TS EAMCET PYQs for System of Linear Equations with Solutions: Practice TS EAMCET Previous Year Questions

Updated 3+ months ago

System of Linear Equations is an important topic in the Mathematics section in TS EAMCET exam. Practising this topic will increase your score overall and make your conceptual grip on TS EAMCET exam stronger.

This article gives you a full set of TS EAMCET PYQs for System of Linear Equations with explanations for effective preparation. Practice of TS EAMCET Mathematics PYQs including System of Linear Equations questions regularly will improve accuracy, speed, and confidence in the TS EAMCET 2026 exam.

TS EAMCET PYQs for System of Linear Equations with Solutions

1.
If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is
- $[-1, 0) \cup [\frac{24}{25}, \infty)$
- $[\frac{24}{25}, \infty)$
- $[-1, 0)$
- $\mathbb{R}$
View Solution
2.
If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is
- 0
- 2+i
- -4-4i
- 8/3
View Solution
3.
If the quotient and remainder obtained when the expression $3x^5-6x^4+2x^3+4x^2-5x+8$ is divided by the expression $x^2-2x+3$ are $ax^3+bx^2+cx+d$ and $px+q$ respectively, then $ab+cd =$
- $p+2q$
- $p+2q-2$
- $2p+q$
- $2p+q-2$
View Solution
4.
If $f(x) = x^2 - 2(4K-1)x + g(K)>0$ $\forall x \in \mathbb{R}$ and for $K \in (a,b)$, and if $g(K) = 15K^2 - 2K - 7$, then
- g(K) attains its maximum at the midpoint of (a,b)
- g(K) attains its minimum at two points in (a,b)
- g(K) attains its both maximum and minimum in (a,b)
- g(K) attains no maximum and no minimum in (a,b)
View Solution
5.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$
- 5
- 7
- 11
- 13
View Solution
6.
If $\tan\theta$ and $\cot\theta$ are two distinct roots of the equation $ax^2+bx+c=0, a\neq0, b\neq0$, then
- $\cos 2\theta = -\frac{2b}{c}$
- $\sin 2\theta = -\frac{2c}{b}$
- $\tan 2\theta = \frac{2b}{c}$
- $\cot 2\theta = \frac{2c}{a}$
View Solution
7.
If $AX = D$ represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?
- $\text{Rank}(A) = \text{Rank}([A|D])= 1$
- $\text{Rank}(A) = \text{Rank}([A|D])= 2$
- $\text{Rank}(A) = \text{Rank}([A|D])= 3$
- $\text{Rank}(A) \neq \text{Rank}([A|D])$
View Solution
8.
The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is
- $x^2 + 2x - 3 = 0$
- $x^2 - 3x + 2 = 0$
- $x^2 + x - 2 = 0$
- $x^2 - 4x + 3 = 0$
View Solution
9.
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2}x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$, $(\beta-\alpha)(\beta-\gamma)$, $(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$, then $\frac{L}{K}= $
- $\frac{32b^2}{a}$
- $\frac{16a^2}{b}$
- $\frac{18b^2}{a}$
- $\frac{12a^2}{b}$
View Solution
10.
Sum of all the roots of the equation $||2x-3|-4| = 2$ is
- 8
- 0
- 6
- 9
View Solution
11.
If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is
- -3
- 3
- 6
- -6
View Solution
12.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta = \gamma\delta = 1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta} =$
- $65/6$
- $13/2$
- $17/15$
- $15/13$
View Solution
13.
The system of equations $ x + 3y + 7 = 0 $, $ 3x + 10y - 3z + 18 = 0 $, and $ 3y - 9z + 2 = 0 $ has:
- unique solution
- infinitely many solutions
- no solution
- finite number of solutions \bigskip
View Solution
14.
If local maximum of $f(x) = \frac{ax+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$
- 0
- -1
- 1
- 2
View Solution
15.
The system of simultaneous linear equations :

