Mathematical Series Questions for Competitive Exams
Q. The value of k for which the graphs of (k-1) x+y-2 = 0 and (2-k) x -3y + 1 = 0 are parallel is-
a. ½
b. -1/2
c. 2
d. -2
Ans : (k – 1) x + y – 2 = 0
We know y = (1 – k) x + 2 ….(1)
and (2 –k) x – 3y – 1 = 0
3y = (2 – k) x +1
Y = 2 – k/3 x + 1/3 ….(2)
We know that m1 = m2
=> 1 – k = 2 – k/3
=> 3 – 3k = 2 – k
We know k = 1/2
Q. If a2 + b2 + c2 = 2 (a-b-c) – 3, then the value of (a – b + c) is-
a. -1
b. 3
c. 1
d. -2
Ans : a2 + b2 + c2 = 2(a – b – c) – 3
=> a2 – 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
=> (a – 1)2 + (b + 1)2 + (c + 1)2 = 0
=> a – 1 = 0, b + 1 = 0, c + 1 = 0
=> a = 1, b = -1, c = -1
We know a + b – c = 1 – 1 + 1 =1
Q. If x2 + 3x + 1 = 0, then the value of x3 + 1/x3 is-
a. -18
b. 18
c. 36
d. -36
Ans : We know that x2 + 3x + 1 = 0
=> x + 3 + 1/x = 0
=> x + 1/x = -3
=> (x + 1/x)3 = (-3)3
=> x3 + 1/x3 + 3 (-3) = -27
We know x3 + 1/ x3 = -18
Q. If xa, xb, xc = 1, then the value of a3 + b3 + c3 is –
a. 9
b. abc
c. a + b + c
d. 3abc
Ans : We know that xa. xb. xc = 1
=> xa + b + c = x0
=> a +b + c =0
We know a3 + b3 + c3 = 3abc
Q. Base of a right pyramid is a square, length of diagonal of the base is 24?2 m. If the volume of the pyramid is 1728 cu.m, its height is-
a. 7 m
b. 8 m
c. 9 m
d. 10 m
Ans : Area of the base of the pyramid
= ½ (24?2)2 = 576m2
We know Height of pyramid + 1728*3/576 = 9m
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