Question 1 : State true or false: If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

Question 4 : State true or false: The only value of $k$ for which the quadratic polynomial $kx^2+x+k$ has equal zeroes is $\frac{1}{2}$.

Question 6 : State true or false: If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial.

Question 8 : Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$

Question 9 : If on division of a polynomial $p\left(x\right)$ by a polynomial $g\left(x\right)$, the quotient is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$ ?

Question 10 : 3, –1, $-\frac {1}{3}$ are the zeroes of the cubic polynomial $p\left(x\right)=3x^3-5x^2-11x-3$. Is it correct or not?

Question 11 : The number of polynomials having zeroes as -2 and 5 is:

Question 12 : If the zeroes of the polynomial $x^3-3x^2+x+1$ are a – b, a, a + b, then a and b are 1 and $\pm \sqrt{2}$.

Question 13 : Given that the zeroes of the cubic polynomial $x^3-6x^2+3x+10$ are of the form a, a+b, a+2b for some real numbers a and b, find the value of a.

Question 14 : What will the remainder be on division of $ax^2+bx+c$ by $px^3+qx^2+rx+s$, $p\ne0$ ?

Question 15 : If one of the zeroes of the quadratic polynomial $\left(k-1\right)x^2+kx+1$ is -3, then the value of k is:

Question 16 : Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.

Question 17 : Find all the zeros of $2x^4-3x^3-3x^2+6x-2$, if you know that two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}$ .

Question 18 : State true or false: If the zeroes of a quadratic polynomial $ax^2+bx+c$ are both positive, then a,b and c all have the same sign.

Question 19 : If the remainder on division of $x^3+2x^2+kx+3$ by $x-3$ is 21, find the value of k.

Question 20 : Find a quadratic polynomial, the sum and product of whose zeroes are 1 and 1, respectively.

Question 21 : Can $x-1$ be the remainder on division of a polynomial $p\left(x\right)$ by $2x+3$ ?

Question 22 : If one of the zeroes of the quadratic polynomial of the form $x^2+ax+b$ is the negative of the other, then it:

Question 23 : Can the quadratic polynomial $x^2+kx+k$ have equal zeroes for some odd integer k>1?

Question 24 : What will the quotient be on division of $ax^2+bx+c$ by $px^3+qx^2+rx+s$, $p\ne0$ ?

Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be1273b230584979a36.png' /> Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.

Question 26 : The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Which of these represent the situation algebraically?

Question 27 : Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are intersecting lines.

Question 28 : Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x – 2y – 2 = 0 , 4x – 4y – 5 = 0$

Question 29 : Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 ; \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = -1$.

Question 30 : On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations intersect at a point, are parallel or coincident: $9x + 3y + 12 = 0 ; 18x + 6y + 24 = 0$

Question 31 : Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Question 32 : Romila went to a stationery shop and purchased 2 pencils and 3 erasers for Rs. 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs. 18. Which of these represent this situation algebraically ?

Question 33 : Solve the following pair of equations by substitution method: $7x – 15y =2 ; x + 2y =3$

Question 34 : On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $\frac{4}{3}x + 2y = 8 ; 2x + 3y = 12$

Question 35 : If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are intersecting when _____________.

Question 36 : Solve the following pair of linear equations by the elimination method and the substitution method : $3x + 4y = 10 ~and ~2x – 2y = 2$

Question 37 : Solve the following pair of linear equations by the elimination method and the substitution method : $x + y = 5 ~and ~2x – 3y = 4$

Question 38 : Solve $2x + 3y = 11$ and $2x – 4y = – 24$ and hence find the value of ‘m’ for which $y = mx + 3$.

Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdc273b230584979a2f.png' /> In the above fig, the lines represents ____________ lines.

Question 40 : One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?

Question 41 : Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received.

Question 42 : Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Question 43 : Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.

Question 44 : State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $3x – 5y = 20 ; 6x – 10y = 40$

Question 45 : The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pencil box.

Question 46 : State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$

Question 47 : Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Question 48 : Solve the following pair of linear equations: $152x – 378y = – 74 ; –378x + 152y = – 604$

Question 49 : Solve the following pair of equations by substitution method: $s-7t+42=0 ; s-3t=6$

Question 50 : A pair of linear equations which has no solution, is called an __________________ pair of linear equations.

Question 51 : Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Question 53 : Is it true to say that the pair of equations – x + 2y + 2 = 0 and $\frac{1}{2}x-\frac{1}{4}y-1=0$ has a unique solution?

Question 54 : Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{10}{x+y} + \frac{2}{x-y} = 4 ; \frac{15}{x+y} - \frac{5}{x-y} = -2$.

Question 55 : Solve the following pair of linear equations: $px + qy = p – q ; qx – py = p + q$

Question 56 : Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: $5x – 8y + 1 =0 ; 3x - \frac{24}{5}y + \frac{3}{5} = 0$

Question 58 : The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Question 59 : The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.

Question 60 : On comparing the ratios $\frac{a_1}{a_2]$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$, find out whether the lines representing a pair of linear equations are consistent or inconsistent: $3x + 2y = 5 ; 2x – 3y = 7$

Question 61 : An equation which can be put in the form ax + by + c = 0,where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables x and y. TRUE or FALSE?

Question 62 : Solve the following pair of linear equations by the substitution method : $0.2x + 0.3y = 1.3 ; 0.4x + 0.5y = 2.3$

Question 63 : For which values of p does the pair of equations given below has unique solution?$4x + py + 8 =0 ; 2x + 2y + 2 =0$

Question 64 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b5c273b230584979988.png' /> In the above given graph of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0, calculate the area of the triangle formed by the lines so drawn and the x-axis.

Question 65 : Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $2x + y – 6 = 0 , 4x – 2y – 4 = 0$

Question 66 : Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines.

Question 67 : Use elimination method to find all possible solutions of the following pair of linear equations :$2x + 3y =8 , 4x + 6y =7$

Question 68 : Solve the following pair of equations by reducing them to a pair of linear equations : $\frac{1}{2x} + \frac{1}{3y} = 2 ; \frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}$.

Question 69 : Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}$, then the pair of linear equations is _______.

Question 70 : 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. Find the solution graphically.