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All questions of Chapter 2: Equations for CA Foundation Exam
Solve 9x2 = 36- a)±2
- b)±6
- c)±4
- d)2
Correct answer is option 'A'. Can you explain this answer?
Solve 9x2 = 36
a)
±2
b)
±6
c)
±4
d)
2
|
Nilanjan Shah answered |
Solution:
To solve this equation, we need to isolate the variable x.
Given equation is 9x2 = 36
Step 1: Divide both sides by 9
9x2/9 = 36/9
Step 2: Simplify
x2 = 4
Step 3: Take square root on both sides
√(x2) = √4
Step 4: Simplify
x = ±2
Therefore, the solution of the given equation 9x2 = 36 is x = ±2.
Explanation:
The given equation is a quadratic equation in which we need to find the value of x. To solve the equation, we need to isolate the variable x by following the steps mentioned above. We divided both sides by 9 to simplify the equation. After simplification, we got x2 = 4 which means x can be either positive or negative 2. We took the square root of both sides and simplified the equation to get the final solution x = ±2.
To solve this equation, we need to isolate the variable x.
Given equation is 9x2 = 36
Step 1: Divide both sides by 9
9x2/9 = 36/9
Step 2: Simplify
x2 = 4
Step 3: Take square root on both sides
√(x2) = √4
Step 4: Simplify
x = ±2
Therefore, the solution of the given equation 9x2 = 36 is x = ±2.
Explanation:
The given equation is a quadratic equation in which we need to find the value of x. To solve the equation, we need to isolate the variable x by following the steps mentioned above. We divided both sides by 9 to simplify the equation. After simplification, we got x2 = 4 which means x can be either positive or negative 2. We took the square root of both sides and simplified the equation to get the final solution x = ±2.
The present age of a father is the sum of the ages of his three sons. Ten years from now his age will be a three quarter of the sum of their ages then. How old is the father?
- a)50 years
- b)30 years
- c)40 years
- d)60 years
Correct answer is option 'A'. Can you explain this answer?
The present age of a father is the sum of the ages of his three sons. Ten years from now his age will be a three quarter of the sum of their ages then. How old is the father?
a)
50 years
b)
30 years
c)
40 years
d)
60 years
|
Kashish Juneja answered |
If am ≠ bl, then the system of equations, ax + by = c, lx + my = n- a)has a unique solution
- b)has no solution
- c)has infinitely many solutions
- d)may or may not have a solution
Correct answer is option 'A'. Can you explain this answer?
If am ≠ bl, then the system of equations, ax + by = c, lx + my = n
a)
has a unique solution
b)
has no solution
c)
has infinitely many solutions
d)
may or may not have a solution
|
Vivek Rana answered |
If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.
Given,
Pair of lines represented by the equations
ax + by = c
lx + my = n
For unique solution
For infinite solutions
For no solution
Given,
This can be transformed into
Therefore, If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.
A pair of linear equations which has a unique solution x = 2, y = - 3 is
- a)x + y = -1; 2x - 3y = -5
- b)x - 4y - 14 = 0; 5x - y - 13 = 0
- c)2x - y = 1 ; 3x + 2y = 0
- d)2x + 5y = -11; 4x + 10y = -23
Correct answer is option 'B'. Can you explain this answer?
A pair of linear equations which has a unique solution x = 2, y = - 3 is
a)
x + y = -1; 2x - 3y = -5
b)
x - 4y - 14 = 0; 5x - y - 13 = 0
c)
2x - y = 1 ; 3x + 2y = 0
d)
2x + 5y = -11; 4x + 10y = -23
|
|
Vikram Kapoor answered |
x - 4y -14 = 0
x = 4y+14
putting this in 5x - y -13 = 0
5(4y+14) - y -13 =0
19y = -57
y = -3
putting y = -3 in x = 4y+14
x = 4(-3)+14
x = 2
so option b is correct
The sum of two numbers is 45 and one is twice the other. What is the smaller number?
- a)30
- b)35
- c)15
- d)25
Correct answer is option 'C'. Can you explain this answer?
The sum of two numbers is 45 and one is twice the other. What is the smaller number?
a)
30
b)
35
c)
15
d)
25
|
Kailash mukherjee answered |
To solve this problem, we can use algebraic equations. Let's assume that the smaller number is x.
