NDA Mathematics 14 November 2021

Q1. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. Two regression lines are given as 3x - 4y + 8 = 0 and 4x - 3y - 1 = 0. --- Consider the following statements: 1. The coefficient of correlations r is $\rm \frac{3}{4}$. 2. The means of x and y are 3 and 4 respectively. Which of the above statements is/are correct?

Q2. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. Two regression lines are given as 3x - 4y + 8 = 0 and 4x - 3y - 1 = 0. --- Consider the following statements: 1. The regression line of y on x is $\rm y = \frac{3}{4}x+2$ 2. The regression line of x on y is $\rm x = \frac{3}{4}y+\frac{1}{4}$ Which of the above statements is/are correct?

Q3. mcq single +2.5 / 0.83

When the measure of central tendency is available in the form of mean, which one of the following is the most reliable and accurate measure of variability?

Q4. mcq single +2.5 / 0.83

What is the mean of natural numbers in the interval [15, 64]?

Q5. mcq single +2.5 / 0.83

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

Q6. mcq single +2.5 / 0.83

If $\rm \displaystyle \sum_{i = 1}^{10}x_i = 110$ and $\rm \displaystyle \sum_{i = 1}^{10}x_i^2 = 1540$ then what is the variance?

Q7. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The marks obtained by 60 students in a certain subject out of 75 are given below: Marks Number of Students 15 - 20 4 20 - 25 5 25 - 30 11 30 - 35 6 35 - 40 5 40 - 45 8 45 - 50 9 50 - 55 6 55 - 60 4 60 - 65 2 --- What is the median?

Q8. mcq single +2.5 / 0.83

For the set of numbers x, x, x + 2, x + 3, x + 10 where x is a natural number, which of the following is/are correct? 1. Mean > Mode 2. Median > Mean Select the correct answer using the code given below.

Q9. mcq single +2.5 / 0.83

The mean of 10 observations is 5.5. If each observation is multiplied by 4 and subtracted from 44, then what is the new mean?

Q10. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The marks obtained by 60 students in a certain subject out of 75 are given below: Marks Number of Students 15 - 20 4 20 - 25 5 25 - 30 11 30 - 35 6 35 - 40 5 40 - 45 8 45 - 50 9 50 - 55 6 55 - 60 4 60 - 65 2 --- What is the mode?

Q11. mcq single +2.5 / 0.83

If g is the geometric mean of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, then which one of the following is correct?

Q12. mcq single +2.5 / 0.83

Consider the following statements in respect of relations and functions: 1. All relations are functions but all functions are not relations. 2. A relation from A to B is a subset of Cartesian product A × B. 3. A relation in A is a subset of Cartesian product A × A. Which of the above statements are correct?

Q13. mcq single +2.5 / 0.83

Suppose set A consists of first 250 natural numbers that are multiple of 3 and set B consists of first 200 even natural numbers. How many elements does A ∪ B have?

Q14. mcq single +2.5 / 0.83

Consider three sets X, Y and Z having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S = (X - Y) ∪ Z. How many proper subsets does S have?

Q15. mcq single +2.5 / 0.83

Consider the following statements in respect of sets: 1. The union over the intersection of sets is distributive. 2. The complement of the union of two sets is equal to the intersection of their complements. 3. If the difference between the two sets is equal to the empty set, then the two sets must be equal. Which of the above statements are correct?

Q16. mcq single +2.5 / 0.83

If $f(x) = \frac{[x]}{|x|}$, x ≠ 0, where [⋅] denotes the greatest integer function, then what is the right-hand limit of f(x) at x = 1?

Q17. mcq single +2.5 / 0.83

Consider the following statements in respect of the function $\rm f(x) = sin \left(\frac{1}{x^2}\right)$, x ≠ 0: 1. It is continuous at x = 0, if f(0) = 0. 2. It is continuous at $x = \frac{2}{\sqrt{\pi}}$. Which of the above statements is/are correct?

