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NDA 2024 (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
    Let XX be a matrix of order 3×33 \times 3, YY be a matrix of order 2×32 \times 3 and ZZ be a matrix of order 3×23 \times 2. Which of the following statements are correct? A. (ZY)X(ZY)X is defined and is a square matrix of order 3. B. Y(XZ)Y(XZ) is defined and is a square matrix of order 2. C. X(YZ)X(YZ) is not defined. Select the answer using the code given below.

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  2. 2
    Consider the following statements: A. The set of all irrational numbers between 12\sqrt{12} and 15\sqrt{15} is an infinite set. B. The set of all odd integers less than 1000 is a finite set. Which of the statements given above is/are correct?

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  3. 3
    How many 4-digit numbers are there having all digits as odd?

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  4. 4
    If ω≠1\omega \neq 1 is a cube root of unity, then what is (1+ω−ω2)100+(1−ω+ω2)100\left(1+\omega-\omega^{2}\right)^{100}+\left(1-\omega+\omega^{2}\right)^{100} equal to?

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  5. 5
    Let AA and BB be two square matrices of same order. If ABAB is a null matrix, then which one of the following is correct?

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  6. 6
    In the expansion of (1+x)p(1+x)q(1+x)^{p}(1+x)^{q}, if the coefficient of x3x^{3} is 35, then what is the value of (p+q)(p+q)?

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  7. 7
    If pp times the pthp^{th} term of an AP is equal to qq times the qthq^{th} term (p≠qp \neq q), then what is the (p+q)th(p+q)^{th} term equal to?

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  8. 8
    Let p=ln⁡xp=\ln x, q=ln⁡x3q=\ln x^3 and r=ln⁡x5r=\ln x^5, where x>1x>1. Which of the following statements is/are correct? A. p,qp,q and rr are in AP. B. p,qp,q and rr can never be in GP. Select the answer using the code given below.

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  9. 9
    If Z=13∣i2i12i12i3i23∣Z=\frac{1}{3}\begin{vmatrix}i & 2i & 1 \\ 2i & 1 & 2i \\ 3i & 2 & 3 \end{vmatrix} where i=−1i=\sqrt{-1}, then what is the modulus of ZZ?

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  10. 10
    What is the value of the sum ∑n=120(in−1+in+in+1)\displaystyle\sum_{n=1}^{20}\left(i^{n-1}+i^{n}+i^{n+1}\right) where i=−1i=\sqrt{-1}?

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  11. 11
    Let x>1,  y>1,  z>1x>1,\; y>1,\; z>1 be in GP. Then 11+ln⁡x,  11+ln⁡y,  11+ln⁡z\dfrac{1}{1+\ln x},\; \dfrac{1}{1+\ln y},\; \dfrac{1}{1+\ln z} are

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  12. 12
    If ω=−12+i32\omega=-\dfrac{1}{2}+i\dfrac{\sqrt{3}}{2}, then what is ∣1+ω1+ω2ω+ω21∣⋅∣ωω21ω2∣⋅∣1ω1ω2∣\begin{vmatrix}1+\omega & 1+\omega^2 \\ \omega+\omega^2 & 1 \end{vmatrix} \cdot \begin{vmatrix}\omega & \omega^2 \\ 1 & \omega^2 \end{vmatrix} \cdot \begin{vmatrix}1 & \omega \\ 1 & \omega^2 \end{vmatrix} equal to?

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  13. 13
    If the sum of the first nn terms of a series is n(2n+1)n(2n+1), then what is the nthn^{th} term?

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  14. 14
    In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

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  15. 15
    The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

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  16. 16
    If nn is a root of the equation x2+px+m=0x^2+px+m=0 and mm is a root of the equation x2+px+n=0x^2+px+n=0, where m≠nm\neq n, then what is the value of p+m+np+m+n?

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  17. 17
    In how many ways can a student choose (n−2)(n-2) courses out of nn courses if 2 courses are compulsory (n>4n>4)?

