NDA Mathematics 1st September 2024

Q1. mcq single +2.5 / 0.83

Let x - 3y + 4 = 0 and 2x - 7y + 8 = 0 be two lines of regression computed from some bivariate data. If b~yx~ and b~xy~ are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of b~xy~ + 7b~yx~?

Q2. mcq single +2.5 / 0.83

Let $\rm \Sigma_{i=1}^9x_i^2=885$ If M is the mean and σ is the standard deviation of x~1~, x~2~, x~3~.....x~9~ then what is the value of M^(2) + σ^(2)?

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The mean of the series x~1~, x~2~...x~n~ is x̅ If x~n~ is replaced by k, then what is the new mean?

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

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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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Let P and Q be two non-void relations on a set A. Which of the following statements are correct? I. P and Q are reflexive ⇒ P ∩ Q is reflexive. II. P and Q are symmetric ⇒ P ∪ Q is symmetric. III. P and Q are transitive ⇒ P ∩ Q is transitive. Select the answer using the code given below.

Q7. mcq single +2.5 / 0.83

Consider the following statements: I. The set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is an infinite set. II. 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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If A and B are two non-empty sets having 10 elements in common, then how many elements do A x B and B x A have in common?

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**Passage:** Direction : Consider the following for the items that follow : Let f(x) = |x|^(2) - |x^(2)| --- Consider the following statements : I. f(x) is continuous at x = 0. Il. f(x) is continuous at x = 1 Which of the statements given above is/are correct?

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Which one of the following is correct regarding $\rm \lim\limits_{x\rightarrow 3}\frac{|x-3|}{x-3}$?

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What is $\rm \lim\limits_{x\rightarrow \frac{\pi}{2}}(\sec \theta-\tan \theta)$ equal to?

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**Passage:** Direction : Consider the following for the items that follow : The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. --- What is the sum of all five terms?

Q13. mcq single +2.5 / 0.83

If the sum of the first n terms of a series is n(2n+1), then what is the nth term?

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The mean of n observations 1, 4, 9, 16 ...., n^(2) is 130. What is the value of n?

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In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is p^(2) : q^(2). Which one of the following is correct?

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If p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to?

Q17. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. --- What is the common difference?

Q18. mcq single +2.5 / 0.83

Let p = ln(x), q = ln(x^(3)) and r = ln(x^(5)), where x > 1. Which of the following statements is/are correct? I. p, q and r are in AP. Il. p, q and r can never be in GP. Select the answer using the code given below.

Q19. mcq single +2.5 / 0.83

Let x >1, y >1, z >1 be in GP. Then $\rm \frac{1}{1+ln x}, \frac{1}{1+lny}, \frac{1}{1+\ln z}$ are

Q20. mcq single +2.5 / 0.83

For what value of the angle between the vectors $\rm \vec a\ and \ \vec b$ is the quantity $\rm |\vec a\times \vec b|+\sqrt3|\vec a.\vec b|$ maximum?

Q21. mcq single +2.5 / 0.83

The vectors $\rm \vec a, \vec b\ and\ \vec c$ are of the same length. If taken pairwise they form equal angles. If $\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,$ then what can $\vec c$ be equal to? I. î + k̂ II. $\rm \frac{-\hat i+4\hat j-\hat k}{3}$ Select the correct answer using the code given below.

Q22. mcq single +2.5 / 0.83

What is 3α + 2β equal to if (2î + 6ĵ + 27k̂) × (î + αĵ + βk̂) is a null vector?

Q23. mcq single +2.5 / 0.83

Let θ be the angle between two unit vectors $\rm \vec a\ and\ \vec b. \ if\ \vec a+2\vec b$ is perpendicular to $\rm 5\vec a-4\vec b$ then what is cos θ + cos 2θ equal to?

Q24. mcq single +2.5 / 0.83

Let ABCDEF be a regular hexagon. If $\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}$ then what is mn equal to

Q25. mcq single +2.5 / 0.83

If 4 sin^(-1 )x + cos^(-1) x = π, then what is sin^(-1) x + 4 cos^(-1) x equal to?

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What is cot^(2)(sec^(-1) 2) + tan^(2) (cosec^(-1) 3) equal to ?

Q27. mcq single +2.5 / 0.83

In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?

Q28. mcq single +2.5 / 0.83

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

Q29. mcq single +2.5 / 0.83

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?

