NDA Mathematics 3 September 2023

Q1. mcq single +2.5 / 0.83

If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of $\displaystyle \sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right) ?$ ?

Q2. mcq single +2.5 / 0.83

If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

Q3. mcq single +2.5 / 0.83

The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2 = 10000, then what is the value of n?

Q4. mcq single +2.5 / 0.83

If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?

Q5. mcq single +2.5 / 0.83

Consider the following statements 1. A = (A ∪ B) ∪ (A - B), 2. A ∪ (B - A) = (A ∪ B) 3. B = (A ∪ B) - (A - B) Which of the statements given above are correct?

Q6. mcq single +2.5 / 0.83

The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct? 1. It is possible to determine set A. 2. A × A contains the element (3, 2). Select the correct answer using the code given below:

Q7. mcq single +2.5 / 0.83

Let A = {1, 2, 3, ..., 20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where x, y ∈ A. Which of the following statements is/are correct? 1. The domain of R is {1, 4, 7, 10, 13, 16). 2. The range of R is {1, 5, 9, 13, 17). 3. The range of R is equal to codomain of R. Select the correct answer using the code given below:

Q8. mcq single +2.5 / 0.83

A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?

Q9. mcq single +2.5 / 0.83

Consider the following statements: 1. The relation f defined by $f(x)= \begin{cases}x^3, & 0 \leq x \leq 2 \\ 4 x, & 2 \leq x \leq 8\end{cases}$ is a function. 2. The relation g defined by $g(x)= \begin{cases}x^2, & 0 \leq x \leq 4 \\ 3 x, & 4 \leq x \leq 8\end{cases}$ is a function. Which of the statements given above is/are correct?

Q10. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)=\frac{a^{x-1}+b^{x-1}}{2}$ and g(x) = x - 1. --- What is $\displaystyle \lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$ equal to?

Q11. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$ --- What is $\displaystyle \lim _{x \rightarrow 0} $ f(x) equal to ?

Q12. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)=\left\{\begin{array}{cc} a x(x+1)+b, & x<1 \\ x-1, & 1 \leq x \leq 2 \end{array}\right.$ --- If the function f(x) is differentiable at x = 1, then what is the value of (a + b)?

Q13. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function. Let $ h(x)=\frac{f(g(x))}{g(f(x))}$. --- What is $\displaystyle \lim _{x \rightarrow 0-}$ h(x) equal to ?

Q14. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)=\frac{a^{x-1}+b^{x-1}}{2}$ and g(x) = x - 1. --- What is $\displaystyle \lim _{x \rightarrow 1} \frac{f(x)-1}{g(x)}$ equal to?

Q15. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)= \begin{cases}\frac{x-3}{|x-3|}+a ; & x<3 \\ a-b ; & x=3 \\ \frac{x-3}{|x-3|}+b ; & x>3\end{cases}$ and f(x) be continuous at x = 3. --- What is the value of a ?

Q16. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function. Let $ h(x)=\frac{f(g(x))}{g(f(x))}$. --- What is $\displaystyle \lim _{x \rightarrow 0+}$ h(x) equal to ?

Q17. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)= \begin{cases}\frac{x-3}{|x-3|}+a ; & x<3 \\ a-b ; & x=3 \\ \frac{x-3}{|x-3|}+b ; & x>3\end{cases}$ and f(x) be continuous at x = 3. --- What is the value of b?

Q18. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let a function f be defined on ℝ - {0} and $\rm 2 f(x)+f\left(\frac{1}{x}\right)=x+3 $. --- What is f(0.5) equal to ?

Q19. mcq single +2.5 / 0.83

Let t1, t2, t3 ... be in GP. What is $\rm \left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}$ equal to ?

Q20. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let a1, a2, a3 ... be in AP such that a1 + a5 + a10 + a15 + a20 + a25 + a30 + a34 = 300. --- What is a1 + a5 - a10 - a15 - a20 - a25 + a30 + a34 equal to ?

Q21. mcq single +2.5 / 0.83

If (a + b), 2b, (b + c) are in HP, then which one of the following is correct?

