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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If the probability of simultaneous occurrence of two events A and B is p and the probability that exactly one of A, B occurs is q, then which of the following is/are correct? 1. P(bar A) + P(bar B) = 2 - 2p - q2. P(bar A ∩ bar B) = 1 - p - qSelect the correct answer using the code given below: a. 1 only b. 2 only c. Both 1 and 2 d. Neither 1 nor 2 |
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Answer» Correct option c. Both 1 and 2 Explanation: P(A) + p(B) - 2P(A ∩ B) = q P(A ∩ B) p P(A) + P(B) = 2p +q 1 - p(bar A) + 1 - P(bar B) = p + q P(bar A) + P(bar B) = 2 - 2p - q P(bar A ∩ bar B) = 1 - P(A ∪ B) = 1 - (q + p) = 1 - p - q |
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| 2. |
If f(x) = √(x - 1)/(x - 4) defines a function of R, then what is its domain?a. (- ∞, 4) ∪ (4, ∞)b. [4, ∞]c. (1, 4) ∪ (4, ∞)d. [1, 4) ∪ (4, ∞) |
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Answer» Correct option d. [1, 4) ∪ (4, ∞) Explanation: f(x) is defined if x ≥ 1 and x ≠ 4 ∴ Domain = [1, 4) ∪ (4, ∞] |
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| 3. |
What is i1000 + i1001 + i1002 + i1003 equal to (where i = √–1)? a. 0 b. i c. –i d. 1 |
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Answer» Correct option a. 0 Explanation: i1000 + i1001 + i1002 + i1003 = 1 + i + i2 + i3 ⇒ 1 + i – 1 – i = 0 |
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| 4. |
The binary number expression of the decimal number 31 is a. 1111 b. 10111 c. 11011 d. 11111 |
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Answer» Correct option d. 11111 Explanation: 31 = 16 + 8 + 4 + 2 + 1 ∴ Binary expression of decimal number 31 = 11111 |
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| 5. |
It is given that bar X = 10, bar Y = 90, σx = 3, σy = 12 and rxy = 0.8. The regression equation of x on y is A. y = 3.2x + 58 B. x = 3.2y + 58 C. x = −8 + 0.2y D. y= −8 + 0.2x |
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Answer» Correct option C. x = −8 + 0.2y Explanation: Regression equation of X on Y is X - bar X = r(σx/σy)(Y - bar Y) After Substituting the values and solving it, we get X = - 8 + 0.2Y |
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| 6. |
The angle between the two lines lx + my + n = 0 and l’x + m’y + n’ = 0 is given by tan–1θ . What θ equal to?a. |(lm' - l'm)/(ll' - mm')|b. |(lm' + l'm)/(ll' + mm')|c. |(lm' - l'm)/(ll' + mm')|d. |(lm' + l'm)/(ll' - mm')| |
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Answer» Correct option c. |(lm' - l'm)/(ll' + mm')| Explanation: tan–1θ = tan–1|(lm' - l'm)/(ll' + mm')| ⇒ θ = |(lm' - l'm)/(ll' + mm')| |
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| 7. |
The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions? a. 0.6 b. 0.7 c. 0.8 d. 0.9 |
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Answer» Correct option b. 0.7 Explanation: P(A ∪ B) = 1 - P(A'∩ B') = 1 –[(1 – 0.4) × (1 – 0.5)] = 1 – 0.3 = 0.7 |
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| 8. |
The equation of the line passing through the point (2, 3) and the point of intersection of lines 2x − 3y + 7 = 0 and 7x + 4y + 2 = 0 is A. 21x + 46y − 180 = 0 B. 21x − 46y + 96 = 0 C. 46x + 21y − 155 = 0 D. 46x − 21y − 29 = 0 |
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Answer» Correct option B. Explanation: Equation of line passing through intersection of 2x – 3y + 7 = 0 and 7x + 4y + 2 = 0 is: (2x – 3y + 7)+ λ(7x + 4y + 2) = 0 →(1) This line passes through (2,3) ∴ (4 – 9 + 7) + λ(14 + 12 + 2) = λ = - 1/14 Putting in (1): 21 x – 41y + 96 = 0 |
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| 9. |
The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x + 3y + 4z = 7, and perpendicular to the plane x −5y + 3z = 5 is given by A. x + 2y + 3z −6 = 0 B. x + 2y + 3z +6 = 0 C. 3x + 4y +5z − 8 = 0 D. 3x + 4y + 5z + 8 = 0 |
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Answer» Correct option A. x + 2y + 3z −6 = 0 Explanation: Equation of plane passing through the intersection of lines x + y + z = 1 and 2x + 3y + 4z = 7 is: x + y + z – 1 + λ (2x + 3y + 4z – 7) = 0 Or x(1+2λ) + y(1+3λ) + z(1+4λ) –(1-7λ) = 0 →(1) This plane is perpendicular to the line, x – 5y – 3z = 5 ∴ Dot product of these will be equal to zero. ∴ (1+2λ)1 - (1+3λ)5 + (1+4λ)3 = 0 So λ = -1 Putting in (1) Required equation is: x + 2y + 3z – 6 = 0 |