Q30. mcq single +2.5 / 0.83

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?

Q31. mcq single +2.5 / 0.83

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?

Q32. mcq single +2.5 / 0.83

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

Q33. mcq single +2.5 / 0.83

For two events A and B, P(A) = P(A|B) = 0.25 and P(BIA) = 0.5. Which of the following are correct? I. A and B are independent. II. P(A^(c) ∪ B^(c)) = 0.875 III. P(A^(c) ∩ B^(c)) = 0.375 Select the answer using the code given below.

Q34. mcq single +2.5 / 0.83

A box 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?

Q35. mcq single +2.5 / 0.83

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

Q37. mcq single +2.5 / 0.83

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 lose?

Q38. mcq single +2.5 / 0.83

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)?

Q39. mcq single +2.5 / 0.83

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

Q40. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2, 3), B(4, 3), C(5, 1) be the vertices. --- What is the point of intersection of the diagonals of the trapezium?

Q41. mcq single +2.5 / 0.83

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

Q42. mcq single +2.5 / 0.83

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

Q43. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2, 3), B(4, 3), C(5, 1) be the vertices. --- What are the coordinates of vertex D?

Q44. mcq single +2.5 / 0.83

What is sin12° sin48° equal to?

Q45. mcq single +2.5 / 0.83

What is $\rm \frac{\cos 17^\circ-\sin 17^\circ}{\cos 17^\circ+\sin ^\circ}$ equal to

Q46. mcq single +2.5 / 0.83

Consider the following numbers : I. tan 22.5° II. cot 22.5° III. tan 22.5° - cot 22.5° How many of the above are irrational numbers?

Q47. mcq single +2.5 / 0.83

The roots of the equation 7x^(2) - 6x + 1 = 0 are tan α and tan β, where 2α and 2β are the angles of a triangle. Which one of the following is correct?

Q48. mcq single +2.5 / 0.83

If p tan (θ - 30°) = q tan (θ + 120°), then what is (p + q) / (p - q) equal to?

Q49. mcq single +2.5 / 0.83

What is the number of solutions of the equation cot2x cot3x = 1 for 0 < x

Q50. mcq single +2.5 / 0.83

What is the maximum value of a cos x + b sin x + c?

Q51. mcq single +2.5 / 0.83

What is the general solution of cos^(100) x - sin^(100) x = 1?

Q52. mcq single +2.5 / 0.83

If $\rm \frac{x}{\cos \theta}=\frac{y}{\cos \left(\frac{2\pi}{3}-\theta\right)}=\frac{z}{\cos\left(\frac{2\pi}{3}+\theta\right)}$ then what is x + y + z equal to?

Q53. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(x) = cos2x + x on [-π/2, π/2]. --- What is the least value of f(x)?

Q54. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(x) = cos2x + x on [-π/2, π/2]. --- What is the greatest value of f(x)?

Q55. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : The area bounded by the parabola y^(2) = kx and the line x = k, where k > 0, is 4/3 square units. --- What is the area of the parabola bounded by the latus rectum?

Q56. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : The area bounded by the parabola y^(2) = kx and the line x = k, where k > 0, is 4/3 square units. --- What is the value of k?

Q57. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: Let S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8. --- Which of the following are the direction ratios of S?

Q58. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: Let L : x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P : x + 2y + 3z + 1 = 0 be a plane. --- What is the point of intersection of L and P?

Q59. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: Let S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8. --- If 〈l, m, n〉 are direction cosines of S, then what is the value. of 43 (I^(2) - m^(2) - n^(2))?

Q60. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: Let 2x^(2) + 2y^(2) + 2z^(2) + 3x + 3y + 3z - 6 = 0 be a sphere. --- The centre of the sphere lies on the plane

Q61. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: Let 2x^(2) + 2y^(2) + 2z^(2) + 3x + 3y + 3z - 6 = 0 be a sphere. --- What is the diameter of the sphere?

Q62. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: Let L : x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P : x + 2y + 3z + 1 = 0 be a plane. --- What are the direction ratios of the line?

Q63. mcq single +2.5 / 0.83

Consider the points P(4k, 4k) and Q(4k, -4k) lying on the parabola y^(2) = 4kx. If the vertex is A, then what is ∠PAQ equal to?