Given that one number is twice the other, we can express the larger number in terms of the smaller number as:
Larger number = 2x
And the sum of the two numbers is 45, so we can write the equation:
x + 2x = 45
Simplifying the equation, we have:
3x = 45
Dividing both sides of the equation by 3, we get:
x = 15
Therefore, the smaller number is 15.
So, option C, 15, is the correct answer.
Given that one number is twice the other, we can express the larger number in terms of the smaller number as:
Larger number = 2x
And the sum of the two numbers is 45, so we can write the equation:
x + 2x = 45
Simplifying the equation, we have:
3x = 45
Dividing both sides of the equation by 3, we get:
x = 15
Therefore, the smaller number is 15.
So, option C, 15, is the correct answer.
The pair of equations y = 0 and y = - 7 has- a)one solution
- b)two solutions
- c)infinitely many solutions
- d)no solution
Correct answer is option 'D'. Can you explain this answer?
The pair of equations y = 0 and y = - 7 has
a)
one solution
b)
two solutions
c)
infinitely many solutions
d)
no solution
|
Gaurav Kumar answered |
The equation are y=0 and y=-7
y=0 is on the x-axis and y=-7 is the line parallel to the x-axes at a distance 7 units from y=0
The line will be parallel
if we try to solve these equations we get 0=7 which is absurd.
So the equations are inconsistent.
Therefore there is no solution.
y=0 is on the x-axis and y=-7 is the line parallel to the x-axes at a distance 7 units from y=0
The line will be parallel
if we try to solve these equations we get 0=7 which is absurd.
So the equations are inconsistent.
Therefore there is no solution.
Which of the following in not a quadratic equation:- a)(x – 2)2 + 1 = 2x – 3
- b)(x + 2)2 = x3 – 4
- c)x(2x + 3) = x2 + 1
- d)x(x + 1) + 8 = (x + 2) (x – 2)
Correct answer is option 'D'. Can you explain this answer?
Which of the following in not a quadratic equation:
a)
(x – 2)2 + 1 = 2x – 3
b)
(x + 2)2 = x3 – 4
c)
x(2x + 3) = x2 + 1
d)
x(x + 1) + 8 = (x + 2) (x – 2)
|
Krishna Iyer answered |
Option (B) and (D) , both are the correct answers. We have x(x + 1) + 8 = (x + 2) (x – 2)
=x2 + x + 8 = x2 - 4
= x = -12, which is not a quadratic equation
Also, in (B) (x + 2)2 = x3 – 4
=x2 +4x + 4=x3 - 4, which is a cubic equation
=x2 + x + 8 = x2 - 4
= x = -12, which is not a quadratic equation
Also, in (B) (x + 2)2 = x3 – 4
=x2 +4x + 4=x3 - 4, which is a cubic equation
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of number get reversed. The number is- a)25
- b)72
- c)63
- d)36
Correct answer is option 'D'. Can you explain this answer?
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of number get reversed. The number is
a)
25
b)
72
c)
63
d)
36
|
Avinash Patel answered |
Lets,
First digit number = x
Second digit number = y
Number = (x+10y)
A/Q,
x + y = 9 ...................... (i)
A/Q,
(x+10y) = (10x+y) + 27
x + 10y = 10x + y +27
9x - 9y = 27
9(x - y) = 27
x - y = 27/9
x - y = 3 ......................... (ii)
Equation (i) and (ii) we get,
x = 3
Putting the value of x in eq.(i)
we get,
y = 6
Number = (10x +y)
= 10 x 3 + 6
= 30 + 6
= 36
Write the general form of a quadratic polynomia- a)ax2 + bx + c where a, b and c are real numbers
- b)ax2 + bx + c=0
- c)ax2 + bx + c where a, b and c are real numbers and a is not equal to zero.
- d)ax2 + bx + c or bx + ax2 + c or c+ bx + ax2
Correct answer is option 'C'. Can you explain this answer?
Write the general form of a quadratic polynomia
a)
ax2 + bx + c where a, b and c are real numbers
b)
ax2 + bx + c=0
c)
ax2 + bx + c where a, b and c are real numbers and a is not equal to zero.
d)
ax2 + bx + c or bx + ax2 + c or c+ bx + ax2
|
|
Krishna Iyer answered |
If the coefficient of x2 is zero , then the equation is not a quadratic equation , its a linear equation. So its necessary condition for the quadratic equation.
Find the solution to the following system of linear equations:
x-2y = 6
2x+y = 17- a)(8,1)
- b)(12,3)
- c)(1,2)
- d)(10,2)
Correct answer is option 'A'. Can you explain this answer?
