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NDA 2026 (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. For the following two (02) items that follow : From the top of a building, the angles of depression of the top and bottom of a tower of height hh are α\alpha and β\beta respectively. Let HH be the height of the building and DD be the horizontal distance between the building and the tower.
    1
    What is H2+D2H^2 + D^2 equal to?

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  2. 2
    If α=15∘\alpha = 15^\circ and β=45∘\beta = 45^\circ, then which one of the following is correct?

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  3. For the next two (02) items that follow : The angles AA, BB and CC of a triangle ABCABC are in the ratio 1:2:71 : 2 : 7.
    3
    What is the ratio of the side of greatest length to the side of least length?

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  4. 4
    What is sin⁡A⋅cos⁡B\sin A \cdot \cos B equal to?

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  5. For the next two (02) items that follow : In a triangle ABCABC, a+b13=b+c11=c+a12\frac{a + b}{13} = \frac{b + c}{11} = \frac{c + a}{12}.
    5
    What is sin⁡A:sin⁡B:sin⁡C\sin A : \sin B : \sin C equal to?

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  6. 6
    What is cos⁡A:cos⁡B:cos⁡C\cos A : \cos B : \cos C equal to?

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  7. For the next two (02) items that follow : Given that tan⁡(A2+B2)=p\tan\left(\frac{A}{2} + \frac{B}{2}\right) = p and tan⁡(A2−B2)=q\tan\left(\frac{A}{2} - \frac{B}{2}\right) = q, where pq≠±1pq \ne \pm 1.
    7
    What is tan⁡A\tan A equal to?

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  8. 8
    What is tan⁡B\tan B equal to?

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  9. For the next two (02) items that follow : Let 4(A+B)=π4(A + B) = \pi.
    9
    What is (1+tan⁡A)(1+tan⁡B)(1 + \tan A)(1 + \tan B) equal to?

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  10. 10
    What is (cot⁡A−1)(cot⁡B−1)(\cot A - 1)(\cot B - 1) equal to?

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  11. 11
    What is 6sin⁡(π/18)−8sin⁡3(π/18)6 \sin(\pi/18) - 8 \sin^3(\pi/18) equal to?

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  12. 12
    How many values of θ\theta satisfy the equation tan⁡2θ+cot⁡2θ=2\tan^2 \theta + \cot^2 \theta = 2, where 0∘<θ<360∘0^\circ < \theta < 360^\circ?

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  13. 13
    What is sin⁡(tan⁡−10.75)\sin(\tan^{-1} 0.75) equal to?

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  14. 14
    What is tan⁡2(12cos⁡−113)\tan^2\left(\frac{1}{2} \cos^{-1} \frac{1}{3}\right) equal to?

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  15. 15
    What is tan⁡(1125∘)cot⁡(405∘)+tan⁡(765∘)cot⁡(675∘)\tan(1125^\circ) \cot(405^\circ) + \tan(765^\circ) \cot(675^\circ) equal to?

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  16. 16
    If AA is a square matrix of order 3 and ∣A∣=2|A| = 2, then what is adj(adjA)\text{adj}(\text{adj} A) equal to?

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  17. 17
    If AA is a square matrix of order 3 such that A(adjA)=[640006400064]A(\text{adj} A) = \begin{bmatrix} 64 & 0 & 0 \\ 0 & 64 & 0 \\ 0 & 0 & 64 \end{bmatrix} then what is ∣A∣|A| equal to?

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  18. 18
    Let A=[cos⁡θ−sin⁡θsin⁡θcos⁡θ]A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} What is the least value of θ\theta for which A+AT=IA + A^T = I, where II is the identity matrix of order 2?

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  19. 19
    Let AA, BB and CC be the square matrices of order 2 such that AB=ACAB = AC. Which of the statements given below is/are correct? I. BB and CC are not necessarily equal if AA is a singular matrix. II. BB and CC are equal if AA is a non-singular matrix. Select the answer using the code given below.

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  20. 20
    If AA is a square matrix of order 3 and ∣A∣=4|A| = 4, then what is ∣adjA∣|\text{adj} A| equal to?