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  18. 18
    If Dn=∣n2030n24050n36070∣D_n=\begin{vmatrix}n & 20 & 30 \\ n^2 & 40 & 50 \\ n^3 & 60 & 70\end{vmatrix}, then what is the value of ∑n=14Dn\displaystyle\sum_{n=1}^{4}D_n?

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  19. 19
    Consider the following in respect of the matrices P=(0c−b−c0ab−a0)P=\begin{pmatrix}0&c&-b\\-c&0&a\\b&-a&0\end{pmatrix} and Q=(a2abacabb2bcacbcc2)Q=\begin{pmatrix}a^2&ab&ac\\ab&b^2&bc\\ac&bc&c^2\end{pmatrix}: A. PQPQ is a null matrix. B. QPQP is an identity matrix of order 3. C. PQ=QPPQ=QP Which of the above is/are correct?

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  20. 20
    If PP is a skew-symmetric matrix of order 3, then what is det⁡(P)\det(P) equal to?

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  21. 21
    If 4sin⁡−1x+cos⁡−1x=π4\sin^{-1}x+\cos^{-1}x=\pi, then what is sin⁡−1x+4cos⁡−1x\sin^{-1}x+4\cos^{-1}x equal to?

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  22. 22
    What is cot⁡2 ⁣(sec⁡−12)+tan⁡2 ⁣(cosec⁡−13)\cot^2\!\left(\sec^{-1}2\right)+\tan^2\!\left(\operatorname{cosec}^{-1}3\right) equal to?

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  23. 23
    In a triangle ABCABC, acos⁡A=bcos⁡B=ccos⁡Ca\cos A=b\cos B=c\cos C. What is the area of the triangle if a=6a=6 cm?

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  24. 24
    The roots of the equation 7x2−6x+1=07x^2-6x+1=0 are tan⁡α\tan\alpha and tan⁡β\tan\beta, where 2α2\alpha and 2β2\beta are the angles of a triangle. Which one of the following is correct?

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  25. 25
    In a triangle ABCABC, ∠A=75∘\angle A=75^\circ and ∠B=45∘\angle B=45^\circ. What is 2a−b2a-b equal to?

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  26. 26
    What is the number of solutions of the equation cot⁡2x⋅cot⁡3x=1\cot 2x\cdot\cot 3x=1 for 0<x<π0<x<\pi?

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  27. 27
    What is the general solution of cos⁡100x−sin⁡100x=1\cos^{100}x-\sin^{100}x=1? (where nn is an integer)

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  28. 28
    In a triangle ABCABC, tan⁡A+tan⁡B+tan⁡C=k\tan A+\tan B+\tan C=k. What is the value of cot⁡Acot⁡Bcot⁡C\cot A\cot B\cot C?

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  29. 29
    What is sin⁡12°sin⁡48°\sin 12°\sin 48° equal to?

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  30. 30
    What is cos⁡17°−sin⁡17°cos⁡17°+sin⁡17°\dfrac{\cos17°-\sin17°}{\cos17°+\sin17°} equal to?

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  31. 31
    Consider the following numbers: A. tan⁡22.5°\tan22.5° B. cot⁡22.5°\cot22.5° C. tan⁡22.5°−cot⁡22.5°\tan22.5°-\cot22.5° How many of the above are irrational numbers?

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  32. 32
    If xcos⁡θ=ycos⁡ ⁣(2π3−θ)=zcos⁡ ⁣(2π3+θ)\dfrac{x}{\cos\theta}=\dfrac{y}{\cos\!\left(\dfrac{2\pi}{3}-\theta\right)}=\dfrac{z}{\cos\!\left(\dfrac{2\pi}{3}+\theta\right)}, then what is x+y+zx+y+z equal to?

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  33. 33
    If ptan⁡(θ−30°)=qtan⁡(θ+120°)p\tan(\theta-30°)=q\tan(\theta+120°), then what is p+qp−q\dfrac{p+q}{p-q} equal to?