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| 10. |
What is equation of straight line pass through the point of intersection of the line x/2 + y/3 = 1 and x/3 + y/2 = 1, and parallel the line 4x + 5y – 6 = 0 ? a. 20x + 25y – 54 = 0 b. 25x + 20y – 54 = 0 c. 4x + 5y – 54 = 0 d. 4x + 5y – 45 = 0 |
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Answer» Correct option a. 20x + 25y – 54 = 0 Explanation: Point of intersection (6/5, 6/5) Let equation of line be 4x + 5y + k = 0 Putting (6/5, 6/5), k = - 54/5 ∴ Equation of line is 20x + 25y – 54 = 0 |
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| 11. |
The second degree equation x2 + 4y – 2x – 4y + 2 = 0 represents a. A point b. An ellipse of semi-major axis 1 c. An ellipse with eccentricity √3/2 d. None of the above |
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Answer» Correct option a. A point Explanation: (x2 - 2x + 1) + (4y2 - 4y + 1) = 0 (x - 1)2 + (2y - 1)2 = 0 x = 1, y = 1/2 It is a point |
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| 12. |
What is the equation of the line passing through the point of intersection of the lines x + 2y – 3 = 0 and 2x – y + 5 = 0 and parallel to the line y – x + 10 = 0 ? a. 7x – 7y + 18 = 0 b. 5x – 7y + 18 = 0 c. 5x – 5y + 18 = 0 d. x – y + 5 = 0 |
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Answer» Correct option c. 5x – 5y + 18 = 0 Explanation: Equation of line is x + 2y - 3 + λ(2x - y + 5) = 0 ⇒ (1 + 2λ)x + (2 - λ)y + 5λ - 3 = 0 Now, (1 + 2λ)/(λ - 2) = 1 ⇒ λ = - 3 ∴ Equation is –5x + 5y – 18 = 0 ⇒ 5x – 5y + 18 = 0 |
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| 13. |
The order and degree of the differential equation [1 + (dy/dx)2]3 = ρ2[d2y/dx2]2 are respectively A. 3 and 2 B. 2 and 2 C. 2 and 3 D. 1 and 3 |
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Answer» Correct option B. 2 and 2 Explanation: Both order and degree are equal to 2. |
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| 14. |
Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6). Let L, M, N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides side LK are each of length √2. What are the values of m and n respectively? a. 6, 2 b. 1, 3 c. 3, 1 d. None of the above |
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Answer» Correct option c. 3, 1 |
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| 15. |
The line (x - 1)/2 - (y - 2)/3 = (z - 3)/3 is given by a. x + y + z = 6, x + 2y – 3z = – 4 b. x + 2y – 2z = –1, 4x + 4y – 5z – 3 = 0 c. 3x + 2y – 3z = 0, 3x – 6y + 3z = – 2 d. 3x + 2y – 3z = – 2, 3x – 6y + 3z = 0 |
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Answer» Correct option b. x + 2y – 2z = –1, 4x + 4y – 5z – 3 = 0 Explanation: drs of line is 2, 3, 4 going through option, 2(1) + 3(2) + 4(-2) = 0, 2(4) + 3(4) - 4(5) = 0 |
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| 16. |
If y = sin(lnx), then which one of the following is correct?a. d2y/dx2 + y = 0b. d2y/dx2 = 0c. x2(d2y/dx2) + x(dy/dx) + y = 0d. x2(d2y/dx2) - x(dy/dx) + y = 0 |
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Answer» Correct option c. x2(d2y/dx2) + x(dy/dx) + y = 0 Explanation: y = sin(logx) ⇒ dy/dx = (cos(logx))/x ⇒ x(dy/dx) = cos(logx) Again, Differentiating, x(d2y/dx2) + dy/dx = (sinlogx/x) = -y/x ⇒ x2(d2y/dx2) + x(dy/dx) + y = 0 |
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| 17. |
The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 − y columns. Both AB and BA exist. What are the values of x and y respectively? A. 8 and 3 B. 3 and 4 C. 3 and 8 D. 8 and 8 |
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Answer» Correct option C. 3 and 8 Explanation: For existence of both matrices, number of rows of matrix A = number of columns of matrix B and number of rows of matrix B = number of columns of matrix A i.e., x = 11 - y and y = x + 5 Solving above equations, we get x = 8 and y = 3. |
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| 18. |
What is the period of the function f(x) = sin x? a. π/ 4 b. π/ 2 c. π d. 2π |
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Answer» Correct option d. 2π Explanation: Period of f(x) = sin x is 2π |
