Algebra

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. 52 years
2. 54 years
3. 56 years
4. 50 years
Solve 2x−3y= 6 , x+y= 1
1. 9/5,−4/5
2. −4/5,9/5
3. 4/5,9/5
4. 9/5,4/5
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 = 1, y = 2 , z = 3
3. x = 3, y = 2 , z = 1
4. x = 1, y = 3 , z = 2
Solve 3x+y−3z=1,−2x−y+2z=1,−x−y+z=2
1. x = 1, y = 2 , z = 3
2. x = 1, y = 2 , z = 0
3. x = 1, y = 0 , z = 3
4. no solution.
Find the GCD of the polynomials x³+x²−x+2 & x³−5x²+5x−3
1. x²−x+1
2. x+1
3. x²−x
4. x²+x+5
Find the LCM of 8x⁴y² , 48x²y⁴
1. x⁴y²
2. x⁴y⁴
3. x⁴
4. y⁴
Find the zeroes of the quadratic expression x²+8x+12
1. 2 and 6
2. -2 and -6
3. -2 and 3
4. None
Find the sum and product of the roots x²+8x−65=0
1. −8 , −65
2. −8 , 5
3. −8 , 65
4. −8 , −5
Solve x⁴−13x²+42=0
1. ±√7, √6
2. ±√7, ±√6
3. √7, -√6
4. -√7, 6
Find the value of ?a? for which m=1/√3 is a root of the equation.am²+(√3−√2)m−1=0.
1. √2
2. 2
3. √6
4. 5
Which of the following equations has no real roots?
1. x²−4x+3√2=0
2. x²+2x-6√2=0
3. x²-4x-3√2=0
4. None
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. 60
2. 49
3. 30
4. 40
If the roots of the equation 3ax²+2bx+c=0 are in the ratio 2 : 5, then
1. 8ac=25b²
2. 6ac=19b²
3. 40b²=75ac
4. none
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
If α and β are the root of the equation2x²−3x−7=0 then the value ofαβ²+α²β+αβ are.
1. 6
2. -35/4
3. 3/4
4. -15/8
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. a²x²−(b²−2ac)x+c²=0
2. (a²−r)x²+(b²−r)x+c²r=0
3. (a²−ac)x²+(b²+2ac)x+cv=0
4. 2a²x²−(b²+2ac)x+2c²=0
If A=dig(2,−1,3),B=dig(−1,3,2), then A²B=
1. dig (5, 4, 11)
2. dig (-4, 3, 18)
3. dig (3, 1, 8)
4. None
If AB=C, then matrices A,B,Care
1. A2×3,B3×2,C2×3
2. A3×2,B2×3,C3×2
3. A3×3,B2×3,C3×3
4. A3×2,B2×3,C3×3
Choose the correct answer
1. Every identity matrix is a scalar matrix
2. Every scalar matrix is an identity matrix
3. Every diagonal matrix is an identity matrix
4. A square matrix whose each element is 1 is an identity matrix
1. a = −1, b = −2, c = 7, d = −19
2. a = 3, b = 2, c = 7, d = 19
3. a = −1, b = −12, c = 7, d = −1
4. a = −1, b = −8, c = 7, d = −9
1. a = 7, b = -3/2,c=3/4 ,d = 12.
2. a = 7, b = -3, c=4 ,d = –1.
3. a = 7, b = -3/2,c=3/4 ,d = –1.
4. a = 7, b = -2,c=4 ,d = –1.
1. x = 2 , y = 1
2. x = 1 , y = 2 .
3. x = 1 , y = -1 .
4. x = 1 , y = -2 .

Algebra

Quiz