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  34. 34
    Let PP and QQ be two non-void relations on a set AA. Which of the following statements are correct? A. PP and QQ are reflexive ⇒P∩Q\Rightarrow P\cap Q is reflexive. B. PP and QQ are symmetric ⇒P∪Q\Rightarrow P\cup Q is symmetric. C. PP and QQ are transitive ⇒P∩Q\Rightarrow P\cap Q is transitive. Select the answer using the code given below.

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  35. 35
    If AA and BB are two non-empty sets having 10 elements in common, then how many elements do A×BA\times B and B×AB\times A have in common?

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  36. 36
    What is the remainder when 7n−6n7^n-6n is divided by 36 for n=100n=100?

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  37. 37
    What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as between circle and lines)?

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  38. 38
    In an AP, the ratio of the sum of the first pp terms to the sum of the first qq terms is p2:q2p^2:q^2. Which one of the following is correct?

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  39. 39
    What is the number of real roots of the equation (x−1)2+(x−3)2+(x−5)2=0(x-1)^2+(x-3)^2+(x-5)^2=0?

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  40. 40
    In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 110 passed in only two subjects and 10 passed in none of the subjects. How many passed in all three subjects?

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  41. Let Z1Z_1 and Z2Z_2 be any two complex numbers such that Z12+Z22+Z1Z2=0Z_1^2+Z_2^2+Z_1 Z_2=0.
    41
    What is the value of ∣Z1Z2∣\left|\dfrac{Z_1}{Z_2}\right|?

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  42. 42
    What is the value of 12+Re ⁣(Z1Z2)\dfrac{1}{2}+\text{Re}\!\left(\dfrac{Z_1}{Z_2}\right)?

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  43. The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP.
    43
    What is the common difference?

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  44. 44
    What is the sum of all five terms?

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  45. Let (8+37)20=U+V(8+3\sqrt{7})^{20}=U+V and (8−37)20=W(8-3\sqrt{7})^{20}=W, where UU is an integer and 0<V<10<V<1.
    45
    What is V+WV+W equal to?

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  46. 46
    What is the value of (U+V)W(U+V)W?

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  47. The roots of the quadratic equation (a2b2−c2)x2+(b2c2−a2)x+(c2a2−b2)=0(a^2b^2-c^2)x^2+(b^2c^2-a^2)x+(c^2a^2-b^2)=0 are equal, a2≠b2≠c2a^2\neq b^2\neq c^2.
    47
    Which one of the following statements is correct?

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  48. 48
    Which one of the following is a root of the equation?

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  49. Let A=(3−342−340−11)A=\begin{pmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{pmatrix}.
    49
    What is A(adj A)A(\text{adj}\,A) equal to?

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  50. 50
    What is A−1A^{-1} equal to?

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  51. 51
    What is 3α+2β3\alpha+2\beta equal to if (2i^+6j^+27k^)×(i^+αj^+βk^)(2\hat{i}+6\hat{j}+27\hat{k})\times(\hat{i}+\alpha\hat{j}+\beta\hat{k}) is a null vector?

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  52. 52
    For what value of the angle between the vectors a⃗\vec{a} and b⃗\vec{b} is the quantity ∣a⃗×b⃗∣+3∣a⃗⋅b⃗∣|\vec{a}\times\vec{b}|+\sqrt{3}|\vec{a}\cdot\vec{b}| maximum?

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  53. 53
    Let θ\theta be the angle between two unit vectors a⃗\vec{a} and b⃗\vec{b}. If a⃗+2b⃗\vec{a}+2\vec{b} is perpendicular to 5a⃗−4b⃗5\vec{a}-4\vec{b}, then what is cos⁡θ+cos⁡2θ\cos\theta+\cos2\theta equal to?

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  54. 54
    Let ABCDEFABCDEF be a regular hexagon. If AD→=mBC→\overrightarrow{AD}=m\overrightarrow{BC} and CF→=nAB→\overrightarrow{CF}=n\overrightarrow{AB}, then what is mnmn equal to?

