Algebra

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The age of a man is the square of his son's age. One year ago, the man's age was eight times the age of his son. What is the present age of the man?
1. 30
2. 40
3. 60
4. 49
Find the LCM of 8x⁴y² , 48x²y⁴
1. x⁴y⁴
2. x⁴
3. y⁴
4. x⁴y²
Find the sum and product of the roots x²+8x−65=0
1. −8 , 65
2. −8 , −65
3. −8 , 5
4. −8 , −5
Solve 2x−3y= 6 , x+y= 1
1. −4/5,9/5
2. 4/5,9/5
3. 9/5,−4/5
4. 9/5,4/5
Solve x⁴−13x²+42=0
1. √7, -√6
2. -√7, 6
3. ±√7, ±√6
4. ±√7, √6
If the roots of the equation 3ax²+2bx+c=0 are in the ratio 2 : 5, then
1. none
2. 40b²=75ac
3. 8ac=25b²
4. 6ac=19b²
1. a = −1, b = −12, c = 7, d = −1
2. a = 3, b = 2, c = 7, d = 19
3. a = −1, b = −2, c = 7, d = −19
4. a = −1, b = −8, c = 7, d = −9
The father’s age is six times his son’s age. Six years hence the age of father will be four times his son’s age. Find the present ages (in years) of the son and father.
1. 54 years
2. 56 years
3. 52 years
4. 50 years
Find the value of ?a? for which m=1/√3 is a root of the equation.am²+(√3−√2)m−1=0.
1. 5
2. √2
3. 2
4. √6
Find the GCD of the polynomials x³+x²−x+2 & x³−5x²+5x−3
1. x²−x
2. x²−x+1
3. x²+x+5
4. x+1
Find the zeroes of the quadratic expression x²+8x+12
1. -2 and -6
2. -2 and 3
3. None
4. 2 and 6
Solve the following system of linear equations in three variables
3x−2y+z=0 ,2x+3y−z=5,x+y+z=6.
1. x = 1, y = 2 , z = 3
2. x = 3, y = 2 , z = 1
3. x = 1, y = 3 , z = 2
4. x = 1, y = -2 , z = -3
If α and β are the root of the equation2x²−3x−7=0 then the value ofαβ²+α²β+αβ are.
1. -15/8
2. 3/4
3. -35/4
4. 6
Choose the correct answer
1. Every identity matrix is a scalar matrix
2. A square matrix whose each element is 1 is an identity matrix
3. Every diagonal matrix is an identity matrix
4. Every scalar matrix is an identity matrix
1. a = 7, b = -3/2,c=3/4 ,d = 12.
2. a = 7, b = -2,c=4 ,d = –1.
3. a = 7, b = -3, c=4 ,d = –1.
4. a = 7, b = -3/2,c=3/4 ,d = –1.
Solve 3x+y−3z=1,−2x−y+2z=1,−x−y+z=2
1. x = 1, y = 2 , z = 0
2. no solution.
3. x = 1, y = 2 , z = 3
4. x = 1, y = 0 , z = 3
Which of the following equations has no real roots?
1. x²+2x-6√2=0
2. None
3. x²-4x-3√2=0
4. x²−4x+3√2=0
If the roots of the quadratic equation ax²+bx+c=0are α and β, then the equation whose roots are α² and β² is
1. 2a²x²−(b²+2ac)x+2c²=0
2. a²x²−(b²−2ac)x+c²=0
3. (a²−r)x²+(b²−r)x+c²r=0
4. (a²−ac)x²+(b²+2ac)x+cv=0
If A=dig(2,−1,3),B=dig(−1,3,2), then A²B=
1. None
2. dig (3, 1, 8)
3. dig (5, 4, 11)
4. dig (-4, 3, 18)
1. x = 1 , y = -1 .
2. x = 1 , y = 2 .
3. x = 2 , y = 1
4. x = 1 , y = -2 .
If AB=C, then matrices A,B,Care
1. A3×2,B2×3,C3×2
2. A3×2,B2×3,C3×3
3. A3×3,B2×3,C3×3
4. A2×3,B3×2,C2×3
The equation 9y²(m+3)+6(m−3)y+(m+3)=0, where m is real, has real roots. Which of the following is true?
1. m≤0
2. m=0
3. m<0
4. m≥0

Algebra

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