The mean of \(x\) and \(y\) is \(a\), the mean of \(y\) and \(z\) is \(b\) and the mean of \(x\) and \(z\) is \(c\). What is the mean of \(x, y\) and \(z\)?
A\(\frac{a+b+c}{3}\)
B\(\frac{a+b+c}{2}\)
C\(a+b+c\)
D\(\frac{abc}{a+b+c}\)
Mathematics · Question Bank
algebra
342 of 433 questions match · page 5 of 18. Answer in your head first, then check the solution.
Find the mean proportional of \(4\) and \(36\).
A\(72\)
B\(24\)
C\(12\)
D\(20\)
The arithmetic mean of \(80\) numbers is \(55\). If two numbers namely \(250\) and \(850\) are removed, what is the arithmetic mean of the remaining numbers?
A\(42.31\)
B\(50\)
C\(38.62\)
D\(57.12\)
The arithmetic mean of \(6\) numbers is \(17\). If two numbers are added to the progression, the new set of numbers will have an arithmetic mean of \(19\). What are the two numbers if their difference is \(4\)?
A\(21, 25\)
B\(23, 27\)
C\(8, 12\)
D\(16, 20\)
The equation of whose roots are the reciprocal of the roots of \(2x^2-3x-5=0\) is,
A\(5x^2+3x-2=0\)
B\(2x^2+3x-5=0\)
C\(3x^2-3x+2=0\)
D\(2x^2+5x-3=0\)
In the equation \(x^2+x=0\) one root is \(x\) equal to
A1
B5
C\(1/4\)
Dnone of these
Solve for the value of "a" in the equation \(a^8-17a^4+16=0\)
A\(\pm 2\)
B\(\pm 3\)
C\(\pm 4\)
D\(\pm 5\)
Solve for \(x\) that satisfies the equation \(6x^2-7x-5=0\).
A\(\frac{5}{3}\) or \(\frac{-1}{2}\)
B\(\frac{3}{2}\) or \(\frac{3}{8}\)
C\(\frac{7}{5}\) or \(\frac{-7}{15}\)
D\(\frac{3}{5}\) or \(\frac{3}{4}\)
Find the values of \(x\) in the equation \(24x^2+5x-1=0\)
A\((\frac{1}{6}, 1)\)
B\((\frac{1}{6}, \frac{1}{5})\)
C\((\frac{1}{2}, \frac{1}{5})\)
D\((\frac{1}{8}, -\frac{1}{3})\)
Determine \(k\) so that the equation \(4x^2+kx+1=0\) will have just one real solution.
A3
B4
C5
D6
Solve for \(x\): \(10x^2+10x+1=0\)
A\(-0.113, -0.887\)
B\(-0.331, -0.788\)
C\(-0.113, -0.788\)
D\(-0.311, -0.887\)
If \(1/3\) and \(-3/2\) are the roots of a quadratic equation, then the equation is
A\(6x^2+7x-3=0\)
B\(6x^2-7x+3=0\)
C\(6x^2-7x-3=0\)
D\(6x^2-7x+1=0\)
Which of the following is a root of this quadratic equation, \(30x^2+49x+20=0\)?
A0.6
B-0.6
C-0.8
D0.75
What is the discriminant of the equation \(4x^2=8x-5\)?
A8
B-16
C16
D-8
Given the equation \(3x^2+Bx+12=0\). What is the value of \(B\) so that the roots of the equation are equal?
A4
B8
C10
D-12
Find the term involving \(y^5\) in the expansion of \((2x^2+y)^{10}\)
A\(8064 x^{10}y^5\)
B\(8046 x^5y^5\)
C\(8046 x^{10}y^5\)
D\(4680 x^5y^5\)
Find the \(5^{th}\) term of the expansion of \((x^2+\frac{1}{x})^{10}\)
A\(260 x^8\)
B\(5040 x^8\)
C\(210 x^8\)
D\(420 x^8\)
In the expression of \((x+4y)^{12}\), the numerical coefficient of the \(5^{th}\) term is,
A63,360
B126,720
C506,880
D253,440
What is the fourth term of the expansion of \((x+x^2)^{100}\)?
A\(1650 x^{103}\)
B\(161700 x^{103}\)
C\(167100 x^{16}\)
D\(167100 x^{100}\)
What is the numerical coefficient of the term next to \(495x^8y^4\)?
A660
B792
C990
D1100