}ax(x-1), & x<1\\ x-1, & 1\leq x\leq3\\ px^2+qx+2, & x>3\end{cases}. Given that f(x)f(x) is continuous for all x but not differentiable at x=1. Further f′(x)f'(x) is continuous at x=3.
    95
    What is the value of p?

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  96. 96
    What is the value of q?

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  97. For the next two (02) items that follow: Consider the differential equation ex+ydydx=ex−ye^{x+y}\dfrac{dy}{dx}=e^{x-y}.
    97
    What is d2ydx2(dxdy)2\dfrac{d^2y}{dx^2}\left(\dfrac{dx}{dy}\right)^2 equal to?

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  98. 98
    What is the solution of the differential equation with y(0)=0y(0)=0?

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  99. For the next two (02) items that follow: Let f(x)=tan⁡(x2)f(x)=\tan(x^2) and g(x)=x∣x∣g(x)=x|x| for ∣x∣<π/2|x|<\sqrt{\pi/2}.
    99
    If p(x)=f(x)g(x)p(x)=f(x)g(x), then which of the following statements is/are correct? I. p(x)p(x) is continuous at x=0x=0. II. p(x)p(x) is differentiable at x=0x=0. Select the answer using the code given below.

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  100. 100
    If q(x)=f∘g(x)q(x)=f\circ g(x), then which of the following statements is/are correct? I. q(x)q(x) is continuous at x=0x=0. II. q(x)q(x) is differentiable at x=0x=0. Select the answer using the code given below.

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  101. For the next five (05) items that follow: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed).
    101
    What is the probability that the number selected is divisible by 2?

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  102. 102
    What is the probability that the number selected is divisible by 3?

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  103. 103
    What is the probability that the number selected is divisible by 4?

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  104. 104
    What is the probability that the number selected is divisible by 6?

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  105. 105
    What is the probability that the number selected does not contain zero at any position?

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  106. For the next three (03) items that follow: Let A, B, C and D be mutually exclusive and exhaustive events and P(A)2=P(B)3=P(C)5=P(D)8\dfrac{P(A)}{2}=\dfrac{P(B)}{3}=\dfrac{P(C)}{5}=\dfrac{P(D)}{8}.
    106
    What is P(A)+P(B)+P(C) equal to?

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  107. 107
    What is [2P(A)+3P(B)][4P(C)+5P(D)]\dfrac{[2P(A)+3P(B)]}{[4P(C)+5P(D)]} equal to?

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  108. 108
    If G is the geometric mean of P(A), P(B), P(C) and P(D), then what is 9G equal to?

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  109. For the next two (02) items that follow: Four dice are rolled.
    109
    What is the probability that getting a total of the numbers on the dice is 6?

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  110. 110
    What is the probability that getting a total of the numbers on the dice is at least 23?

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  111. 111
    Let two lines of regression be x+y+11=0x+y+11=0 and 2x+3y+4=02x+3y+4=0 for some data. What is the value of correlation coefficient between x and y?

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  112. 112
    If the mean of 20 observations, namely x1,x2,x3,…,x20x_1,x_2,x_3,\ldots,x_{20} is 1.414, then what is the value of ∑i=120100(2xi+4)\sum_{i=1}^{20}100(2x_i+4)?

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  113. 113
    In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then what is the probability that he was guessing?

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  114. 114
    Consider the following statements in respect of the events A, B, C: I. (A∪B∪C)∩(Aˉ∩Bˉ∩Cˉ)(A\cup B\cup C)\cap(\bar{A}\cap\bar{B}\cap\bar{C}) is an impossible event. II. (A∩B∩C)∩(Aˉ∪Bˉ∪Cˉ)(A\cap B\cap C)\cap(\bar{A}\cup\bar{B}\cup\bar{C}) is a possible event. Which of the statements given above is/are correct?

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  115. 115
    The standard deviation of 100 observations is 10. If 5 is multiplied to each of the observations, then what is the new standard deviation?

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  116. 116
    For a Binomial distribution with mean 6 and standard deviation 2\sqrt{2}, what is the value of P(X=0)?

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  117. 117
    If the random variable X has mean 3 and standard deviation 5, then what is the variance of the random variable Y=2X-5?

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  118. 118
    Three events A, B and C are such that A and B are disjoint, A and C are independent, B and C are independent. If 4P(A)=2P(B)=P(C)4P(A)=2P(B)=P(C) and P(A∪B∪C)=5P(A)P(A\cup B\cup C)=5P(A), then what is the value of P(C)?

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  119. For the next two (02) items that follow: The frequency distribution of marks obtained by 100 students in a certain subject is given below: Marks: 0-10, 10-20, 20-30, 30-40; No. of students: 10, 20, f, 40.
    119
    What is the mean deviation about the arithmetic mean?

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  120. 120
    What is the standard deviation?

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