Find the solution to the following system of linear equations:
x-2y = 6
2x+y = 17
x-2y = 6
2x+y = 17
a)
(8,1)
b)
(12,3)
c)
(1,2)
d)
(10,2)
|
Thor Kss answered |
X-2y=6 and 2x+y=17
by eliminating
x-2y=6*2
2x+y=17*1
2x will be cancelled
then y will be 1
and when we value of y in equation 1
we get x=8
by eliminating
x-2y=6*2
2x+y=17*1
2x will be cancelled
then y will be 1
and when we value of y in equation 1
we get x=8
Find the solution to the following system of linear equations:
2p+3q = 9
p – q = 2
- a)(4,2)
- b)(3,1)
- c)(2,-3)
- d)(-4,1)
Correct answer is option 'B'. Can you explain this answer?
Find the solution to the following system of linear equations:
2p+3q = 9
p – q = 2
2p+3q = 9
p – q = 2
a)
(4,2)
b)
(3,1)
c)
(2,-3)
d)
(-4,1)
|
Clifford Academy answered |
Alright, we have a system of two linear equations with two variables, p and q. Let's write them down:
1) 2p + 3q = 9
2) p - q = 2
Our goal is to find the values of p and q that satisfy both equations. We can use either the substitution method or the elimination method to solve this system. I'll use the substitution method here.
First, we'll solve the second equation for one of the variables. Let's solve for p:
p = q + 2
Now, we'll substitute this expression for p into the first equation:
2(q + 2) + 3q = 9
Distribute the 2:
2q + 4 + 3q = 9
Combine like terms:
5q + 4 = 9
Now, solve for q:
5q = 9 - 4
5q = 5
q = 1
Now that we have the value for q, we can plug it back into the expression for p:
p = q + 2
p = 1 + 2
p = 3
1) 2p + 3q = 9
2) p - q = 2
Our goal is to find the values of p and q that satisfy both equations. We can use either the substitution method or the elimination method to solve this system. I'll use the substitution method here.
First, we'll solve the second equation for one of the variables. Let's solve for p:
p = q + 2
Now, we'll substitute this expression for p into the first equation:
2(q + 2) + 3q = 9
Distribute the 2:
2q + 4 + 3q = 9
Combine like terms:
5q + 4 = 9
Now, solve for q:
5q = 9 - 4
5q = 5
q = 1
Now that we have the value for q, we can plug it back into the expression for p:
p = q + 2
p = 1 + 2
p = 3
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. The present ages (in years) of the son and the father are, respectively. - a)4 and 24
- b)5 and 30
- c)6 and 36
- d)3 and 24
Correct answer is option 'C'. Can you explain this answer?
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. The present ages (in years) of the son and the father are, respectively.
a)
4 and 24
b)
5 and 30
c)
6 and 36
d)
3 and 24
|
|
Divisha shah answered |
Let the present age of father's be x years and present age of son's be y years.
According to the problem
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is- a)inconsistent
- b)Both
- c)consistent
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is
a)
inconsistent
b)
Both
c)
consistent
d)
none of these
|
|
Amit Sharma answered |
a1 / a2 = b1 / b2 = c1 / c2
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a1 / a2 = b1 / b2 = c1 / c2
When these are equal then it is consistent.
Therefore option (C) is correct .
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a1 / a2 = b1 / b2 = c1 / c2
When these are equal then it is consistent.
Therefore option (C) is correct .
If x = 1 is a common root of the equation x2 + ax – 3 = 0 and bx2 – 7x + 2 = 0 then ab =
- a)10
- b)-3
- c)6
- d)7
Correct answer is option 'A'. Can you explain this answer?
If x = 1 is a common root of the equation x2 + ax – 3 = 0 and bx2 – 7x + 2 = 0 then ab =
a)
10
b)
-3
c)
6
d)
7
|
Zachary Foster answered |
Given:
- x = 1 is a common root of the equations:
- x² + ax - 3 = 0
- bx² - 7x + 2 = 0
To find:
- The value of ab.
Solution:
Since x = 1 is a root of both equations, we can substitute x = 1 in both equations.
Equation 1:
- 1² + a(1) - 3 = 0
- 1 + a - 3 = 0
- a = 2
Equation 2:
- b(1)² - 7(1) + 2 = 0
- b - 7 + 2 = 0
- b = 5
Therefore, ab = 2 * 5 = 10
So, the value of ab is 10.