Q18. mcq single +2.5 / 0.83

What is $\rm \displaystyle\lim_{n \rightarrow \infty} \frac{a^n+b^n}{a^n-b^n}$ where a > b > 1, equal to?

Q19. mcq single +2.5 / 0.83

Let $\rm f(x) = \left\{\begin{matrix} 1+\frac{x}{2k}, & 0 < x < 2\\\ kx, & 2 \le x < 4 \end {matrix}\right.$ If $\displaystyle\lim_{x\rightarrow 2}$ f(x) exists, then what is the value of k?

Q20. mcq single +2.5 / 0.83

Consider the following statements in respect of f(x) = |x| - 1 1. f(x) is continuous at x = 1. 2. f(x) is differentiable at x = 0. Which of the above statements is/are correct?

Q21. mcq single +2.5 / 0.83

If a~n~ = n(n!), then what is a~1~ + a~2~ + a~3~ +...+ a~10~ equal to?

Q22. mcq single +2.5 / 0.83

If the harmonic mean of 60 and x is 48, then what is the value of x?

Q23. mcq single +2.5 / 0.83

If p = (1111 ... up to n digits), then what is the value of 9p^(2) + p?

Q24. mcq single +2.5 / 0.83

Let p, q and 3 be respectively the first, third and fifth terms of an AP. Let d be the common difference. If the product (pq) is minimum, then what is the value of d?

Q25. mcq single +2.5 / 0.83

If log102, log10(2x - 1), log10(2x + 3) are in AP, then what is x equal to?

Q26. mcq single +2.5 / 0.83

If x, y, z are in GP, then which of the following is/are correct? 1. ln(3x), ln(3y), ln(3z) are in AP 2. xyz + ln(x), xyz + ln(y), xyz + ln(z) are in HP Select the correct answer using the code given below.

Q27. mcq single +2.5 / 0.83

Let S~k~ denote the sum of first k terms of an AP. What is $\rm \frac{S_{30}}{S_{20}-S_{10}}$ equal to?

Q28. mcq single +2.5 / 0.83

$\frac{1}{b+c}, \frac{1}{c+a},\frac{1}{a+b}$ are in HP, then which of the following is/are correct? 1. a, b, c are in AP 2. (b + c)^(2), (c + a)^(2), (a + b)^(2 )are in GP. Select the correct answer using the code given below.

Q29. mcq single +2.5 / 0.83

If $\rm\vec{a}+3\vec{b} = 3\hat{i}- \hat{j}$ and $\rm2\vec{a}+\vec{b} = \hat{i}- 2\hat{j}$, then what is the angle between $\rm\vec{a}$ and $\rm\vec{b}$

Q30. mcq single +2.5 / 0.83

Let $\rm \vec{a}, \vec{b}$ and $\rm\vec{c}$ be unit vectors such that $\rm\vec{a} \times \vec{b}$ is perpendicular to $\vec{c}$. If θ is the angle between $\rm\vec{a}$ and $\rm\vec{b}$, then which of the following is/are correct? 1. $\rm\vec{a} \times \vec{b} = sin ~\theta~ \vec{c} $ 2. $\rm\vec {a} \cdot (\vec{b}\times \vec{c})=0$ Select the correct answer using the code given below.

Q31. mcq single +2.5 / 0.83

If $\rm(\vec {a} + \vec{b})$ is perpendicular to $\rm\vec {a}$ and magnitude of $\rm\vec {b}$ is twice that of $\rm\vec {a}$, then what is the value of $\rm(4\vec {a} + \vec{b})\cdot \vec{b}$ equal to?

Q32. mcq single +2.5 / 0.83

Let $\rm\vec {a}, \vec{b}$ and $ \rm \vec {c}$ be three vectors such that $\rm\vec {a}, \vec{b}$ and $ \rm \vec {c}$ are co-planar. Which of the following is/are correct? 1. $\rm(\vec{a}\times \vec{b})\times \vec{c}$ is co-planar with $\rm\vec {a}$ and $\rm\vec {b}$ 2. $\rm(\vec{a}\times \vec{b})\times \vec{c}$ is perpendicular to $\rm\vec {a}$ and $\rm\vec {b}$ Select the correct answer using the code given below.

