 # Class 10 Maths Problems for Linear equation

Given below are the Class 10 Maths Problems for Linear equation
a. Concepts questions
b. Calculation problems
c. Multiple choice questions
e. Fill in the blank's

Question 1.
In a cyclic quadrilateral ABCD,Find the four angles.
a. $\angle A = (2x + 4)$, $\angle B = (y + 3)$, $\angle C = (2y + 10)$, $\angle D = (4x -5)$.
b. $\angle A = (2x - 1)$, $\angle B = (y + 5)$, $\angle C = (2y + 15)$ and $\angle D = (4x -7)$

Question 2.
Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs:
$3x - 2y = 4$
$6x + 2y = 4$
$9x -6y = 12$

Question 3
Find the values of a and b for which the following system of linear equations has infinite number of solutions:
$2x + 3y = 7$
$2ax + (a + b)y = 28$

Question 4
Find the values of a and b for which the following system of linear equations has infinite number of solutions:
$2x -3y = 7$
$(a + b)x - (a + b- 3)y = 4a + b$

Question 5.
In a ABC, $\angle A = x$, $\angle B = (3x -2)$, $\angle C = y$ Also $\angle C - \angle B = 9$. Find the three angles.

Question 6.
Find the value of k for which the system of equations x + 2y -3 = 0 and ky + 5x + 7 = 0 has a unique solution.

Question 7
For what value of a the system of linear equations $2x + 3y = 7$ and $(a -1)x + (a + 1)y = 3a - 1$ represent parallel lines.

Question 8
If the lines $x + 2y + 7 = 0$ and $2x + ky + 18 = 0$ intersect at a point, then find the value of k.

Question 9
Is $x = 5, y = -5$ a solution of the linear equation $3x + 2y - 5 = 0$?

Question 10.
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. Find the present ages of the son and the father.

Question 11.
Replace p by an appropriate number so that the following system of equations has a unique solution.
$2x + 3y = 5$
$px +9y = 12$

Question 12.
For what value of k, the following pair of linear equations has infinitely many solutions?
i. $kx + 4y - (k + 8) = 0$
$4x + ky + 4 = 0$
ii. $2x + 3y = 4$
$(k + 2)x + 6y = 3k + 2$

Question 13
For what value of k, will the following system of equations have no solutions?
i. $(3k + 1) x + 3y = 2$
$(k^2 + 1) x + (k - 2) y = 5$
ii. $3x + y = 1$
$(2k - 1) x + (k - 1) y = 2k + 1$
iii. $2x + ky = 11$
$5x -7y = 5$

Question 14.
For what value of k, does the pair of equations given below has a unique solution?
$2x + ky = 6$
$4x + 6y = 0$

Question 15.
Find the value of k for which the following system of linear equations has infinite solutions:
i. $x + (k + 1) y = 5$
$(k + 1) x + 9y = 8k - 1$
ii. $8x + 5y = 9$
$kx + 10y = 18$
iii. $2x + 3y = k$
$(k - 1) x + (k + 2) y = 3k$

Question 16
For what value of α, the system of equations
$\alpha x + 3y = \alpha - 3$
$12x + \alpha y = \alpha$
will have no solution?
-6

Question 17.
Find the value of k for which the system
$kx + 2y = 5$
$3x + y = 1$
has (i) a unique solution, and (ii) no solution.
k ≠6 , k=6

Question 18.
Find the value of k for which the system
$2x + ky = 1$
$3x - 5y = 7$
has (i) a unique solution, and (ii) no solution.
k ≠ -10/3 , k=10/3

Question 19
find the value of a and b for which the following system of equations has infinitely many solutions:
$2x - (2a + 5) y = 5$
$(2b + 1) x - 9y = 15$
(-1, 5/2)
Question 20.
Find the value of a for which the following system of equations has infinitely many solutions:
$2x + 3y - 7 = 0$
$(a - 1) x + (a + 1) y = (3a - 1)$
a=5

Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

You can use above books for extra knowledge and practicing different questions.

### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20

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