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Question 1 of 30
1. Question
The lines L₁: y−x =0 and L₂: 2x+y=0 intersect the line L₃: y+2=0 at P and Q respectively. The bisector of the acute angle between L₁ and L₂ intersect L₃ at R.
Statement – 1: The ratio PR: RQ equals 2√2 : √5
Statement – 2: In any triangle, bisector of an angle divides the triangle into two similar triangles.
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Question 2 of 30
2. Question
If A= sin²x+cos⁴x, then for all real x
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Question 3 of 30
3. Question
The coefficient of x⁷ in the expansion of (1–x–x²+x³)⁶ is
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Question 4 of 30
4. Question
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Question 5 of 30
5. Question
Statement – 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃.
Statement – 2: The number of ways of choosing any 3 places from 9 different places is ⁹C₃.
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Question 6 of 30
6. Question
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Question 7 of 30
7. Question
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Question 8 of 30
8. Question
Let R be the set of real numbers
Statement – 1: A = {(x, y)∈R×R: y−x is an integer} is an equivalence relation on R.
Statement – 2: B = {(x, y)∈R×R: x= αy for some rational number α} is an equivalence relation on R.
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Question 9 of 30
9. Question
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Question 10 of 30
10. Question
Let α, β be real and z be a complex number. If z²+αz+β = 0 has two distinct roots on the line Re z = 1, then it is necessary that
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Question 11 of 30
11. Question
Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32, then p lies in the interval
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Question 12 of 30
12. Question
A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after
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Question 13 of 30
13. Question
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Question 14 of 30
14. Question
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Question 15 of 30
15. Question
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Question 16 of 30
16. Question
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is
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Question 17 of 30
17. Question
Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation , where k>0 is a constant and T is the total life in years of the equipment Then the scrap value V(T) of the equipment is
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Question 18 of 30
18. Question
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Question 19 of 30
19. Question
The two circles x²+y² = ax and x²+y² = c²(c>0) touch each other if
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Question 20 of 30
20. Question
If C and D are two events such that C ⊂ D and P(D) ≠ 0, then the correct statement among the following is
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Question 21 of 30
21. Question
The number of values of k for which the linear equations 4x+ky+2z = 0; kx+4y+z =0; 2x + 2y + z = 0 possess a non–zero solution is
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Question 22 of 30
22. Question
Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as
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Question 23 of 30
23. Question
The shortest distance between line y−x=1 and curve x= y² is
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Question 24 of 30
24. Question
If the mean deviation about the median of the numbers a, 2a, …, 50a is 50, then a equals
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Question 25 of 30
25. Question
Statement – 1: The point A(1, 0, 7) is the mirror image of the point B(1,6,3) in the line
Statement – 2: The line: bisects the line segment joining A(1, 0, 7) and B(1, 6,3).
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Question 26 of 30
26. Question
Let A and B be two symmetric matrices of order 3.
Statement – 1: A(BA) and (AB)A are symmetric matrices.
Statement – 2: AB is symmetric matrix if matrix multiplication of A and B is commutative.
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Question 27 of 30
27. Question
If ω(≠ 1) is a cube root of unity, and (1+ω)⁷= A+Bω. Then (A, B) equals
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Question 28 of 30
28. Question
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Question 29 of 30
29. Question
The area of the region enclosed by the curves y=x, x=e, y= 1/x and the positive x–axis is
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Question 30 of 30
30. Question
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