Q22. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let a1, a2, a3 ... be in AP such that a1 + a5 + a10 + a15 + a20 + a25 + a30 + a34 = 300. --- What is $\displaystyle \sum_{n=1}^{34} a_n$ equal to ?

Q23. mcq single +2.5 / 0.83

If the nth term of a sequence is $\frac{2 n+5}{7}$, then what is the sum of its first 140 terms?

Q24. mcq single +2.5 / 0.83

If $\rm (\vec{a} \times \vec{b})^2+(\vec{a} \cdot \vec{b})^2=144$ and $\rm|\vec{b}|=4 $, then what is the value of $\rm|\vec{a}|$ ?

Q25. mcq single +2.5 / 0.83

Consider the following in respect of the vectors $\rm \vec{a}=(0,1,1)$ and $\rm \vec{b}=(1,0,1) $ : 1. The number of unit vectors perpendicular to both $\rm \vec{a}$ and $\rm \vec{b}$ is only one. 2. The angle between the vectors is $\frac{\pi}{3}$. Which of the statements given above is/are correct?

Q26. mcq single +2.5 / 0.83

What is the length of projection of the vector $\rm \hat{i}+2 \hat{j}+3 \hat{k}$ on the vector $\rm2 \hat{i}+3 \hat{j}-2 \hat{k}$ ?

Q27. mcq single +2.5 / 0.83

If θ is the angle between vectors $\vec{a}$ and $ \vec{b}$ such that $\vec{a} \cdot \vec{b} \geq 0$, then which one of the following is correct?

Q28. mcq single +2.5 / 0.83

The vectors $\rm 60 \hat{i}+3 \hat{j}, 40 \hat{i}-8 \hat{j}$ and $\rm \beta \hat{i}-52 \hat{j}$ are collinear if :

Q29. mcq single +2.5 / 0.83

What is $1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)$ equal to ?

Q30. mcq single +2.5 / 0.83

If sec-1 p - cosec-1q = 0, where p > 0, q > 0; then what is the value of p-2 + q-2 ?

Q31. mcq single +2.5 / 0.83

What is 2 cot $\left(\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right)$ equal to ?

Q32. mcq single +2.5 / 0.83

Two dice are thrown. What is the probability that difference of numbers on them is 2 or 3 ?

Q33. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. --- What is the probability that no two girls sit together?

Q34. mcq single +2.5 / 0.83

A fair coin is tossed 6 times. What is the probability of getting a result in the 6^(t)h toss which is different from those obtained in the first five tosses ?

Q35. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. --- What is the probability that all three boys sit together?

Q36. mcq single +2.5 / 0.83

In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly?

Q37. mcq single +2.5 / 0.83

Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?

Q38. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. --- What is the probability that Q and U sit together?

Q39. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. --- What is the probability that boys and girls sit alternatively?

Q40. mcq single +2.5 / 0.83

Three dice are thrown. What is the probability of getting a sum which is a perfect square?

Q41. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph. --- What is the probability that P and Q take the two end positions?

Q42. mcq single +2.5 / 0.83

The probability that a person recovers from a disease is 0.8. What is the probability that exactly 2 persons out of 5 will recover from the disease?

Q43. mcq single +2.5 / 0.83

Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty, otherwise it is 45%. If it is seen that the building has collapsed, then what is the probability that it is due to faulty design?

Q44. mcq single +2.5 / 0.83

A, B, C and D are mutually exclusive and exhaustive events. If 2P(A) = 3P(B) = 4P(C) = 5P(D), then what is 77P(A) equal to ?

Q45. mcq single +2.5 / 0.83

The points (-a, -b), (0, 0), (a, b) and (a2, ab) are:

Q46. mcq single +2.5 / 0.83

What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which the normal makes with positive direction of x-axis is 15°?

Q47. mcq single +2.5 / 0.83

For what values of k is the line (k - 3)x - (5 - k2) y + k2 - 7k + 6 = 0 parallel to the line x + y = 1?

Q48. mcq single +2.5 / 0.83

The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR ∶ RQ equal to ?

Q49. mcq single +2.5 / 0.83

Given that 16p2 + 49q2 - 4r2 - 56pq = 0. Which one of the following is a point on a pair of straight lines (px + qy + r) (px + qy - r) = 0?

