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

The sum of first six terms of an arithmetic progression is \(345\) and the difference between the first term and the sixth term is \(55\). Its first term and common difference are respectively

If \[ \sin\theta+\cos\theta=\sqrt2 \] then \[ \sin\theta\cos\theta= \]

The number of terms in the geometric progression \[ 3,\; \frac32,\; \frac34,\dots \] that are needed to give a sum \[ \frac{3069}{512} \] is

If \[ \frac{x+a}{b+c}+\frac{x+b}{c+a}+\frac{x+c}{a+b}=3 \] and \[ a+b+c=5, \] then \(x=\)

If \[ \frac{4}{x+y}+\frac{2}{x-y}=2 \] and \[ \frac{3}{x+y}+\frac{1}{x-y}=\frac54 \] then \(y:x=\)

The present age of father is four times the age of his son. Five years hence the age of father will be three times the age of his son. Then the present age of the son, in years, is

If a polynomial in \(x\) leaves remainders \(-2,19\) respectively when divided by \(x+3\) and \(x-4\), then the remainder it leaves when it is divided by \[ x^2-x-12 \] is

If \[ ax^2+bx+c \] is exactly divisible by \((x-1)\) and \((x-2)\) but leaves a remainder \(6\) when divided by \((x+1)\), then \(a+b-c=\)

If \[ 10.\overline{36}=\frac{p}{q}, \qquad \gcd(p,q)=1 \] then \(p+q=\)

If \[ x=5+\sqrt{24} \] then \[ \sqrt{x}-\frac{1}{\sqrt{x}}= \]

Evaluate: \[ \frac{5}{\sqrt[3]{16}-\sqrt[3]{4}+1}-\frac{3}{\sqrt[3]{16}+\sqrt[3]{4}+1} \]

If \[ a^x=b^{\frac{1}{y}}=c^{\frac{3}{z}} \] and \[ b^3=ac^2 \] then \(9xy-2zx=\)

If \[ 2^a=4^b=8^c \] and \[ abc=288, \] then \[ \frac{1}{2a}+\frac{1}{4b}+\frac{1}{8c}= \]

$ax^{2}-bx+c=0$ has roots $\sin60^\circ$ and $\cos60^\circ$. Then \[ \frac{ac}{b^{2}}+\frac{a+c}{b} = \ ? \]}

$(\cos^{2}0^{\circ}+\sin^{2}30^{\circ})(\tan^{2}45^{\circ}+\cot^{2}60^{\circ})(\cos^{2}180^{\circ}+\sin^{2}90^{\circ})=$

$\tan(A+B)=m$ and $\tan(A-B)=n$. Then $\tan(2A)=$

In an arithmetic progression, the first term is 2 and the sum of its first five terms is one-fourth of the sum of the next five terms. The 20th term of that progression is

Sum of first three terms of a GP is 93 and the product of the first and third terms is 225. Then the 4th term of the GP is

The equation \(x^3-24x^2+\alpha x-\beta=0\) has positive integral roots \(p,q,r\). If geometric mean of the three roots is 8, then \(\alpha=\)

The polynomial \(4x^3+ax^2+bx+c\) leaves remainders 11, -3 and 41 respectively when divided by \(x+1\), \(x+2\) and \(x-2\). Then the remainder when it is divided by \(x-1\) is

A polynomial \( p(x) \) in x leaves remainder 5 and 6 when the polynomial \( p(x) \) is divided by \( x+1 \) and \( x+3 \) respectively. If it leaves remainder \( ax+b \) when divided by \( x^{2}+4x+3 \), then \( 4a+6b = \)

If \(\frac{48}{x+y}-\frac{6}{x-y}=10\) and \(\frac{15}{x+y}+\frac{4}{x-y}=9\), then \(x^{2}+y^{2}=\)

If \(x, y\) are two real numbers such that \(x+y=23\) and \(x^{2}+y^{2}=289\), then \(x^{3}+y^{3}=\)

If \(\alpha,\beta\) are the zeroes of the polynomial \(x^2-78x+k\) and if \(\alpha=\beta-6\), then \(k=\)

If \(ax+b\) is added to \(4x^4+2x^3-2x^2+x-1\), then it is divisible by \(x^2+2x-3\). Then \(2a+b=\)