Q33. mcq single +2.5 / 0.83

If the position vectors of A and B are (√2 - 1)î - ĵ and î + (√2 + 1)ĵ respectively, then what is the magnitude of $\rm \vec{AB}$?

Q34. mcq single +2.5 / 0.83

What is the slope of the tangent of y = cos^(-1) (cos x) at x = $-\frac{\pi}{4}$?

Q35. mcq single +2.5 / 0.83

What is the value of following? $\rm cot \left[sin^{-1} \frac{3}{5}+cot^{-1}\frac{3}{2} \right]$

Q36. mcq single +2.5 / 0.83

Let sin^(-1)x + sin^(-1)y + sin^(-1)z = $\frac{3\pi}{2}$ for 0 ≤ x, y z ≤ 1. What is the value of x^(1000) + y^(1001) + z^(1002)?

Q37. mcq single +2.5 / 0.83

Consider the following relations for two events E and F : 1. P(E ∩ F) ≥ P(E) + P(F) - 1 2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F) 3. P(E ∪ F) ≤ P(E) + P(F) Which of the above relations is/are correct?

Q38. mcq single +2.5 / 0.83

If A and B are two events such that P(not A) = $\rm \frac{7}{10}$, P(not B) = $\rm \frac{3}{10}$ and P(A|B) = $\rm \frac{3}{14}$, then what is P(B|A) equal to?

Q39. mcq single +2.5 / 0.83

In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?

Q40. mcq single +2.5 / 0.83

What is the probability that the roots of the equation x^(2) + x + n = 0 are real, where n ∈ ℕ and n < 4?

Q41. mcq single +2.5 / 0.83

Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

Q42. mcq single +2.5 / 0.83

A problem is given to three students A, B and C, whose probabilities of solving the problem independently are $\rm \frac{1}{2}$, $\rm \frac{3}{4}$ and p respectively. If the probability that the problem can be solved is $\rm \frac{29}{32}$, then what is the value of p?

Q43. mcq single +2.5 / 0.83

If P(A|B) < P(A), then which one of the following is correct?

Q44. mcq single +2.5 / 0.83

3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?

Q45. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The equations of the sides AB, BC and CA of a triangle ABC are x - 2 = 0, y + 1 = 0 and x + 2y - 4 = 0 respectively. --- What are the coordinates of circumcentre of the triangle?

Q46. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The equations of the sides AB, BC and CA of a triangle ABC are x - 2 = 0, y + 1 = 0 and x + 2y - 4 = 0 respectively. --- What is the equation of the altitude through B on AC?

Q47. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(-1, 2) and C(3, 5). --- What is the area of the parallelogram?

Q48. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(-1, 2) and C(3, 5). --- What is the equation of the diagonal BD?

Q49. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The two vertices of and equilateral triangle are (0, 0) and (2, 2). --- The difference of coordinates of the third vertex is

Q50. mcq single +2.5 / 0.83

Let ABC be a triangle. If cos2A + cos2B + cos2C = -1 then which one of the following is correct?

Q51. mcq single +2.5 / 0.83

Let the equation sec x.cosec x = p have a solution, where p is a positive real number. What should be the smallest value of p?

Q52. mcq single +2.5 / 0.83

If sinθ and cosθ are the roots of the equation ax^(2) + bx + c = 0, then which one of the following is correct?

Q53. mcq single +2.5 / 0.83

Let sin x + sin y = cos x + cos y for all x, y ∈ ℝ. What is $\rm tan \left(\frac{x}{2}+\frac{y}{2}\right)$ equal to?