Q50. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $p=\frac{1}{3}-\frac{\tan 3 x}{\tan x}$ and q = 1 - 3 tan2 x, 0 < x < π, $ x \neq \frac{\pi}{2}$. --- For how many values of x does $\frac{1}{p}$ become zero?

Q51. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$ --- What is a value of cos^(3) x + cos^(3) y?

Q52. mcq single +2.5 / 0.83

If tan (π cos θ) = cot (π sin θ), $0<\theta<\frac{\pi}{2}$; then what is the value of $8 \sin ^2\left(\theta+\frac{\pi}{4}\right)$ ?

Q53. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $\rm p=\cos \left(\frac{\pi}{5}\right) \cos \left(\frac{2 \pi}{5}\right) $ and $\rm q=\cos \left(\frac{4 \pi}{5}\right) \cos \left(\frac{8 \pi}{5}\right)$. --- What is the value of pq?

Q54. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A function is defined by f(x) = π + sin2 x. --- What is the period of the function?

Q55. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let sin x + sin y = √3 (cos y - cos x); x + y = $\rm \frac{\pi}{2}$, x < x, y < $\rm \frac{\pi}{2}$ --- What is a value of sin 3x + sin 3y?

Q56. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $\rm p=\cos \left(\frac{\pi}{5}\right) \cos \left(\frac{2 \pi}{5}\right) $ and $\rm q=\cos \left(\frac{4 \pi}{5}\right) \cos \left(\frac{8 \pi}{5}\right)$. --- What is the value of p + q?

Q57. mcq single +2.5 / 0.83

If $\tan \alpha=\frac{1}{7}$, $\sin \beta=\frac{1}{\sqrt{10}}$; $0<\alpha, \beta<\frac{\pi}{2}$, then what is the value of cos (α + 2β) ?

Q58. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $p=\frac{1}{3}-\frac{\tan 3 x}{\tan x}$ and q = 1 - 3 tan2 x, 0 < x < π, $ x \neq \frac{\pi}{2}$. --- What is pq equal to ?

Q59. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Given that 4x2 + y2 = 9. --- What is the maximum value of y?

Q60. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Given that 4x2 + y2 = 9. --- What is the maximum value of xy ?

Q61. mcq single +2.5 / 0.83

What is the area between the curve f(x) = x |x| and x-axis for x = [-1, 1]?

Q62. mcq single +2.5 / 0.83

Which one of the planes is parallel to the line $\rm \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?

Q63. mcq single +2.5 / 0.83

If L is the line with direction ratios < 3, -2, 6 > and passing through (1, -1, 1), then what are the coordinates of the points on L whose distance from (1, -1, 1) is 2 units?

Q64. mcq single +2.5 / 0.83

What is the equation of the sphere concentric with the sphere x2 + y2 + z2 - 2x - 6y -8z - 5 = 0 and which passes through the origin?

Q65. mcq single +2.5 / 0.83

What is the angle between the lines 2x = 3y = -z and 6x = -y = -4z?

Q66. mcq single +2.5 / 0.83

A point P lies on the line joining A(1, 2, 3) and B(2, 10, 1). If z-coordinate of P is 7, what is the sum of other two coordinates?

Q67. mcq single +2.5 / 0.83

What is the equation of directrix of parabola y2 = 4bx, where b < 0 and b2 + b - 2 = 0?

Q68. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let (1 + x)n = 1 + T1x + T2x2 + T3x3 + ... + Tnxn. --- What is T1 + 2T2 + 3T3 + ... + nTn equal to ?

Q69. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Consider the equation (1 - x)4 + (5 - x)^(4) = 82. --- What is the number of real roots of the equation?

Q70. mcq single +2.5 / 0.83

What is the mean of the numbers 1, 2, 3, ... 10 with frequencies ^(9)C~0~, ^(9)C~1~, ^(9)C~2~ ..., ^(9)C~9~, respectively?

Q71. mcq single +2.5 / 0.83

In a Binomial distribution B(n, p), n = 6 and 9P(X = 4) = P(X = 2). What is p equal to ?