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  55. 55
    The vectors a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} are of the same length. If taken pairwise, they form equal angles. If a⃗=i^+j^\vec{a}=\hat{i}+\hat{j} and b⃗=j^+k^\vec{b}=\hat{j}+\hat{k}, then what can c⃗\vec{c} be equal to? A. i^+k^\hat{i}+\hat{k} B. −i^+4j^−k^3\dfrac{-\hat{i}+4\hat{j}-\hat{k}}{\sqrt{3}} Select the correct answer using the code given below.

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  56. 56
    The diagonals of a quadrilateral ABCDABCD are along the lines x−2y=1x-2y=1 and 4x+2y=34x+2y=3. The quadrilateral ABCDABCD may be a

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  57. 57
    The foci of the ellipse 4x2+9y2=14x^2+9y^2=1 are at QQ and RR. If P(x,y)P(x,y) is any point on the ellipse, then what is PQ+PRPQ+PR equal to?

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  58. 58
    If P(2,4)P(2,4), Q(8,12)Q(8,12), R(10,14)R(10,14) and S(x,y)S(x,y) are vertices of a parallelogram, then what is (x+y)(x+y) equal to?

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  59. 59
    The equation of a circle is (x2−4x+3)+(y2−6y+8)=0(x^2-4x+3)+(y^2-6y+8)=0. Which of the following statements are correct? A. The end points of a diameter of the circle are at (1,2)(1,2) and (3,4)(3,4). B. The end points of a diameter of the circle are at (1,4)(1,4) and (3,2)(3,2). C. The end points of a diameter of the circle are at (2,4)(2,4) and (4,2)(4,2). Select the answer using the code given below.

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  60. 60
    Consider the points P(4k,4k)P(4k,4k) and Q(4k,−4k)Q(4k,-4k) lying on the parabola y2=4kxy^2=4kx. If the vertex is AA, then what is ∠PAQ\angle PAQ equal to?

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  61. A triangle ABCABC is inscribed in the circle x2+y2=100x^2+y^2=100. BB and CC have coordinates (6,8)(6,8) and (−8,6)(-8,6) respectively.
    61
    What is ∠BAC\angle BAC equal to?

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  62. 62
    What are the coordinates of AA?

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  63. ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2,3)A(2,3), B(4,3)B(4,3), C(5,1)C(5,1) be the vertices.
    63
    What are the coordinates of vertex DD?

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  64. 64
    What is the point of intersection of the diagonals of the trapezium?

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  65. Let 2x2+2y2+2z2+3x+3y+3z−6=02x^2+2y^2+2z^2+3x+3y+3z-6=0 be a sphere.
    65
    What is the diameter of the sphere?

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  66. 66
    The centre of the sphere lies on the plane

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  67. Let SS be the line of intersection of two planes x+y+z=1x+y+z=1 and 2x+3y−4z=82x+3y-4z=8 with direction ratios ⟨−7,6,1⟩\langle -7,6,1\rangle. If (l,m,n)(l,m,n) are direction cosines of SS, then what is the value of 43l2−m2−n243l^2-m^2-n^2?
    67
    Which of the following are the direction ratios of SS?

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  68. 68
    66

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  69. Let L:x+y+z+4=0=2x−y−z+8L:x+y+z+4=0=2x-y-z+8 be a line and P:x+2y+3z+1=0P: x+2y+3z+1=0 be a plane.
    69
    What are the direction ratios of the line?

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  70. 70
    What is the point of intersection of LL and PP?

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  71. 71
    Let z=[y]z=[y] and y=[x]−xy=[x]-x, where [⋅][\cdot] is the greatest integer function. If xx is not an integer but positive, then what is the value of zz?

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  72. 72
    If f(x)=4x+1f(x)=4x+1 and g(x)=kx+2g(x)=kx+2 such that f∘g(x)=g∘f(x)f\circ g(x)=g\circ f(x), then what is the value of kk?

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  73. 73
    What is the minimum value of the function f(x)=log⁡10(x2+2x+11)f(x)=\log_{10}(x^2+2x+11)?

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  74. 74
    Which one of the following is correct regarding lim⁡x→3∣x−3∣x−3\displaystyle\lim_{x\to3}\dfrac{|x-3|}{x-3}?