Q54. mcq single +2.5 / 0.83

For what value of θ, where 0 < θ < $\frac{\pi}{2}$, does sin θ + sin θ cos θ maximum value?

Q55. mcq single +2.5 / 0.83

If sin(A + B) = 1 and 2 sin(A - B) = 1, where 0 < A, B < $\frac{\pi}{2}$, then what is tan A ∶ tan B equal to?

Q56. mcq single +2.5 / 0.83

Let 4sin^(2) x = 3, where 0 ≤ x ≤ π. What is tan3x equal to?

Q57. mcq single +2.5 / 0.83

Where does the tangent to the curve y = e^(x) at the point (0, 1) meet x-axis?

Q58. mcq single +2.5 / 0.83

Consider the following statements in respect of the function f(x) = x + $\rm \frac{1}{x}$: 1. The local maximum value of f(x) is less than its local minimum value. 2. The local maximum value of f(x) occurs at x = 1. Which of the above statements is/are correct?

Q59. mcq single +2.5 / 0.83

What is the condition that f(x) = x^(3) + x^(2) + kx has no local extremum?

Q60. mcq single +2.5 / 0.83

What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?

Q61. mcq single +2.5 / 0.83

If the function f(x) = x^(2) - kx is monotonically increasing in the interval (1, ∞), then which one of the following is correct?

Q62. mcq single +2.5 / 0.83

Consider the following statements in respect of the function f(x) = x^(2) + 1 in the interval [1, 2]: 1. The maximum value of the function is 5. 2. The minimum value of the function is 2. Which of the above statements is/are correct?

Q63. mcq single +2.5 / 0.83

The tangent to the curve x^(2) = y at (1, 1) makes an angle θ with the positive direction of x-axis. Which one of the following is correct?

Q64. mcq single +2.5 / 0.83

What is the area bounded by y = [x], where [⋅] is the greatest integer function, the x-axis and the lines x = -1.5 and x = -1.8?

Q65. mcq single +2.5 / 0.83

The locus of a point P(x, y, z) which moves in such a way that z = 7 is a

Q66. mcq single +2.5 / 0.83

ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α is the angle between AB and AG; β is the angle between AC and AG, then what is the value of cos 2α + cos 2β?

Q67. mcq single +2.5 / 0.83

The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)

Q68. mcq single +2.5 / 0.83

The number of spheres of radius r touching the coordinate axes is

Q69. mcq single +2.5 / 0.83

Consider the following statements: 1. A-line in space can have infinitely many direction ratios. 2. It is possible for certain lines that the sum of the squares of direction cosines can be equal to the sum of its direction cosines. Which of the above statements is/are correct?

Q70. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The two ends of the latus rectum of a parabola are (-2, 4) and (-2, -4). --- Consider the following statements in respect of such parabolas: 1. One of the parabolas passes through the origin (0, 0). 2. The focus of one of the parabolas lies at (-2, 0). Which of the above statements is/are correct?

Q71. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The two ends of the latus rectum of a parabola are (-2, 4) and (-2, -4). --- What is the maximum number of parabolas that can be drawn through these two points as end points of latus rectum?

Q72. mcq single +2.5 / 0.83

How many terms are there in the expansion of $\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}$ where a ≠ 0, b ≠ 0?

Q73. mcq single +2.5 / 0.83

Consider the expansion of (1 + x)^(n). Let p, q, r and s be the coefficients of first, second, nth and (n + 1)th terms respectively. What is (ps + qr) equal to?

Q74. mcq single +2.5 / 0.83

If log10 2 log~2~~ ~10 + log~10~(10^(x)) = 2, then what is the value of x?

Q75. mcq single +2.5 / 0.83

Which one of the following is a square root of $\rm 2a+2\sqrt{a^2 + b^2}$, where a, b ∈ ℝ?

Q76. mcq single +2.5 / 0.83

What is $\rm \sum\limits_{n=1}^{8n+7} i^n$ equal to, where i = √-1?