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]
- Infinitely many solutions
- No solution
- Unique solution having z = 2
- Unique solution having z =1⁄2
View Solution

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TS EAMCET PYQs for System of Linear Equations with Solutions: Practice TS EAMCET Previous Year Questions

TS EAMCET PYQs for System of Linear Equations with Solutions

1.
If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

2.
If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

3.
If the quotient and remainder obtained when the expression $3x^5-6x^4+2x^3+4x^2-5x+8$ is divided by the expression $x^2-2x+3$ are $ax^3+bx^2+cx+d$ and $px+q$ respectively, then $ab+cd =$

4.
If $f(x) = x^2 - 2(4K-1)x + g(K)>0$ $\forall x \in \mathbb{R}$ and for $K \in (a,b)$, and if $g(K) = 15K^2 - 2K - 7$, then

5.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

6.
If $\tan\theta$ and $\cot\theta$ are two distinct roots of the equation $ax^2+bx+c=0, a\neq0, b\neq0$, then

7.
If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?

8.
The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

9.
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2}x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$, $(\beta-\alpha)(\beta-\gamma)$, $(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$, then $\frac{L}{K}= $

10.
Sum of all the roots of the equation $||2x-3|-4| = 2$ is

11.
If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

12.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta = \gamma\delta = 1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta} =$

13.
The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:

14.
If local maximum of $f(x) = \frac{ax+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$

15.
The system of simultaneous linear equations :

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]

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TS EAMCET PYQs for System of Linear Equations with Solutions

1.If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

2.If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

3.If the quotient and remainder obtained when the expression $3x^5-6x^4+2x^3+4x^2-5x+8$ is divided by the expression $x^2-2x+3$ are $ax^3+bx^2+cx+d$ and $px+q$ respectively, then $ab+cd =$

4.If $f(x) = x^2 - 2(4K-1)x + g(K)>0$ $\forall x \in \mathbb{R}$ and for $K \in (a,b)$, and if $g(K) = 15K^2 - 2K - 7$, then

5.If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

6.If $\tan\theta$ and $\cot\theta$ are two distinct roots of the equation $ax^2+bx+c=0, a\neq0, b\neq0$, then

7.If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?

8.The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

9.If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2}x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$, $(\beta-\alpha)(\beta-\gamma)$, $(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$, then $\frac{L}{K}= $

10.Sum of all the roots of the equation $||2x-3|-4| = 2$ is

11.If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

12.If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta = \gamma\delta = 1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta} =$

13.The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:

14.If local maximum of $f(x) = \frac{ax+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$

15.The system of simultaneous linear equations : \[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]

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1.
If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

2.
If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

3.
If the quotient and remainder obtained when the expression $3x^5-6x^4+2x^3+4x^2-5x+8$ is divided by the expression $x^2-2x+3$ are $ax^3+bx^2+cx+d$ and $px+q$ respectively, then $ab+cd =$

4.
If $f(x) = x^2 - 2(4K-1)x + g(K)>0$ $\forall x \in \mathbb{R}$ and for $K \in (a,b)$, and if $g(K) = 15K^2 - 2K - 7$, then

5.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

6.
If $\tan\theta$ and $\cot\theta$ are two distinct roots of the equation $ax^2+bx+c=0, a\neq0, b\neq0$, then

7.
If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?

8.
The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

9.
If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2}x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$, $(\beta-\alpha)(\beta-\gamma)$, $(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$, then $\frac{L}{K}= $

10.
Sum of all the roots of the equation $||2x-3|-4| = 2$ is

11.
If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

12.
If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta = \gamma\delta = 1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta} =$

13.
The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:

14.
If local maximum of $f(x) = \frac{ax+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$

15.
The system of simultaneous linear equations :

\[ \begin{array}{rcl} x - 2y + 3z &=& 4 \\ 2x + 3y + z &=& 6 \\ 3x + y - 2z &=& 7 \end{array} \]