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1 What is A.P. and G.P. series. Explain with 2 examples for each?
2 Solve the following linear equations by using Gauss eliminatin method: x+2y+z =7; x+3z=11; 2x-3y=1.
3 If the roots of the equation x2+ax-b=0 differ by unity, prove that a2 +4b-1=0.
4 What is a Matrix? Explain any three types of it.
5 Of the 100 boarders of a hostel 80 drink tea, 40 drink coffee and 25 drink tea and coffee both. How many of them drink neither tea nor coffee?
6 If nP5 : nP3 = 2:1, then find the value of n.
7 solve xy =yx, x=2y
8 Prove that nCr = nCn-r
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Case study:
The total cost C(x) associated with producing and marketing x units of an item is given by: C(x) = 0.005×3 – 0.02×2 + 30x +3000. From this information, solve the following s:
Q.No 1: Find total cost when output is 4 units.
Answer:
Q.No 2: Find average cost of output of 10 units.
Answer:
Q.No 3: Find marginal cost when output is 3 units.
Answer:
1. (am)n =…
(A): amn
(B): am+n
(C): am-n
(D): am
2. Express v72 = 6v2 in logarthmic form.
(A): 1/2= log72 6v1
(B): 1/2= 6v1
(C): 1/2= log72 6v2
(D): 1/2= log72 6v3
3. Rational and irrational numbers together are called——-.
(A): whole numbers
(B): real numbers
(C): prime numbers
(D): none
4. Express log4 4 =1 in exponential form.
(A): 41=4
(B): 41=5
(C): 41=6
(D): 41=7
5. solve x2-x-56=0
(A): 5,6
(B): -7, 8
(C): -7, 9
(D): -7, 10
6. v2 is an example of ——
(A): whole numbers
(B): natural numbers
(C): prime numbers
(D): irrational numbers
7. If two rows or columns of a determinant are identical, the value of the determinant is —-.
(A): 0
(B): 1
(C): -1
(D): 2
8. In number system 1,2,3,4 …… are
(A): whole numbers
(B): natural numbers
(C): prime numbers
(D): functional numbers
9. ¦4¦= …
(A): 1
(B): 2
(C): 3
(D): 4
10. (-a)(-b) =…
(A): ab
(B): -ab
(C): a(-b)
(D): (-a)b
11. x +3 is a polynomial in x of degree—.
(A): 1
(B): 2
(C): 3
(D): 4
12. Integrate the function x sinx
(A): sinx- x cosx
(B): sin x
(C): cos x
(D): sec x – cosec x
13. The 5th and the 12th terms of an A.P. series are 14 and 25 respectively. Find the common difference.
(A): 1
(B): 2
(C): 3
(D): 4
14. Which term of the following series is 575? 4.5,9,18….
(A): 7th
(B): 8th
(C): 9th
(D): 10th
15. A null set is also called—–.
(A): singleton set
(B): none set
(C): subset
(D): void set
16. Find the sum of the series 1+5+25+125….upto fifth terms.
(A): 781
(B): 700
(C): 125
(D): 625
17. If A = {a,b}, B ={ b,c} then A?B= …
(A): {0}
(B): {a,b,c}
(C): {a,b}
(D): b,c}
18. Find the value of 10C3
(A): 120
(B): 10
(C): 30
(D): 3
19. Find the value of 6P4
(A): 6
(B): 4
(C): 24
(D): 360
20. If A= {1,2} and B={3,7}, then AnB= …
(A): {1,2}
(B): {3}
(C): {7}
(D): f
21. How many permutations could be made from the word ‘Calcutta’ ?
(A): 5440
(B): 5000
(C): 5040
(D): 6040
22. In how many ways a committee of 5 can be selected out of 8 persons.
(A): 5
(B): 8
(C): 56
(D): 40
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23. Find the minimum value of the function 2×2-x3 .
(A): at x=0 is 0
(B): at x=0 is 1
(C): at x=0 is 2
(D): at x=0 is 3
24. In coordinate geometary, how many quadrants are there?
(A): 1
(B): 2
(C): 3
(D): 4
25. The —— of a point is the path through which a point passes under certain given conditions.
(A): locus
(B): point
(C): origin
(D): 0
26. Solve the equation 25×2= 16
(A): x= ±2/5
(B): x= ±4/5
(C): x= 5
(D): x= ±4
27. Find the value of 7P4 ÷ 8P3
(A): 2.5
(B): 7.5
(C): 3.5
(D): 9.6
28. The value of (81).5 is …
(A): 3
(B): 6
(C): 27
(D): 9
29. If a set contains a finite/limited number of elements then it is called a ——.
(A): finite set
(B): limit
(C): singleton set
(D): null set
30. A ——-is a straight line with number units positive, zero and negative.
(A): directed line
(B): locus
(C): positive slope
(D): negative slope
31. If A = {1,2,3}, B ={2,3,4} then A-B =?
(A): {0}
(B): {1}
(C): {2,3}
(D): {3,4}
32. If two sets A and B are such that they donot have any common element then the sets A and B are called ——.
(A): finite set
(B): disjoint sets
(C): singleton set
(D): null set
33. In how many ways the letters of the word ‘Daughter’ can be arranged keeping the vowels together?
(A): 4320
(B): 1223
(C): 1234
(D): 3000
33. If all the elements of a matrix are zero then it is called a ——.
(A): empty matrix
(B): diagonal matrix
(C): null matrix
(D): none
34. While adding matrices, (A+B)+C = …
(A): ABC
(B): A+BC
(C): AB+C
(D): A+(B+C)
35. Find the average value of the function over the given interval. f(x) = 4 – x on [0, 4]
(A): 8
(B): 2
(C): 4
(D): 16
36. cos (-x) = …
(A): Cos x
(B): Cos 3x
(C): sin (-x)
(D): none of the above
37. Let V = {0,1,2,3,4,5,6,7,8,9}. Find (ø?V)nø
(A): {0,1,2,3,4,5}
(B): {0,2,4,6,8}
(C): ø
(D): {3,5,7}
38. If y= xx , find dy/dx
(A): x
(B): 1+logx
(C): xx(1+logx)
(D): logx
39. If U = {1,2,3,…..8,9} be the universal set. A = {1,2,3,4}. Find A’
(A): {1,2,3,4,}
(B): {2,3,4}
(C): {5,6,7,8,9}
(D): ø
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