Q77. mcq single +2.5 / 0.83

If i = √-1, then how many values does i^(-2n) have for different n ∈ ℤ?

Q78. mcq single +2.5 / 0.83

If z = x + iy, where i = √-1, then what does the equations zz̅ + ∣z∣^(2) + 4(z + z̅) - 48 = 0 represent?

Q79. mcq single +2.5 / 0.83

If x^(2) + x + 1 = 0, then what is the value of x^(199) + x^(200) + x^(201)?

Q80. mcq single +2.5 / 0.83

Consider the following statements in respect of the roots of the equation x^(3) - 8 = 0 : 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above statements is/are correct?

Q81. mcq single +2.5 / 0.83

What is the range of the function f(x) = 1 - sinx defined on entire real line?

Q82. mcq single +2.5 / 0.83

What is the period of the function f(x) = ln(2 + sin^(2)x)?

Q83. mcq single +2.5 / 0.83

What is the differential equation of $\rm y = A- \frac{B}{x}$?

Q84. mcq single +2.5 / 0.83

What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?

Q85. mcq single +2.5 / 0.83

What is the order of the differential equation of all ellipses whose axes are along the coordinate axes?

Q86. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. A circle is passing through the points (5, -8), (-2, 9) and (2, 1). --- What are the coordinates of the center of the circle?

Q87. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. A circle is passing through the points (5, -8), (-2, 9) and (2, 1). --- If r is the radius of the circle, then which one of the following is correct?

Q88. mcq single +2.5 / 0.83

If the roots of the equation 4x^(2) - (5k + 1)x + 5k = 0 differ by unity, then which one of the following is a possible value of k?

Q89. mcq single +2.5 / 0.83

If p and q are the non-zero roots of the equation x^(2) + px + q = 0, then how many possible values can q have?

Q90. mcq single +2.5 / 0.83

The quadratic equation 3x^(2) - (k^(2) + 5k)x + 3k^(2) - 5k = 0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?

Q91. mcq single +2.5 / 0.83

Consider all the real roots of the equation x^(4) - 10x^(2) + 9 = 0. What is the sum of the absolute values of the roots?

Q92. mcq single +2.5 / 0.83

Let f(x) be a polynomial function such that f ∘ f(x) = x^(4). What is f'(1) equal to ?

Q93. mcq single +2.5 / 0.83

If y = (1 + x)(1 + x^(2))(1 + x^(4))(1 + x^(8))(1 + x^(16)) then what is $\frac{dy}{dx}$ at x = 0 equal to?

Q94. mcq single +2.5 / 0.83

If y = cos x ⋅ cos 4x ⋅ cos 8x, then what is $\rm \frac{1}{y}\frac{dy}{dx}$ at $\rm x = \frac{\pi}{4}$ equal to?

Q95. mcq single +2.5 / 0.83

What is the derivative of $\rm e^{e^x}$ with respect to e^(x)?

Q96. mcq single +2.5 / 0.83

Let S = {2, 3, 4, 5, 6, 7, 9}. How many different 3-digit numbers (with all digits different) from S can be made which are less than 500?

Q97. mcq single +2.5 / 0.83

Consider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits appears?

Q98. mcq single +2.5 / 0.83

Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

Q99. mcq single +2.5 / 0.83

Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two of these points is 380. 2. The number of triangles that can be drawn by joining any three of these points is 1140. Select the correct answer using the code given below.

Q100. mcq single +2.5 / 0.83

How many 4 - letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

Q101. mcq single +2.5 / 0.83

If C(n, 4), C(n, 5) and C(n, 6) are in AP, then what is the value of n?

Q102. mcq single +2.5 / 0.83

How many distinct matrices exist with all four entries taken from (1, 2)?

Q103. mcq single +2.5 / 0.83

What is $\rm \int^\pi _0 ln\left(tan\frac{x}{2}\right) dx$ equal to?

