List of top Mathematical Ability Questions on Algebra asked in TG ICET

r is a rational number such that if 2 is added to its denominator its value is \( \frac{1}{2} \) and if 5 is subtracted from its numerator, its value is \( \frac{1}{3} \). Then \( \frac{1+r}{1-r} = \)

If \(a=\frac{\sqrt5+1}{\sqrt5-1}\) and \(b=\frac{\sqrt5-1}{\sqrt5+1}\), then \(a^2+ab+b^2=\)

\(\frac{2}{\sqrt{10+2\sqrt{21}}}-\frac{1}{\sqrt{12-2\sqrt{35}}}+\frac{1}{\sqrt{8-2\sqrt{15}}}=\)

\(\left(\dfrac{x^{m^2}}{x^{n^2}}\right)^{\frac{1{m-n}}=\)}

If \(\frac{x+y}{xy}=\frac{12}{35}\) and \(\frac{x-y}{xy}=\frac{2}{35}\), then \(5x+7y=\)

The cost of two mangoes and three oranges together is ₹88, and the cost of four mangoes and seven oranges together is ₹188. Then, the cost of four mangoes and three oranges together, in rupees, is:

If \(k\) is the minimum value of the algebraic expression \(x^2 + 3x + 2\) attained at \(x = a\), then \((k,a)=\)

What is the sum of all natural numbers strictly between 100 and 1000 which are multiples of 5?

In a geometric progression the difference between the fifth term and the fourth term is 576 and the difference between the second term and the first term is 9. The fifth term is:

If A and B are any two non-empty sets, then \[ [(A \cap (A \cup B)^C)] \cup [(A \cap B)\cup(A\cap B^C)] = \]

If \(\alpha, \beta,\) and \(\gamma\) are the zeros of the polynomial \(6x^3 - 29x^2 + 46x + 24\), then the polynomial whose zeros are \(\frac1\alpha,\frac1\beta,\frac1\gamma\) is:

If \(P(x)=x^3+ax^2+bx+c\) is a polynomial such that \(P(1)=0\), \(P(2)=0\), and \(P(3)=6\), then \(6a+4b+3c=\)

If the quadratic polynomial \((x^2-x-2)\) is a factor of the polynomial \((x^4-x^3+ax^2+bx+4)\), then \((a,b)=\)

The polynomial \(f(x)\) when divided by \((x-4)\) and \((x-6)\) leaves remainders 6 and 8 respectively. Then the remainder of \(f(x)\) when divided by \((x^2-10x+24)\) is:

If \[ \frac{7}{\sqrt3+\sqrt{10}} + \frac{8}{\sqrt3+\sqrt7} + \frac{9}{\sqrt7+\sqrt{10}} = p\sqrt3+q\sqrt7+r\sqrt{10}, \] then \(p^2+q^2+r^{-2}\) equals:

The sum of a rational number \(x\) and its reciprocal is \(\frac{113}{56}\). If \(x=\frac{m}{n}\), where \(\gcd(m,n)=1\), then \(m^2+n^2=\ ?\)

\[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]

\[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]

If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]