Q72. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let (1 + x)n = 1 + T1x + T2x2 + T3x3 + ... + Tnxn. --- What is 1 - T1 + 2T2 - 3T3 + ... + (-1)nnTn equal to ?

Q73. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let (1 + x)n = 1 + T1x + T2x2 + T3x3 + ... + Tnxn. --- What is T1 + T2 + T3 + ... + Tn equal to ?

Q74. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Consider the equation (1 - x)4 + (5 - x)^(4) = 82. --- What is the sum of all the roots of the equation?

Q75. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0. --- What are the roots of equation-I ?

Q76. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0. --- Which one of the following is a root of equation-II?

Q77. mcq single +2.5 / 0.83

If z z̅ = |z + z̅ |, where z = x + iy, i = $\sqrt{-1}$, then the locus of z is a pair of:

Q78. mcq single +2.5 / 0.83

Which one of the following is a square root of $-\sqrt{-1} $?

Q79. mcq single +2.5 / 0.83

What is the value of $\sqrt{12+5 i}+\sqrt{12-5 i}$ where $i=\sqrt{-1}$ ?

Q80. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Consider equation-I : z3 + 2z2 + 2z + 1 = 0 and equation-II : z1985 + z100 + 1 = 0. --- What is the number of common roots of equation-I and equation-II?

Q81. mcq single +2.5 / 0.83

Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$. 1. The equation represents an ellipse if k = 19. 2. The equation represents a hyperbola if k = 12. 3. The equation represents a circle if k = 20. How many of the statements given above are correct?

Q82. mcq single +2.5 / 0.83

Consider the following statements in respect of hyperbola $\frac{x^2}{\cos ^2 \theta}-\frac{y^2}{\sin ^2 \theta}=1$ : 1. The two foci are independent of θ. 2. The eccentricity is sec θ. 3. The distance between the two foci is 2 units. How many of the statements given above are correct?

Q83. mcq single +2.5 / 0.83

A function satisfies $f(x-y)=\frac{f(x)}{f(y)}$, where f(y) ≠ 0. If f(1) = 0.5, then what is f(2) + f(3) + f(4) + f(5) + f(6) equal to ?

Q84. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A function is defined by f(x) = π + sin2 x. --- What is the range of the function?

Q85. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let f(x) = x2 - 1 and gof(x) = x - √x + 1. --- Which one of the following is a possible expression for g(x)?

Q86. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let f(x) = x2 - 1 and gof(x) = x - √x + 1. --- What is g(15) equal to ?

Q87. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$. --- What is the domain of the function?

Q88. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$. --- What is the greatest value of the function?

Q89. mcq single +2.5 / 0.83

What is the differential equation of all parabolas of the type y2 = 4a (x - b)?

Q90. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A parabola passes through (1, 2) and satisfies the differential equation $\frac{d y}{d x}=\frac{2 y}{x}, x>0, y>0 .$ --- What is the length of latus rectum of the parabola?

Q91. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A parabola passes through (1, 2) and satisfies the differential equation $\frac{d y}{d x}=\frac{2 y}{x}, x>0, y>0 .$ --- What is the directrix of the parabola ?

Q92. mcq single +2.5 / 0.83

What are the order and the degree respectively of the differential equation $\rm x^2\left(\frac{d^3 y}{d x^3}\right)^2+\left(\frac{d y}{d x}\right)^4+\sin x=0$ ?

Q93. mcq single +2.5 / 0.83

Consider the following in respect of the circle 4x2 + 4y2 - 4ax - 4ay + a2 = 0: 1. The circle touches both the axes. 2. The diameter of the circle is 2a. 3. The centre of the circle lies on the line x + y = a. How many of the statements given above are correct?

Q94. mcq single +2.5 / 0.83

If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?

Q95. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A quadratic equation is given by (a + b) x2 - (a + b + c) x + k = 0, where a, b, c are real. --- If $\rm {k}=\frac{{c}}{2},({c} \neq 0)$, then the roots of the equation are :

Q96. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A quadratic equation is given by (a + b) x2 - (a + b + c) x + k = 0, where a, b, c are real. --- If k = c, then the roots of the equation are:

Q97. mcq single +2.5 / 0.83

If f'(x) = cos (In x) and $y=f\left(\frac{2 x-3}{x}\right)$, then what is $\frac{d y}{d x}$ equal to ?