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| 19. |
Which one of the following differential equations has a periodic solution?a. d2x/dt2 + μx = 0b. d2x/dt2 - μx = 0c. x(dx/dt) + μt = 0d. dx/dt + μxt = 0 |
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Answer» Correct option a. d2x/dt2 + μx = 0 |
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| 20. |
The perpendiculars that fall from any point of the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x – 3y = 2 are a. 12 and 4 respectively b. 11 and 5 respectively c. Equal to each other d. Not equal to each other |
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Answer» Correct option c. Equal to each other Explanation: Let (5/2, 0) be a point on 2x + 11y = 5. Now, perpendicular from (5/2, 0) to 24x + 7y = 20 is 8/5 Perpendicular from (5/2, 0) to 4x – 3y = 2 is 8/5 |
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| 21. |
What is the solution of the differential equation xdy – ydx = 0? a. xy = c b. y = cx c. x + y = c d. x – y = c |
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Answer» Correct option b. y = cx Explanation: xdy – ydx = 0 ⇒ (xdy - ydx)/x2 = 0 ⇒ d(y/x) = 0 Integrating, we get y/x = c ⇒ y = cx |
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| 22. |
Suppose cos A is given. If only one value of cos (A/2) is possible, then A must bea. An odd multiple of 90° b. A multiple of 90° c. An odd multiple of 180° d. A multiple of 180° |
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Answer» Correct option c. An odd multiple of 180° Explanation: A must be odd multiple of 180° |
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| 23. |
If x, x – y and x + y are the angles of a triangle (not an equilateral triangle) such that tan (x – y), tan x and tan (x + y) are in GP, then what is x equal to? a. π/4 b. π/3 c. π/6 d. π/2 |
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Answer» Correct option b. π/3 Explanation: Sum of angles of a triangle = π ⇒ x – y + x + x + y = π ⇒ x = π/ 3 |
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| 24. |
What is the principal value of sin–1(sin2π/3)? a. π/4 b. π/2 c. π/3 d. 2π/3 |
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Answer» Correct option c. π/3 Explanation: sin-1(sin2π/3) = sin-1sin(π - π/3) = sin-1sinπ/3 = π/3 |
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| 25. |
The principal value of sin-1x lies in the intervalA. (-π/2, π/2)B. [-π/2, π/2]C. [0, π/2]D. [0, π] |
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Answer» Correct option B. [-π/2, π/2] Explanation: Sin-1x lies in the interval [−π/2, π/2] |
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| 26. |
If vector r = xi + yj + zk, then what is vector r.(i + j + k) equal to? a. x b. x + y c. –(x + y + z) d. (x + y + z) |
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Answer» Correct option d. (x + y + z) Explanation: (xi + yj + zk) x (i + j + k) = x + y + z |
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| 27. |
The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and the of the group of women is 21 years, then the percentage of men and women in the group is respectively a. 20, 80 b. 40, 60 c. 60, 40 d. 80, 20 |
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Answer» Correct option d. 80, 20 Explanation: Let No. of Man = M Let No. of Women = W 26 M + 21 W = 25 (M + W) M = 4 W M : W = 4 : 1 |
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| 28. |
The correlation coefficient computed from a set of 30 observations is 0.8. Then the percentage of variation not explained by linear regression is a. 80% b. 20% c. 64% d. 36% |
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Answer» Correct option b. 20% |
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| 29. |
In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.What is the number of students who are good in Hindi and Mathematics but not in English? a. 18 b. 12 c. 10 d. 8 |
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Answer» Correct option d. 8 Explanation: Required No. = 18 – 10 = 8 |
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| 30. |
In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.What is the number of students who are good in either Hindi or Mathematics but not in English? a. 99 b. 107 c. 125 d. 130 |