Q64. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let (8 + 3√7) ^(20) = U + V and (8 - 3√7) ^(20) = W, where U is an integer and 0 < V < 1. --- What is V + W equal to?

Q65. mcq single +2.5 / 0.83

What is the remainder when 7^(n )- 6n is divided by 36 for n = 100?

Q66. mcq single +2.5 / 0.83

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

Q67. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let (8 + 3√7) ^(20) = U + V and (8 - 3√7) ^(20) = W, where U is an integer and 0 < V < 1. --- What is the value of (U + V)W?

Q68. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let Z ~1~ and Z ~2~ be any two complex numbers such that $\rm Z_1^2+Z_2^2+Z_1Z_2=0$ --- what is the value of $\rm \left|\frac{Z_1}{Z_2}\right|$,

Q69. mcq single +2.5 / 0.83

What is the value of the sum $\rm \sum\limits_{n=1}^{20}(i^{n-1}+i^n+i^{n+1})$ where i = √-1 ?

Q70. mcq single +2.5 / 0.83

If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω^(2))^(100) + (1 - ω + ω^(2))^(100) equal to?

Q71. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let Z ~1~ and Z ~2~ be any two complex numbers such that $\rm Z_1^2+Z_2^2+Z_1Z_2=0$ --- what is the value of $\rm \frac{1}{2}+Re\left(\frac{Z_1}{Z_2}\right)?$

Q72. mcq single +2.5 / 0.83

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

Q73. mcq single +2.5 / 0.83

Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?

Q74. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(t) = $\rm \ln(t+\sqrt{1+t^2})$ and g(t) = tan(f(t)). --- Consider the following statements : I. f(t) is an odd function. Il. g(t) is an odd function. Which of the statements given above is/are correct?

Q75. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f o g(x) =cos^(2) √x and g o f(x) = |cos x|. --- Which one of the following is g(x)?

Q76. mcq single +2.5 / 0.83

If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?

Q77. mcq single +2.5 / 0.83

Let f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?

Q78. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f o g(x) =cos^(2) √x and g o f(x) = |cos x|. --- Which one of the following is f(x)?

Q79. mcq single +2.5 / 0.83

What is the minimum value of the function f(x) = log~10~(x^(2) + 2x + 11)?

Q80. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(x) = |x|^(2) - |x^(2)| --- What is f(0.999) + f(1.001) equal to

Q81. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let ydx + (x - y^(3))dy = 0 be a differential equation. --- What is the solution of the differential equation?

Q82. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let ydx + (x - y^(3))dy = 0 be a differential equation. --- What are the order and degree respectively of the differential equation?

Q83. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: A triangle ABC is inscribed in the circle x^(2) + y^(2) = 100. B and C have coordinates (6, 8) and (-8, 6) respectively. --- What is BAC equal to?

Q84. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the items that follow: A triangle ABC is inscribed in the circle x^(2) + y^(2) = 100. B and C have coordinates (6, 8) and (-8, 6) respectively. --- What are the coordinates of A?

Q85. mcq single +2.5 / 0.83

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

Q86. mcq single +2.5 / 0.83

f f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?

Q87. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : The roots of the quadratic equation a^(2)(b^(2) - c^(2))x^(2) + b^(2)(c^(2) - a^(2))x + c^(2)(a^(2) - b^(2)) = 0 are equal (a^(2) ≠ b^(2) ≠ c^(2)). --- Which one of the following statements is correct?

Q88. mcq single +2.5 / 0.83

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

Q89. mcq single +2.5 / 0.83

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

Q90. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : The roots of the quadratic equation a^(2)(b^(2) - c^(2))x^(2) + b^(2)(c^(2) - a^(2))x + c^(2)(a^(2) - b^(2)) = 0 are equal (a^(2) ≠ b^(2) ≠ c^(2)). --- Which one of the following is a root of the equation?

Q91. mcq single +2.5 / 0.83

If n is a root of the equation x^(2) + px + m = 0 and m is a root of the equation x^(2) + px + n = 0, where m ≠ n, then what is the value of p + m + n?

Q92. mcq single +2.5 / 0.83

The foci of the ellipse 4x^(2) + 9y^(2) = 1 are at Q and R. If P(x, y) is any point on the ellipse, then what is PQ + PR equal to?

Q93. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))^(2). --- What is g’(0) equal to?