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  21. 21
    Let AA and BB be symmetric matrices of the same order. Which of the following statements is/are correct? I. (AB−BA)(AB - BA) is also a symmetric matrix. II. (BA−AB)(BA - AB) is a skew-symmetric matrix. Select the answer using the code given below.

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  22. 22
    If A=[−123−4]A = \begin{bmatrix} -1 & 2 \\ 3 & -4 \end{bmatrix}, then what is ∣A−1∣|A^{-1}| equal to?

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  23. 23
    Let SS be the set of all real numbers and RR be a relation on SS defined by xRy⇒∣x∣≤yxRy \Rightarrow |x| \le y. Then RR is

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  24. 24
    4-digit numbers are formed with 1, 2, 3 and 4. What is the number of the 4-digit numbers in which at least one digit is repeated?

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  25. 25
    Given S={(x, y, z)∈R3:xyz=210, x<y<z,S = \{(x,\ y,\ z) \in R^3 : xyz = 210,\ x < y < z, where x, y, zx,\ y,\ z are positive integers}\} What is the total number of elements in SS?

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  26. 26
    If x=4+ix = 4 + i, where i=−1i = \sqrt{-1}, then what is x3+2x2−63x+171x^3 + 2x^2 - 63x + 171 equal to?

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  27. 27
    Let α\alpha and β\beta be the roots of the equation x2−p(x+1)−q=0x^2 - p(x + 1) - q = 0 What is α2+2α+1α2+2α+q+β2+2β+1β2+2β+q\frac{\alpha^2 + 2\alpha + 1}{\alpha^2 + 2\alpha + q} + \frac{\beta^2 + 2\beta + 1}{\beta^2 + 2\beta + q} equal to?

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  28. 28
    If the sum of the roots of the equation 12x+p+12x+q=1r\frac{1}{2x + p} + \frac{1}{2x + q} = \frac{1}{r} is zero, then what is rr equal to?

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  29. 29
    Let α\alpha and β\beta be the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0 and pn=αn+βnp_n = \alpha^n + \beta^n, where n>1n > 1. What is apn+1+bpn+cpn−1ap_{n+1} + bp_n + cp_{n-1} equal to?

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  30. 30
    If pp, qq and rr are in AP, then what is p3+3pr(p+r)+r3p^3 + 3pr(p + r) + r^3 equal to?

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  31. 31
    If 1b−a+1b−c=2b\frac{1}{b - a} + \frac{1}{b - c} = \frac{2}{b}, then aa, bb and cc are in

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  32. 32
    Let PP, QQ, RR and SS be the sum of nn terms, 2n2n terms, 3n3n terms and 4n4n terms respectively of an AP such that Q=3PQ = 3P. Which one of the following is correct?

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  33. 33
    In a GP, the 3rd, 5th and 7th terms are xx, x2+2x^2 + 2 and x3+10x^3 + 10 respectively, where x>1x > 1. What is the 8th term?

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  34. 34
    If (1+i)n−16=0(1 + i)^n - 16 = 0, where i=−1i = \sqrt{-1} and nn is a positive integer, then what is the least value of nn?

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  35. 35
    What is i×i4×i9×i16×…×i576i \times i^4 \times i^9 \times i^{16} \times \ldots \times i^{576}, where i=−1i = \sqrt{-1}, equal to?

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  36. 36
    If z=x+iyz = x + iy be such that ∣z+λiz−λi∣=1\left| \frac{z + \lambda i}{z - \lambda i} \right| = 1, where i=−1i = \sqrt{-1} and λ\lambda is a positive real number, then which of the following statements is/are correct? I. zz lies on the line y=xy = x. II. The amplitude of zz is π4\frac{\pi}{4}. Select the answer using the code given below.

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  37. 37
    What is ∣1abca31a+1bc(a+b)a3+b31a+1b+1cab+bc+caa3+b3+c3∣\begin{vmatrix} \frac{1}{a} & bc & a^3 \\ \frac{1}{a} + \frac{1}{b} & c(a + b) & a^3 + b^3 \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} & ab + bc + ca & a^3 + b^3 + c^3 \end{vmatrix} equal to?

