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Question 1 of 30
1. Question
Let If 100 S_{n} = n, then n is equal to :
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Question 2 of 30
2. Question
If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of ∆ ABC is :
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Question 3 of 30
3. Question
If x = a, y = b, z = c is a solution of the system of linear equations
x + 8y + 7z = 0
9x + 2y + 3z = 0
x + y + z = 0
such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :
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Question 4 of 30
4. Question
A value of x satisfying the equation sin[cot^{−1}(1 + x)] = cos[tan^{−1} x], is :
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Question 5 of 30
5. Question
The function f : N → N defined by where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :
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Question 6 of 30
6. Question
The equation represents a part of circle having radius equal to :
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Question 7 of 30
7. Question
If the line, lies in the plane, ,2x – 4y + 3z = 2, then the shortest distance between this line and the line, is :
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Question 8 of 30
8. Question
If three positive numbers a, b and c are in A.P. such that abc = 8, then the minimum possible value of b is :
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Question 9 of 30
9. Question
If ∫f(x) dx = A log1 – x + Bx + C, then the ordered pair (A, B) is equal to :
(where C is a constant of integration)
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Question 10 of 30
10. Question
If for some positive real number a, then a is equal to
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Question 11 of 30
11. Question
If 2x = y^{1/5} + y^{−1/5} and
then λ + k is equal to :
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Question 12 of 30
12. Question
The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60°. If the area of the quadrilateral is then the perimeter of the quadrilateral is :
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Question 13 of 30
13. Question
A square, of each side 2, lies above the xaxis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30° with the positive direction of the xaxis, then the sum of the xcoordinates of the vertices of the square is :
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Question 14 of 30
14. Question
Let f be a polynomial function such that f(3x) = fʹ(x) ∙ fʹʹ(x), for all x ϵ R. Then :
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Question 15 of 30
15. Question
The coefficient of x^{−5} in the binomial expansion of where x ≠ 0, 1, is :
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Question 16 of 30
16. Question
If the vector is written as the sum of a vector parallel to and a vector , perpendicular to then is equal to
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Question 17 of 30
17. Question
A line drawn through the point P(4, 7) cuts the circle x^{2} + y^{2} = 9 at the points A and B. Then PA ∙ PB is equal to :
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Question 18 of 30
18. Question
Contrapositive of the statement
‘If two numbers are not equal, then their squares are not equal’, is :
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Question 19 of 30
19. Question
The eccentricity of an ellipse having centre at the origin, axes along the coordinate axes and passing through the points (4, −1) and (−2, 2) is :
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Question 20 of 30
20. Question
The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B_{1} and a particular girl G_{1} never sit adjacent to each other, is :
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Question 21 of 30
21. Question
The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :
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Question 22 of 30
22. Question
For two 3 × 3 matrices A and B, let A + B = 2Bʹ and 3A + 2B = I_{3}, where B’ is the transpose of B and I_{3} is 3 × 3 identity matrix. Then :
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Question 23 of 30
23. Question
A tangent to the curve, y = f(x) at P(x, y) meets xaxis at A and yaxis at B. If AP : BP = 1 : 3 and f(1) = 1, then the curve also passes through the point :
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Question 24 of 30
24. Question
Let E and F be two independent events. The probability that both E and F happen is and the probability that neither E nor F happens is then a value of is :
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Question 25 of 30
25. Question
The value of k for which the function is continuous at is :
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Question 26 of 30
26. Question
If y = mx + c is the normal at a point on the parabola y^{2} = 8x whose focal distance is 8 units, then c is equal to :
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Question 27 of 30
27. Question
If then k is equal to :
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Question 28 of 30
28. Question
The sum of all the real values of x satisfying the equation is :
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Question 29 of 30
29. Question
The function f defined by f(x) = x^{3} – 3x^{2} + 5x + 7, is :
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Question 30 of 30
30. Question
From a group of 10 men and 5 women four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :
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