Q94. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f : (-1, 1) → R be a differentiable function with f(0) = -1 and f’(0) = 1 Let h(x) = f(2f(x) +2) and g(x) = (h(x))^(2). --- What is h’(0) equal to?

Q95. mcq single +2.5 / 0.83

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

Q96. mcq single +2.5 / 0.83

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

Q97. mcq single +2.5 / 0.83

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

Q98. mcq single +2.5 / 0.83

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

Q99. mcq single +2.5 / 0.83

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?

Q100. mcq single +2.5 / 0.83

Three perfect dice D~1~, D~2~ and D~3~ and are rolled. Let x, represent the numbers on D~1~, D~2~ and D~3~ respectively. What is the number of possible outcomes such that x < y < z?

Q101. mcq single +2.5 / 0.83

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

Q102. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(x) = |x^(2) - x - 2| --- What is $\rm \int_0^2f(x)dx$ equal to

Q103. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(t) = $\rm \ln(t+\sqrt{1+t^2})$ and g(t) = tan(f(t)). --- What is $\rm \int_{-\pi}^\pi g(t)dt$ equal to

Q104. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let f(x) = |x^(2) - x - 2| --- What is $\rm \int_h^3f(x)dx$ equal to

Q105. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let $\rm I=\int_0^{\pi/2}\frac{f(x)}{g(x)}dx$, where f(x) = sin x and g(x) = sin x + cos x + 1 --- What is I equal to?

Q106. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let $\rm I=\int_0^{\pi/2}\frac{f(x)}{g(x)}dx$, where f(x) = sin x and g(x) = sin x + cos x + 1 --- What is $\rm \int_0^{\pi/2}\frac{d(x)}{g(x)}$ equal to

Q107. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let $\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}$ --- What is A^(-1) equal to?

Q108. mcq single +2.5 / 0.83

Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?

Q109. mcq single +2.5 / 0.83

Consider the following in respect of the matrices $\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}$ I. PQ is a null matrix. II. QP is an identity matrix of order 3. III. PQ = QP Which of the above is/are correct?

Q110. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let $\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}$ --- What is A(adj A) equal to?

Q111. mcq single +2.5 / 0.83

Let X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct? I. (ZY)X is defined and is a square matrix of order 3. II. Y(XZ) is defined and is a square matrix of order 2. III. X(YZ) is not defined. Select the answer using the code given below.

Q112. mcq single +2.5 / 0.83

In a triangle ABC $\rm \frac{a}{\cos A}=\frac{b}{\cos B}=\frac{c}{\cos C}$ What is the area of the triangle if a = 6 cm?

Q113. mcq single +2.5 / 0.83

In a triangle ABC tan A + tan B + tan C = k What is the value of cot A cot B cot C?

Q114. mcq single +2.5 / 0.83

In a triangle ABC, ∠A = 75° and ∠B = 45°. What is 2a - b equal to?

Q115. mcq single +2.5 / 0.83

If $\rm \omega=-\frac{1}{2}+i\frac{\sqrt3}{2}$ then what is $\rm \begin{vmatrix}1+\omega &1+\omega^2&\omega+\omega^2\\\ 1&\omega\ & \omega^2\\\ \frac{1}{\omega}&\frac{1}{\omega^2}&1\end{vmatrix}$ equal to?

Q116. mcq single +2.5 / 0.83

If $\rm D_n=\begin{vmatrix}n&20&30\\\ n^2&40&50\\\ n^3&60&70\end{vmatrix}$ then what is the value of $\rm \sum\limits_{n=1}^4D_n?$

Q117. mcq single +2.5 / 0.83

If $\rm z=\frac{1}{3}\begin{vmatrix}i&2i&1\\\ 2i&3i&2\\\ 3&1&3\end{vmatrix}=x+iy;i=\sqrt{-1}$ then what is modulus of Z equal to?

Q118. mcq single +2.5 / 0.83

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

Q119. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let $\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c$ --- What is U(x) V(x) equal to?

Q120. mcq single +2.5 / 0.83

**Passage:** Direction : Consider the following for the items that follow : Let $\rm 2\int\frac{x^2-1}{\sqrt{x^2+1}}dx=U(x) V(x)-3\ln \{U(x)+V(x)\}+c$ --- What is |U^(2)(x) - V^(2)(x)| equal to?

NDA Mathematics 1st September 2024

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