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  38. 38
    If ae+bg=cf+dh=pae + bg = cf + dh = p, af+bh=ce+dg=qaf + bh = ce + dg = q then what is ∣abcd∣×∣efgh∣\begin{vmatrix} a & b \\ c & d \end{vmatrix} \times \begin{vmatrix} e & f \\ g & h \end{vmatrix} equal to?

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  39. 39
    If x+ay+a2z=1x + ay + a^2 z = 1, x+by+b2z=1x + by + b^2 z = 1, x+cy+c2z=1x + cy + c^2 z = 1 where a≠b≠ca \ne b \ne c, then what is x+y+zx + y + z equal to?

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  40. 40
    Let A=(1−tan⁡θtan⁡θ1)A = \begin{pmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{pmatrix} and B=(1tan⁡θ−tan⁡θ1)B = \begin{pmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{pmatrix} If C=AB−1C = AB^{-1}, then what is det⁡(C)\det(C) equal to?

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  41. 41
    What is the LCM of (11110)2(11110)_2, (10100)2(10100)_2 and (11011)2(11011)_2?

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  42. 42
    What is the coefficient of x2nx^{2n} in the expansion of the following? (1+x)2n(1+1x)2n(1 + x)^{2n} \left(1 + \frac{1}{x}\right)^{2n}

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  43. 43
    Consider the following statements in respect of the expansion of (x2+x−2+2)4(x^2 + x^{-2} + 2)^4 : I. The number of terms in the expansion is 5. II. One of the coefficients in the expansion has a maximum value equal to 70. Which of the statements given above is/are correct?

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  44. 44
    Consider the following relations from AA to BB, where A={1,3,5}A = \{1, 3, 5\} and B={2,4,6,8}B = \{2, 4, 6, 8\} : I. {(1,2),(3,2),(3,6),(5,8)}\{(1, 2), (3, 2), (3, 6), (5, 8)\} II. {(3,4),(5,8),(1,6),(3,2)}\{(3, 4), (5, 8), (1, 6), (3, 2)\} III. {(1,2),(3,6)}\{(1, 2), (3, 6)\} IV. {(1,6),(3,2),(5,2)}\{(1, 6), (3, 2), (5, 2)\} Which of the above is/are function(s) from AA to BB?

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  45. 45
    If x2−2xcos⁡θ+1=0x^2 - 2x\cos\theta + 1 = 0, then what is the magnitude of xx?

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  46. 46
    Consider the following statements in respect of sets AA and BB : I. If x∈Ax \in A and A∈BA \in B, then x∈Bx \in B. II. If A⊂BA \subset B and x∉Bx \notin B, then x∉Ax \notin A. Which of the statements given above is/are correct?

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  47. 47
    A research group conducted a survey of 500 consumers and reported that 370 consumers preferred product XX and 240 consumers preferred product YY. What is the least number that must have preferred both the products?

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  48. 48
    The Cartesian product A×AA \times A has 25 elements among which are found (3, 1), (6, 2), (5, 3). Which of the following statements is/are correct? I. It is possible to determine other elements of A×AA \times A. II. (5,5)∈A×A(5, 5) \in A \times A and (1,3)∉A×A(1, 3) \notin A \times A Select the answer using the code given below.

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  49. 49
    Consider the following statements in respect of a relation RR from a set AA to a set BB : I. The set BB is called codomain of the relation RR. II. The range of the relation is always equal to codomain of the relation RR. III. The domain of the relation RR must be equal to the set AA. Which of the statements given above is/are correct?

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  50. 50
    Consider the following system of linear inequalities : x−y≤3x - y \le 3 and x+y≥5x + y \ge 5 The solution of the inequalities lies in

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  51. 51
    A circle touches each of the lines x−y=0x - y = 0 and x+y=0x + y = 0 at unit distance from the origin. The centre of the circle may be at

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  52. 52
    A line (sin⁡θ)x+(cos⁡θ)y=sin⁡2θ(\sin \theta) x + (\cos \theta) y = \sin 2\theta cuts the coordinate axes at points PP and QQ. Let MM be the midpoint of the line segment PQPQ. What is the distance of MM from the origin?