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Answer» Correct option (c) Explanation: Required No. = (54 + 63) + (18 – 10) = 125 |
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| 31. |
The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is a. 45360 b. 30240 c. 27216 d. 15120 |
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Answer» Correct option c. 27216 Explanation: 9 × 9 × 8 × 7 × 6 = 27, 216 |
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| 32. |
How many fourdigit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits? a. 24 b. 36 c. 44 d. 64 |
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Answer» Correct option a. 24 Explanation: The last digit is fixed as ‘0’. ∴ No. of ways = 4 × 3 × 2 = 24 |
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| 33. |
A survey was conducted among 300 students. If was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.How many students like to play all the three games? a. 14 b. 21 c. 28 d. 35 |
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Answer» Correct option a. 14 Explanation: 300 = 125 + 145 + 90 – (|A ∩ B| + |B C| + |A ∩ C|) + |A ∩ B ∩ C| |A ∩ B| + |B∩ C| + |A ∩ C| = 60 + |A ∩ B ∩ C| .....(i) Again, |A ∩ B| + |B ∩ C| + |A ∩ C| - 3|A ∩ B ∩ C| = 32 |A ∩ B| + |B ∩ C| + |A ∩ C| = 32 + 3|A ∩ B ∩ C| .....(ii) From (i) and (ii) |A ∩ B ∩ C| = 14 |
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| 34. |
The sum of the series 3 - 1 +1/3 - 1/9 + .... is equal toa. 20/9b. 9/20c. 9/4d. 4/9 |
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Answer» Correct option c. 9/4 Explanation: 3/(1 - (-1/3)) = 9/4 |
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| 35. |
A survey of 850 strudents in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance? a. 40 b. 45 c. 50 d. 55 |
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Answer» Correct option b. 45 Explanation: Required No. = 680 + 215 – 850 = 45 |
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| 36. |
What is the sum of all twodigit numbers which when divided by 3 leave 2 as the remainder? a. 1565 b. 1585 c. 1635 d. 1655 |
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Answer» Correct option c. 1635 Explanation: Sum = 11 + 14 + …… + 98 = ((11 + 98)/2) x 30 = 109 x 15 = 1635 |
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| 37. |
The position of the point (1, 2) relative to the ellipse 2x2 + 7y2 = 20 is A. outside the ellipse B. inside the ellipse but not at the focus C. on the ellipse D. at the focus |
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Answer» Correct option A. outside the ellipse Explanation: 2x2 + 7y2 – 20 = 0 Put x = 1, y = 2 2 + 28 – 20 = 10 > 0 ∴ (1, 2) lies outside the ellipse. |
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| 38. |
If 0 < a < 1, the value of log10a is negative. This is justified by a. Negative power of 10 is less that 1 b. Negative power of 10 is between 0 and 1 c. Negative power of 10 is positive d. Negative power of 10 is negative |
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Answer» Correct option b. Negative power of 10 is between 0 and 1 Explanation: Negative power of 10 will always be between 0 & 1. |
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| 39. |
What is the value of log9 27 + log8 32?a. 7/2b. 19/6c. 4d. 7 |
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Answer» Correct option b. 19/6 Explanation: 3/2 + 5/3 = 19/6 |
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| 40. |
What should be the value of x so that the matrix ((2, 4), (- 8, x)) does not have an inverse? a. 16 b. –16 c. 8 d. –8 |
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Answer» Correct option b. –16 Explanation: |(2, 4), (-8, x)| = 0 ⇒ x = - 16 |
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| 41. |
If a + b + c = 0, then one of the solution of |(a - x, c, b), (c, b - x, a), (b, a, c - x)| = 0 is a. x = ab. x = √((3(a2 + b2 + c2))/2)c. x = √((2(a2 + b2 + c2))/3)d. x = 0 |
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Answer» Correct option d. x = 0 Explanation: Going through option, x = 0 |
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| 42. |