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  75. 75
    What is the maximum value of acos⁡x+bsin⁡x+ca\cos x+b\sin x+c?

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  76. 76
    If f(2x)=4x2+1f(2x)=4x^2+1, then for how many real values of xx will f(2x)f(2x) be the GM of f(x)f(x) and f(4x)f(4x)?

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  77. 77
    If f(x)=[x]2−30[x]+221=0f(x)=[x]^2-30[x]+221=0, where [x][x] is the greatest integer function, then what is the sum of all integer solutions?

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  78. 78
    If f(x)=9x−8xf(x)=9^x-8^x such that g(x)=f(x)−1g(x)=f(x)-1, then which one of the following is correct?

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  79. 79
    What is lim⁡θ→π/2(sec⁡θ−tan⁡θ)\displaystyle\lim_{\theta\to\pi/2}(\sec\theta-\tan\theta) equal to?

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  80. 80
    Let f(x)f(y)=f(xy)f(x)f(y)=f(xy) for all real x,yx,y. If f(2)=4f(2)=4, then what is the value of f ⁣(12)f\!\left(\dfrac{1}{2}\right)?

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  81. Let f∘g(x)=cos⁡2xf\circ g(x)=\cos^2\sqrt{x} and g∘f(x)=∣cos⁡x∣g\circ f(x)=|\cos x|.
    81
    Which one of the following is f(x)f(x)?

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  82. 82
    Which one of the following is g(x)g(x)?

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  83. Let f(x)=[x]2−[x2]f(x)=[x]^2-[x^2], where [⋅][\cdot] denotes the greatest-integer function.
    83
    What is f(0.999)+f(1.001)f(0.999)+f(1.001) equal to?

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  84. 84
    Let f(x)=[x]2−[x2]f(x) = [x]^2 - [x^2], where [⋅][\cdot] is the greatest integer function. Consider the following statements: A. f(x)f(x) is continuous at x=0x = 0. B. f(x)f(x) is continuous at x=1x = 1. Which of the statements given above is/are correct?

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  85. Let f(x)=cos⁡2x+xf(x)=\cos 2x+x on [−π2,π2]\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right].
    85
    What is the greatest value of f(x)f(x)?

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  86. 86
    Let f(x)=cos⁡2x+xf(x) = \cos 2x + x on [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]. What is the least value of f(x)f(x)?

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  87. The area bounded by the parabola y2=kxy^2=kx and the line x=kx=k, where k>0k>0, is 43\dfrac{4}{3} square units.
    87
    What is the value of kk?

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  88. 88
    What is the area of the parabola bounded by the latus rectum?

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  89. Let y dx+(x−y3) dy=0y\,dx+(x-y^3)\,dy=0 be a differential equation.
    89
    What are the order and degree respectively of the differential equation?

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  90. 90
    What is the solution of the differential equation?

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  91. Let f(x)=∣x2−x−2∣f(x)=|x^2-x-2|.
    91
    What is ∫02f(x) dx\displaystyle\int_0^2 f(x)\,dx equal to?

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  92. 92
    What is ∫13f(x) dx\displaystyle\int_1^3 f(x)\,dx equal to?

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  93. 93
    Let f(t)=ln⁡ ⁣(t+1+t2)f(t)=\ln\!\left(t+\sqrt{1+t^2}\right) and g(t)=tan⁡(f(t))g(t)=\tan(f(t)). Consider the following statements: A. f(t)f(t) is an odd function. B. g(t)g(t) is an odd function. Which of the statements given above is/are correct?

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  94. Let f(t)=ln⁡ ⁣(t+1+t2)f(t)=\ln\!\left(t+\sqrt{1+t^2}\right) and g(t)=tan⁡(f(t))g(t)=\tan(f(t)).
    94
    What is ∫−ππg(t) dt\displaystyle\int_{-\pi}^{\pi}g(t)\,dt equal to?

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  95. Let f:(−1,1)→Rf:(-1,1)\to\mathbb{R} be a differentiable function with f(0)=−1f(0)=-1 and f′(0)=1f'(0)=1. Let h(x)=f(2f(x)+2)h(x)=f(2f(x)+2) and g(x)=(h(x))2g(x)=(h(x))^2.
    95
    What is h′(0)h'(0) equal to?