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  53. 53
    The centre and one of the foci (F)(F) of an ellipse are at (0,0)(0, 0) and (−c,0)(-c, 0) respectively. If P(x,y)P(x, y) is any point on the ellipse and 2a2a is the length of major axis, then what is PFPF equal to?

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  54. 54
    What is the equation of the line which is equidistant from the lines 2x−4y−7=02x - 4y - 7 = 0 and 6x−12y+1=06x - 12y + 1 = 0?

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  55. 55
    A ray of light passing through the point P(1,2)P(1, 2) reflects on the xx-axis at point NN and the reflected ray passes through the point Q(5,3)Q(5, 3). What is the distance of the point NN from the origin?

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  56. 56
    A line cuts off intercept pp on the xx-axis and intercept qq on the yy-axis, where p>qp > q. The sum of the intercepts is 2 and the product of the intercepts is −15-15. What is the equation of the line?

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  57. 57
    Let PP and QQ be the points on the positive xx-axis and positive yy-axis respectively. A point N(2,1)N(2, 1) divides the line segment PQPQ in the ratio 1:21 : 2. What is the equation of the line?

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  58. 58
    ABCDABCD is a square. The equations of ABAB, ADAD and BDBD are y=0y = 0, x=0x = 0 and x+y−4=0x + y - 4 = 0 respectively. What is the equation of ACAC?

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  59. 59
    ABCABC is a triangle, where the vertices AA and BB are fixed points both lying on the xx-axis. Let AB=10AB = 10 cm. The vertex CC moves such that 1tan⁡A+1tan⁡B=1k\frac{1}{\tan A} + \frac{1}{\tan B} = \frac{1}{k}, where k≠0k \ne 0. What is the equation of the locus of the point CC?

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  60. 60
    What is the eccentricity (e)(e) of the parabola 4x2+y=04x^2 + y = 0?

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  61. 61
    The vertices of a triangle are A(2,0,0)A(2, 0, 0), B(0,6,0)B(0, 6, 0) and C(0,0,4)C(0, 0, 4). If ADAD, BEBE and CFCF are the medians of the triangle, then what is AD2+BE2+CF2AD^2 + BE^2 + CF^2 equal to?

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  62. 62
    A line makes angles α\alpha, β\beta and γ\gamma with the positive directions of xx-axis, yy-axis and zz-axis respectively such that α+β=90∘\alpha + \beta = 90^\circ. Which of the following statements is/are correct? I. The maximum value of cos⁡α+cos⁡β\cos \alpha + \cos \beta is 2\sqrt{2}. II. The minimum value of cos⁡α+cos⁡β+cos⁡γ\cos \alpha + \cos \beta + \cos \gamma is 1. Select the answer using the code given below.

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  63. 63
    What is the area of the triangle whose vertices are (0,7,10)(0, 7, 10), (−1,6,6)(-1, 6, 6) and (−4,9,6)(-4, 9, 6)?

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  64. 64
    If OO is the origin and PP is the point (2,−4,6)(2, -4, 6), then what is the equation of the plane through PP and perpendicular to OPOP?

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  65. 65
    The image of the point P(1,3,4)P(1, 3, 4) with respect to the plane Ax+By+Cz+D=0Ax + By + Cz + D = 0 is (−3,5,2)(-3, 5, 2). If A+B+C=2A + B + C = 2, then what is DD equal to?

