1). What is the number of integral solutions of the equations HCF (a, b) = 5 and a + b = 65 ?
A). None
B). Infinitely many
C). Less than 65
D). Exactly one
2). The difference of two consecutive cubes
A). is odd or even
B). is never divisible by 2
C). is always even
D). None of the above
3). Let a,b be positive integers. What is HCF aHCF(a,b) bHCF(a,b) equal to?
A). a
B). b
C). 1
D). aHCF(a,b)
4). The product of four consecutive natural numbers plus one is
A). anon-square
B). always sum of two square numbers
C). a square
D). None of these
5). For any integers ‘a’ and ‘b’ with HCF (a,b)= 1, what is HCF (a + b, a-b) equal to?
A). It is always 1
B). It is always 2
C). Either 1 or 2
D). None of the above
6). The expression 2×3+x2-2x-1divisible by
A). x+2
B). 2x+1
C). x-2
D). 2x-1
7). A positive number, when increased by 10, equals 200 times its reciprocal. What is that number?
A). 100
B). 10
C). 20
D). 200
8). x3+6×2+11x+6 is divisibke by
A). (x+1)only
B). (x+2)only
C). (x+3)only
D). All the above
9). The present age, of Ravi’s father is four times Ravi’s present age. Five years back he was seven times as old as Ravi was at that time. What is the present age of Ravi’s father?
A). 84 years
B). 70 years
C). 40 years
D). 35 years
10). The average age of male employees in a firm is 52 years and that of female employees is 42 years. The mean age of all employees is 50 years. The percentage of male and female employees are respectively
A). 80% and 20%
B). 20% and 80%
C). 50% and 50%
D). 52% and 48%
11). 15 men complete a work in 16 days. If 24 men are employed, then the time required to complete that work will be
A). 7 days
B). 8 days
C). 10 days
D). 12 days
12). A train takes 9 seconds to cross a pole. If the Speed of the train is 48 km/hr, the length of the train is
A). 150 m
B). 120 m
C). 90 m
D). 80 m
13). Ravi’s brother is 3 years elder to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, the ages of Ravi’s father and mother respectively when his brother was born were
A). 32 years and 23 years
B). 32 years and 29 years
C). 35 years and 29 years
D). 35 years and 33 years
14). In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains 9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was
A). x2+10x+9=0
B). x2-10x+16=0
C). x2-10x+9=0
D). None of the above
15). If m and n are the roots of the equation ax2+bx+c =0 then the equation whose roots are (m2+1)m and (n2+1)n is
A). acx2+(ab+bc)x+b2+(a−c)2=0
B). acx2+(ab−bc)x+b2+(a−c)2=0
C). acx2+(ab−bc)x+b2-(a−c)2=0
D). acx2+(ab+bc)x+b2-(a−c)2=0
16). The value of x2−4x+11 can never be less than
A). 7
B). 8
C). 11
D). 22
17). If (x2+1×2)=174, then what is (x3−1×3) equal to?
A). 7511
B). 638
C). 958
D). None of these
18). 3×4-2×3+3×2-2x+3 divided by (3x+2), then the remainder is
A). 0
B). 18527
C). 18125
D). 34
19). What should be added to the expressionx(x+a)(x+2a)(x+3a) so that the sum may ba a perfect square?
A). 9a2
B). 4a2
C). a4
D). None of these
20). If the roots of the equation Ax2+Bx+C =0 are -1 and 1 then which one of the following is correct?
A). A andC are both zero
B). A and B are both positive
C). A and C are both negative
D). A and C are of opposite sign