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  96. 96
    What is g′(0)g'(0) equal to?

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  97. Let I=∫0π/2f(x)g(x) dxI=\displaystyle\int_0^{\pi/2}f(x)g(x)\,dx, where f(x)=sin⁡xf(x)=\sin x and g(x)=sin⁡x+cos⁡x+1g(x)=\sin x+\cos x+1.
    97
    What is ∫0π/2dxg(x)\displaystyle\int_0^{\pi/2}\dfrac{dx}{g(x)} equal to?

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  98. 98
    What is II equal to?

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  99. Let 2∫x2−1x2+1 dx=U(x)V(x)−3ln⁡{U(x)+V(x)}+c2\displaystyle\int\dfrac{x^2-1}{\sqrt{x^2+1}}\,dx = U(x)V(x)-3\ln\{U(x)+V(x)\}+c.
    99
    What is ∣U2(x)−V2(x)∣|U^2(x)-V^2(x)| equal to?

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  100. 100
    What is U(x)V(x)U(x)V(x) equal to?

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  101. 101
    Let x−3y+4=0x-3y+4=0 and 2x−7y+8=02x-7y+8=0 be two lines of regression computed from some bivariate data. If byxb_{yx} and bxyb_{xy} are regression coefficients of lines of regression of yy on xx and xx on yy respectively, then what is the value of bxy+7byxb_{xy}+7b_{yx}?

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  102. 102
    The mean of nn observations 1,4,9,16,…,n21,4,9,16,\ldots,n^2 is 130. What is the value of nn?

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  103. 103
    Three distinct natural numbers are chosen at random from 1 to 10. What is the probability that they are consecutive?

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  104. 104
    A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If 3P(B)=4P(A)3P(B)=4P(A) and 3P(C)=2P(B)3P(C)=2P(B), then what is P(A)P(A) equal to?

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  105. 105
    A die has two faces with number 4, three faces with number 5 and one face with number 6. If the die is rolled once, then what is the probability of getting 4 or 5?

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  106. 106
    A bowl contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?

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  107. 107
    A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may miss?

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  108. 108
    The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?

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  109. 109
    A natural number xx is chosen at random from the first 100 natural numbers. What is the probability that x2+x>50x^2+x>50?

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  110. 110
    What is the mean deviation of the first 10 natural numbers?

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  111. 111
    Let ∑i=19xi2=855\displaystyle\sum_{i=1}^{9}x_i^2=855. If MM is the mean and σ\sigma is the standard deviation of x1,x2,…,x9x_1,x_2,\ldots,x_9, then what is the value of M2+σ2M^2+\sigma^2?

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  112. 112
    The mean of the series x1,x2,…,xnx_1,x_2,\ldots,x_n is xˉ\bar{x}. If xnx_n is replaced by kk, then what is the new mean?

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  113. 113
    A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?

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  114. 114
    Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?

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  115. 115
    For two events A and B, P(A)=P(A∣B)=0.25P(A)=P(A|B)=0.25 and P(B∣A)=0.5P(B|A)=0.5. Which of the following are correct? A. A and B are independent. B. P(Ac∪Bc)=0.875P(A^c\cup B^c)=0.875. C. P(Ac∩Bc)=0.375P(A^c\cap B^c)=0.375. Select the answer using the code given below.

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  116. 116
    Two perfect dice are thrown. What is the probability that the sum of the numbers on the faces is neither 9 nor 10?

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  117. 117
    The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?

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  118. 118
    Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?

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  119. 119
    Three perfect dice D1,D2D_1,D_2 and D3D_3 are rolled. Let x,yx,y and zz represent the numbers on D1,D2D_1,D_2 and D3D_3 respectively. What is the number of possible outcomes such that x<y<zx<y<z?

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  120. 120
    In a binomial distribution, if the mean is 6 and the standard deviation is 2\sqrt{2}, then what are the values of the parameters nn and pp respectively?

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