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  66. 66
    Let a⃗\vec{a}, b⃗\vec{b}, c⃗\vec{c} and d⃗\vec{d} be the vectors. Consider the following : I. (a⃗×b⃗)⋅(c⃗×d⃗)(\vec{a} \times \vec{b}) \cdot (\vec{c} \times \vec{d}) II. (a⃗×b⃗)×(c⃗×d⃗)(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) III. (a⃗⋅b⃗)⋅(c⃗⋅d⃗)(\vec{a} \cdot \vec{b}) \cdot (\vec{c} \cdot \vec{d}) IV. (a⃗⋅b⃗)×(c⃗⋅d⃗)(\vec{a} \cdot \vec{b}) \times (\vec{c} \cdot \vec{d}) V. {(a⃗×b⃗)⋅c⃗}×d⃗\{(\vec{a} \times \vec{b}) \cdot \vec{c}\} \times \vec{d} where '⋅\cdot' represents dot product and '×\times' represents cross product of vectors. How many of the above are not well-defined?

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  67. 67
    The scalar projection of a⃗=λi^+j^−2k^\vec{a} = \lambda\hat{i} + \hat{j} - 2\hat{k} on b⃗=2i^−j^−λk^\vec{b} = 2\hat{i} - \hat{j} - \lambda\hat{k} is 7/37/3. What is the value of λ\lambda?

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  68. 68
    How much angle does r⃗=(cos⁡θ)i^+(sin⁡θ)j^+k^\vec{r} = (\cos\theta)\hat{i} + (\sin\theta)\hat{j} + \hat{k} make with the positive direction of zz-axis?

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  69. 69
    Let a⃗\vec{a} and b⃗\vec{b} be unit vectors inclined at 30∘30^\circ. What is the area of the parallelogram whose sides are represented by the vectors a⃗+3b⃗\vec{a} + 3\vec{b} and 3a⃗+b⃗3\vec{a} + \vec{b}?

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  70. 70
    Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be unit vectors such that a⃗⋅b⃗=a⃗⋅c⃗=0\vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0. If the angle between b⃗\vec{b} and c⃗\vec{c} is π/6\pi/6, then what is a⃗\vec{a} equal to?

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  71. 71
    What is ∫x1−x3 dx\int \frac{\sqrt{x}}{\sqrt{1 - x^3}}\,dx equal to?

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  72. 72
    What is ∫01dx(ax+bx+c)2\int_0^1 \frac{dx}{(ax + bx + c)^2} equal to?

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  73. 73
    What is ∫exln⁡10ex dx\int e^{x \ln 10} e^x \, dx equal to?

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  74. 74
    What is ∫12xx(1+ln⁡x) dx\int_1^2 x^x (1 + \ln x)\,dx equal to?

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  75. 75
    If f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y), then what is ∫−11f(x) dx\int_{-1}^{1} f(x)\,dx equal to?

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  76. 76
    What is the area bounded by y=e∣x∣y = e^{|x|} and the lines ∣x∣=1|x| = 1 and y=0y = 0?

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  77. 77
    The slope of the tangent to the curve y=f(x)y = f(x) at (x,f(x))(x, f(x)) is 2x2x. If the curve passes through the origin, then what is the area bounded by the curve, the xx-axis and the line x=1x = 1?

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  78. 78
    What is the solution of y dx−x dy−y2cos⁡x dx=0y\,dx - x\,dy - y^2\cos x\,dx = 0?

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  79. 79
    What is the differential equation of the family of straight lines passing through the origin?

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  80. 80
    What is the degree of the differential equation representing the family of curves y2=c xy^2 = \sqrt{c}\,x, where cc is a positive parameter?

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  81. 81
    What is the domain of the function f(x)=log⁡xef(x) = \log_x e?

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  82. 82
    If f(x)f(x) is the integral of 1+cos⁡2x−2cos⁡xxsin⁡2xtan⁡x\frac{1 + \cos^2 x - 2\cos x}{x\sin^2 x\tan x} then what is lim⁡x→0f′(x)\lim_{x \to 0} f'(x) equal to?

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  83. 83
    Consider the following statements in respect of the function f(x)=[3x]f(x) = [3x], where [⋅][\cdot] is the greatest integer function : I. f(x)f(x) is continuous at x=1/3x = 1/3. II. f(x)f(x) is differentiable at x=1/4x = 1/4. Which of the statements given above is/are correct?