Q104. mcq single +2.5 / 0.83

If f(x) = 2^(x), then what is $\int^{10}_2\frac{f'(x)}{f(x)}dx$ equal to?

Q105. mcq single +2.5 / 0.83

If f(x) satisfies f(1) = f(4), then what is $\rm \int^4_1f'(x) dx$ equal to?

Q106. mcq single +2.5 / 0.83

If $\rm \int^0_{-2} f(x)dx=k$, then $\rm \int^0_{-2}|f(x)|dx$ is

Q107. mcq single +2.5 / 0.83

What is $\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx$ equal to?

Q108. mcq single +2.5 / 0.83

Let $A = \begin{bmatrix} 0 & 2 \\ -2 & 0 \end{bmatrix}$ and (mI + nA)^(2) = A where m, n are positive real numbers and I is the identify matrix. What is (m + n) equal to?

Q109. mcq single +2.5 / 0.83

$\rm A=\begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$ where a ∈ ℕ, then is A^(100) - A^(50) - 2A^(25) equal to? where I is the identity matrix.

Q110. mcq single +2.5 / 0.83

The inverse of a matrix A is given by $\rm \begin{bmatrix} -2 & 1 \\ \frac{3}{2} & -\frac{1}{2} \end{bmatrix}$ What is A equal to?

Q111. mcq single +2.5 / 0.83

Consider the following in respect of the matrix $\rm A = \begin{bmatrix} 1 & 1 & 1\\ 1 & 1 & 1\\ 1 & 1 & 1 \end{bmatrix}$ 1. Inverse of A does not exist 2. A^(3) = A 3. 3A = A^(2) Which of the above are correct?

Q112. mcq single +2.5 / 0.83

**Passage:** Direction: Consider the following for the next two (02) items that follow. The two vertices of and equilateral triangle are (0, 0) and (2, 2). --- Consider the following statements: 1. The third vertex has at least one irrational coordinate. 2. The area is irrational. Which of the above statements is/are correct?

Q113. mcq single +2.5 / 0.83

If $\rm \Delta = \begin{vmatrix} a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}$ then what is $\rm \begin{vmatrix} 3d + 5g & 4a + 7g & 6g\\ 3e + 5h & 4b + 7h & 6h\\ 3f + 5i & 4c + 7i & 6i \end{vmatrix}$ equal to?

Q114. mcq single +2.5 / 0.83

What is the value of the following determinant? $\begin{vmatrix} \cos \rm C & \tan \rm A & 0\\ \sin \rm B & 0 & -\tan \rm A\\ 0 & \sin \rm B & \cos \rm C \end{vmatrix}$

Q115. mcq single +2.5 / 0.83

If $x = \frac{a}{b-c}$, $y = \frac{b}{c - a}$, $z = \frac{c}{a - b}$ then what is the value of the following? $\begin{vmatrix} 1 & -x & x\\ 1 & 1 & -y\\ 1 & z & 1 \end{vmatrix}$

Q116. mcq single +2.5 / 0.83

For what values of k is the system of equations 2k^(2)x + 3y - 1 = 0, 7x - 2y + 3 = 0, 6kx + y + 1 = 0 consistent?

Q117. mcq single +2.5 / 0.83

If $\rm \begin{vmatrix} a & -b & a - b - c\\ -a & b & -a + b - c\\ -a & -b & -a - b + c \end{vmatrix} - kabc = 0$ (a ≠ 0, b ≠ 0, c ≠ 0)then what is the value of k?

Q118. mcq single +2.5 / 0.83

If $\rm \int \sqrt{1 - sin 2x} \space dx$ = A sinx + B cosx + C, where 0 < x < $\frac{\pi}{4}$, then which one of the following is correct?

Q119. mcq single +2.5 / 0.83

What is the integral of f(x) = 1 + x^(2) + x^(4) with respect to x^(2)?

Q120. mcq single +2.5 / 0.83

What is $\rm \int \frac{dx}{x(x^2 + 1)}$ equal to?

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