If |a| denotes the absolute value of an integer, then which of the following are correct? 1. |ab| = |a||b| 2. |a +b| ≤ |a| + |b| 3. |a − b| ≥ ||a| −|b|| Select the correct answer using the code given below. A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3 |
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Answer» Correct option D. 1, 2 and 3 Explanation: Each property is true. |
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| 43. |
The roots of the equation (q − r)x2 + (r − p)x + (p − q) = 0 are A. (r − p)/(q −r), 1/2 B. (p − q)/(q − r), 1 C. (q − r)/(p − q), 1 D. (r − p)/(p − q), 1/2 |
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Answer» Correct option B. (p − q)/(q − r), 1 Explanation: For any equation of form, ax2 + bx + c = 0, if sum of its coefficients is zero then one of its root is 1 and other will be given by c/a. Sum of the coefficients of given equation = q - r + r - p + p - q = 0 Therefore roots are: 1, p - q/q - r |
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| 44. |
If A = {x ∶ x is a multiple of 2}, B = {x ∶ x is a multiple of 5} and C = {x ∶ x is a multiple of 10}, then A ∩ (B ∩ C) is equal to A. A B. B C. CD. {x ∶ x is a multiple of 100} |
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Answer» Correct option C. C Explanation: It implies that C is a subset of both A and B. ∴ A Ո (B Ո C) = A Ո C = C |
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| 45. |
If |vector a| 3, |vector b| = 4 and | vector a - vector b| = 5,then what is the value of |vector a + vector b| = ?a. 8 b. 6 c. 5√2 d. 5 |
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Answer» Correct option d. 5 Explanation: |vector a + vector b|2 + |vector a - vector b|2 = 2{|vector a|2 + |vector b|2} = 2 x 25 = 50 ⇒ |vector a + vector b|2 + 25 = 50 ⇒ |vector a + vector b|2 = 25 ⇒ |vector a + vector b|2 = 5 |
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| 46. |
If the regression coefficient of Y on X is –6, and the correlation coefficient between X and Y - 1/2, then the regression coefficient of X on Y would bea. 1/24b. - 1/24c. - 1/6d. 1/6 |
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Answer» Correct option b. - 1/24 Explanation: byx = - 6, r = - 1/2 (-1/2)2 = - 6 x bxy ⇒ bxy = - 1/24 |
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| 47. |
The distance of the point (1, 3) from the line 2x +3y = 6, measured parallel to the line 4x + y = 4, is A. 5/√13 units B. 3/√17 units C. √17 units D. √17/2 units |
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Answer» Correct option A. 5/√13 units Explanation: Required equation of line is: y – 3 = -4 (x – 1) ⇒ 4x + y = 7 Distance is measured from line 2x + 3y=6 Solving these equations, x = 3/2 & y = 1 Distance from the point (1, 3) = √(1/4 + 4) = √17/2 |
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| 48. |
Which one of the following can be considered as appropriate pair of values of regression coefficient of y on x and regression coefficient of x on y?A. (1, 1)B. (-1, 1)C. (-1/2, 2)D. (1/3, 10/3) |
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Answer» Correct option A. (1, 1) Explanation: Regression coefficient of y on x is equal to the regression coefficient of x on y, which implies that (x, y) lies on the line x = y. |
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| 49. |
Consider the following statements: 1. Coefficient of variation depends on the unit of measurement of the variable. 2. Range is a measure of dispersion. 3. Mean deviation is least when measured about median. Which of the above statements are correct? A. 1 and 2 only B. 2 and 3 only C. 1 and 3 only D. 1, 2 and 3 |
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Answer» Correct option B. 2 and 3 only Explanation: 1 and 2 are correct statements. 3rd is incorrect one because mean deviation is leat when measured about mean not median. |
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| 50. |
Given that the arithmetic mean and standard deviation of a sample of 15 observations are 24 and 0 respectively. Then which one of the following is the arithmetic mean of the smallest five observations in the data? A. 0 B. 8 C. 16 D. 24 |
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Answer» Correct option D. 24 Explanation: A.M = 24, S.D = 0 As S.D = 0, therefore average of any 5 observations will be equal to A.M. |
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