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  84. 84
    What is lim⁡x→0sin⁡2xx∣x∣\lim_{x \to 0} \frac{\sin^2 x}{x|x|} equal to?

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  85. 85
    Let f(x)=p∣x∣+qf(x) = p|x| + q, where pp and qq are real constants. If f′(x)f'(x) exists at x=0x = 0, then what is the value of pp?

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  86. 86
    Consider the following statements in respect of the given function : f(x)={x3∣x∣,x≠00,x=0f(x) = \begin{cases} \frac{x^3}{|x|}, & x \ne 0 \\ 0, & x = 0 \end{cases} I. f(x)f(x) is continuous everywhere. II. f(x)f(x) is differentiable everywhere. Which of the statements given above is/are correct?

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  87. 87
    What is lim⁡x→∞(x+x−x)\lim_{x \to \infty} (\sqrt{x + \sqrt{x}} - \sqrt{x}) equal to?

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  88. 88
    If mm and nn are the roots of the equation x2−px+q=0x^2 - px + q = 0, then what is lim⁡x→mex2−px+q−1(x−m)(x−n)\lim_{x \to m} \frac{e^{x^2 - px + q} - 1}{(x - m)(x - n)} equal to?

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  89. 89
    Let f(x)=xn+kf(x) = x^n + k, where nn is a natural number and kk is a positive real constant such that f(x)+f(1x)=f(x)f(1x)f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) and f(2)=9f(2) = 9. What is f(−1)f(-1) equal to?

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  90. 90
    If f(x)=cos⁡{π3[x]+x}f(x) = \cos\left\{\frac{\pi}{3}[x] + x\right\} for 1<x<21 < x < 2, where [⋅][\cdot] is the greatest integer function, then what is f(π2)f\left(\frac{\pi}{2}\right) equal to?

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  91. 91
    Consider the following statements : I. ddxln⁡∣x∣=−1x\frac{d}{dx}\ln|x| = -\frac{1}{x} if x<0x < 0 II. ddxln⁡∣x∣=1x\frac{d}{dx}\ln|x| = \frac{1}{x} if x>0x > 0 Which of the statements given above is/are correct?

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  92. 92
    If y=∣sin⁡(π4−x)∣y = \left| \sin\left(\frac{\pi}{4} - x\right) \right|, then what is dydx\frac{dy}{dx} at x=π4x = \frac{\pi}{4} equal to?

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  93. 93
    Let ff be a differentiable function such that f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y) for all x,y∈Rx, y \in R. Which of the following statements is/are correct? I. If f(x)=x g(x)f(x) = x\, g(x), then the derivative of f(x)f(x) with respect to xx is equal to g(0)g(0). II. If f(x)=x2g(x)f(x) = x^2 g(x), then the derivative of f(x)f(x) with respect to xx is equal to 0. (Here gg is a continuous function) Select the answer using the code given below.

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  94. 94
    If f(x)=xn−1+xn−2+xn−3+…+1f(x) = x^{n-1} + x^{n-2} + x^{n-3} + \ldots + 1 then what is f′(2)f'(2) equal to?

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  95. 95
    ABCABC is a triangle right angled at BB. If AC=8AC = 8 units, then what is the area of the triangle of maximum area?

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  96. 96
    For the curve y=xe2xy = xe^{2x}

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  97. 97
    Let f(x)=∫xexdxf(x) = \int xe^x dx. Then f(x)f(x) decreases in the interval

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  98. 98
    What is the solution of the differential equation dydx=1+xcot⁡(y−x)\frac{dy}{dx} = 1 + x \cot(y - x)?

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  99. 99
    Consider the following statements in respect of the function f:R−{35}→R−{35}f : R - \left\{\frac{3}{5}\right\} \to R - \left\{\frac{3}{5}\right\} such that f(x)=3x+25x−3f(x) = \frac{3x + 2}{5x - 3} : I. f(x)f(x) is a bijective function. II. f−1(x)=f(x)f^{-1}(x) = f(x) Which of the statements given above is/are correct?

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  100. 100
    Let AA and BB be the sets having only 2 and 3 elements respectively. What is the total number of mappings from AA to BB?