Q98. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let a function f be defined on ℝ - {0} and $\rm 2 f(x)+f\left(\frac{1}{x}\right)=x+3 $. --- If f is differentiable, then what is f'(0.5) equal to?

Q99. mcq single +2.5 / 0.83

If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?

Q100. mcq single +2.5 / 0.83

What is the maximum number of points of intersection of 10 circles?

Q101. mcq single +2.5 / 0.83

If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of $\frac{270}{H}$ ?

Q102. mcq single +2.5 / 0.83

If 1! + 3! + 5! + 7! + ... + 199! is divided by 24, what is the remainder?

Q103. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$ --- What is I equal to?

Q104. mcq single +2.5 / 0.83

What is $\displaystyle \rm \int_0^{8 \pi}|\sin x| d x$ equal to?

Q105. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$ --- What is $\displaystyle \int_0^\pi\left(\sin ^4 x+\cos ^4 x\right) d x$ equal to?

Q106. mcq single +2.5 / 0.83

If $A=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{array}\right]$, then which of the following statements are correct? 1. An will always be singular for any positive integer n. 2. An will always be a diagonal matrix for any positive integer n. 3. An will always be a symmetric matrix for any positive integer n. Select the correct answer using the code given below:

Q107. mcq single +2.5 / 0.83

If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$, then what is 23A3 - 19A2 - 4A equal to ?

Q108. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: The angles A, B and C of a triangle ABC are in the ratio 3 ∶ 5 ∶ 4. --- What is the value of a + b + √2 c equal to ?

Q109. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: The angles A, B and C of a triangle ABC are in the ratio 3 ∶ 5 ∶ 4. --- What is the ratio of a2 ∶ b2 ∶ c2 ?

Q110. mcq single +2.5 / 0.83

If $A=\left[\begin{array}{rrr} 0 & 3 & 4 \\ -3 & 0 & 5 \\ -4 & -5 & 0 \end{array}\right]$, then which one of the following statements is correct?

Q111. mcq single +2.5 / 0.83

If $\left|\begin{array}{ccc} x^2+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x \end{array}\right|$ = ax4 + bx3 + cx2 + dx + e, then what is the value of e?"

Q112. mcq single +2.5 / 0.83

If $A_k=\left[\begin{array}{cc} k-1 & k \\ k-2 & k+1 \end{array}\right] $, then what is det(A1) + det(A2) + det(A3) + ... + det(A100) equal to ?

Q113. mcq single +2.5 / 0.83

If all elements of a third order determinant are equal to 1 or -1, then the value of the determinant is:

Q114. mcq single +2.5 / 0.83

If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then what is the value of det(I + AA'), where I is the 3 × 3 identity matrix?

Q115. mcq single +2.5 / 0.83

Let A be a skew-symmetric matrix of order 3. What is the value of det(4A4) - det(3A3) + det(2A2) - det(A) + det(-I) where I is the identity matrix of order 3?

Q116. mcq single +2.5 / 0.83

The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of determinant of C2?

Q117. mcq single +2.5 / 0.83

If A, B and C are square matrices of order 3 and det(BC) = 2 det(A), then what is the value of det(2A^(-1)BC)?

Q118. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A function is defined by$f(x)=\left|\begin{array}{ccc} x+1 & 2 & 3 \\ 2 & x+4 & 6 \\ 3 & 6 & x+9 \end{array}\right|$ . --- The function attains local minimum value at :

Q119. mcq single +2.5 / 0.83

**Passage:** Consider the following for the next items that follow: A function is defined by$f(x)=\left|\begin{array}{ccc} x+1 & 2 & 3 \\ 2 & x+4 & 6 \\ 3 & 6 & x+9 \end{array}\right|$ . --- The function is decreasing on :

Q120. mcq single +2.5 / 0.83

If $A=\left[\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 3 & 0 \\ 1 & 0 & 1 \end{array}\right]$, then what is the value of det[adj(adjA)] ?

Instructions

Paper Structure

Mathematics