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Simplification problems
1. If x = 1 + ?2 + ?3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is
Options
A. 2?2
B. 3?3
C. 5?5
D. 6?6
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Correct Answer: 6?6
2. PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ?RST = 65°, the ?PTS =
Options
A. 65°
B. 130°
C. 115°
D. 55°
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Correct Answer: 115°
3. What is the difference between the total sale of English newspapers and the total sale of Hindi newspapers in all the localities together.
Options
A. 7500
B. 5600
C. 6500
D. 5700
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Correct Answer: 6500
4. x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?
Options
A. 19
B. 23
C. 31
D. 29
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Correct Answer: 31
5. If the roots of the equation a(b ? c)x2 + b(c ? a)x + c(a ? b) = 0 are equal, then which of the following is true?
Options
A. b = ( a + c)/ ac
B. 2/ b = (1/ a) + (1/ c)
C. 2 b = (1/ a) + (1/ c)
D. abc = ab + bc + ca
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Correct Answer: 2/ b = (1/ a) + (1/ c)
6. The point Q(a,b) is first reflected in yaxis to Q1 and Q1 is reflected in xaxis to (6,2). The coordinates of point Q are
Options
A. (-6,2)
B. (2,-6)
C. (6,-2)
D. (-2,6)
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Correct Answer: (6,-2)
7. If cosec 4?/3 = x, then the value of x is
Options
A. ?2
B. 2/?3
C. ?2
D. -1/?3
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Correct Answer: 2/?3
8. If price of oranges is increased by 30%, then a person can buy 12 oranges less for Rs 208. What is the original price (in Rs) of an orange?
Options
A. 2
B. 4
C. 8
D. 3
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Correct Answer: 4
9. What are the roots of the quadratic equation: x2 + 3x - 154 = 0
Options
A. 11, 14
B. 11, -14
C. 14, -11
D. 14, -22
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Correct Answer: 11, -14
10. For triangle ABC, find equation of median AD if coordinates of points A, B and C are (2,4), (3,0) and (5,2) respectively?
Options
A. 3x - 2y = 14
B. 3x - 2y = 2
C. 3x + 2y = 14
D. 3x + 2y = 2
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Correct Answer: 3x - 2y = 14
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