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  101. 101
    The variance of 10 observations is 25. If 2 is multiplied to each of the observations and subsequently 7 is subtracted from each multiplied observation, then what is the new variance?

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  102. 102
    If the random variable XX has mean 5 and standard deviation 4, then what is the standard deviation of the random variable Y=3X+4Y = 3X + 4?

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  103. 103
    For a binomial distribution with mean 4 and standard deviation 3\sqrt{3}, what is the value of P(X=0)P(X = 0)?

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  104. 104
    If the correlation coefficient between the variables XX and YY is zero, then the two lines of regression are

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  105. 105
    Four dice are rolled. What is the probability of getting a total of the numbers on the dice as 7?

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  106. 106
    If P(A∩B)=1/2P(A \cap B) = 1/2 and P(A‾∩B‾)=1/2P(\overline{A} \cap \overline{B}) = 1/2, and 2P(A)=P(B)=k2P(A) = P(B) = k, then what is the value of kk?

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  107. 107
    A committee has 6 men and 4 women. One member is selected randomly which is woman only. What is the probability that she belongs to a subgroup of 2 senior women?

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  108. 108
    The standard deviation of XX is 4 and the standard deviation of YY is 5. If the correlation coefficient rr is 0.8, then what is the regression coefficient of YY on XX?

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  109. 109
    In a class, the probability of passing students in Mathematics is 0.7 and the probability of passing both Mathematics and Statistics is 0.5. What is the probability that a student passes Statistics given that the student passed Mathematics?

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  110. 110
    If the mean of 50 observations is 40 and the standard deviation is 8, then what is the coefficient of variation?

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  111. 111
    If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is neither 5 nor 7?

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  112. 112
    Consider the following statements for three events AA, BB and CC : I. P(A∩B∩C)≤P(A)+P(B)+P(C)−2P(A \cap B \cap C) \le P(A) + P(B) + P(C) - 2 II. P(A∪B∪C)≥P(A)+P(B)+P(C)P(A \cup B \cup C) \ge P(A) + P(B) + P(C) Which of the statements given above is/are correct?

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  113. 113
    A Mathematics problem is given to two students XX and YY to solve. The odds in favour of XX solving the problem are 6 to 9 and the odds against YY in solving the problem are 6 to 5. What is the probability that the problem will be solved if both XX and YY try to solve the problem?

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  114. 114
    The events AA and BB are independent among three events AA, BB and DD. If P(A∩B∩D)=0.04P(A \cap B \cap D) = 0.04, P(D∣A∩B)=0.25P(D \mid A \cap B) = 0.25 and P(B)=4P(A)P(B) = 4P(A), then what is the value of P(A∪B)P(A \cup B)?

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  115. For the next three (03) items that follow : Let AA, BB, CC and DD be mutually exclusive and exhaustive events such that P(A)6=P(B)3=P(C)4=P(D)2\frac{P(A)}{6} = \frac{P(B)}{3} = \frac{P(C)}{4} = \frac{P(D)}{2}
    115
    What is P(A)+2P(B)3P(C)+P(D)\frac{P(A) + 2P(B)}{3P(C) + P(D)} equal to?

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  116. 116
    If GG is the geometric mean of P(A)P(A), P(B)P(B), P(C)P(C) and P(D)P(D), then what is GG equal to?

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  117. 117
    If HH is the harmonic mean of P(A)P(A), P(B)P(B), P(C)P(C) and P(D)P(D), then what is HH equal to?

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  118. For the next three (03) items that follow : Five numbers are randomly picked from the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and arranged them in ascending order [x1<x2<x3<x4<x5x_1 < x_2 < x_3 < x_4 < x_5; x1x_1 being the smallest number and x5x_5 being the largest number selected].
    118
    What is P(x1=4)P(x_1 = 4) equal to?

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  119. 119
    What is P(x3=6)P(x_3 = 6) equal to?

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  120. 120
    What is P(x1=2,x2=3,x3=8)P(x_1 = 2, x_2 = 3, x_3 = 8) equal to?

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