Solve for x : 6x2 + 40 = 31x- a)
- b)
- c)0,8/3
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Solve for x : 6x2 + 40 = 31x
a)
b)
c)
0,8/3
d)
None of the above
|
|
Nirmal Kumar answered |
6x²-31x+40=0,
a=6,
b=-31,
c=40,
by quadratic formula-->
x=-b±√b²-4ac/2a,
by putting the values of a,b and c, we get,
x=-(-31)±√(-31)²-4(6)(40)/2(6),
=31±√961-960/12,
=31±√1/12,
=31±1/12,
x=30/12or ,32/12,
x=5/2 or, 8/3,
hence , option B is correct
a=6,
b=-31,
c=40,
by quadratic formula-->
x=-b±√b²-4ac/2a,
by putting the values of a,b and c, we get,
x=-(-31)±√(-31)²-4(6)(40)/2(6),
=31±√961-960/12,
=31±√1/12,
=31±1/12,
x=30/12or ,32/12,
x=5/2 or, 8/3,
hence , option B is correct
Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2
0.1x – 0.1y = 0.1- a)(1,2)
- b)(2,3)
- c)(3,2)
- d)(2,1)
Correct answer is option 'C'. Can you explain this answer?
Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2
0.1x – 0.1y = 0.1
0.1x – 0.1y = 0.1
a)
(1,2)
b)
(2,3)
c)
(3,2)
d)
(2,1)
|
|
Arun Sharma answered |
0.2x + 0.3y = 1.2
2x+3y=12 …..(1)
0.1x – 0.1y = 0.1x-y=1 ….(2)
From (2), x=1+y
Substituting the values of x in (1)
2(1+y)+3y=12
2+2y+3y=12
5y=10
y=2
x=1+2= 3
2x+3y=12 …..(1)
0.1x – 0.1y = 0.1x-y=1 ….(2)
From (2), x=1+y
Substituting the values of x in (1)
2(1+y)+3y=12
2+2y+3y=12
5y=10
y=2
x=1+2= 3
Which of the following points lie on the line 3x+2y=5 ?- a)(1, 1)
- b)(0, 1)
- c)(1, 0)
- d)(2, 1)
Correct answer is option 'A'. Can you explain this answer?
Which of the following points lie on the line 3x+2y=5 ?
a)
(1, 1)
b)
(0, 1)
c)
(1, 0)
d)
(2, 1)
|
|
Krishna Iyer answered |
When we are given only one equation and two variables we assume values for one variable and find the values for the other variable.
3x+2y=5
Let x=1
3*1+2y=5
2y=2
y=1 hence (1,1) lies on the line.
3x+2y=5
Let x=1
3*1+2y=5
2y=2
y=1 hence (1,1) lies on the line.
Can you explain the answer of this question below: If 4 is a root of the equation 
, then k is
- A:
-28
- B:
-12
- C:
12
- D:
28
The answer is a.
If 4 is a root of the equation , then k is
-28
-12
12
28
|
|
Arun Sharma answered |
4 is the solution , this means that if we put x=4 we get 0. So putting x=4 in the equation x2+3x+k=0 we get 42+3*4+k=0
16+12+k=0 ⇒ k=-28
16+12+k=0 ⇒ k=-28
The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is_____- a)75
- b)25
- c)52
- d)57
Correct answer is option 'D'. Can you explain this answer?
The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is_____
a)
75
b)
25
c)
52
d)
57
|
Neha Patel answered |
Let us assume x and y are the two digits of the number
Therefore, two-digit number is = 10x + y and the reversed number = 10y + x
Given:
x + y = 12
y = 12 – x (1)
Also given:
10y + x - 10x – y = 18
9y – 9x = 18
y – x = 2 (2)
Substitute the value of y from eqn 1 in eqn 2
12 – x – x = 2
12 – 2x = 2
2x = 10
x = 5
Therefore, y = 12 – x = 12 – 5 = 7
Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57
If a pair of linear equations has infinitely many solutions, then the lines representing them will be
- a)Parallel
- b)Intersecting lines
- c)Always intersecting
- d)coincident lines
Correct answer is option 'D'. Can you explain this answer?
If a pair of linear equations has infinitely many solutions, then the lines representing them will be
a)
Parallel
b)
Intersecting lines
c)
Always intersecting
d)
coincident lines
|
|
Ananya Das answered |
If two lines i.e. a pair of linear equations, has infinitely many solutions it means lines are overlapping each other i.e. coincident lines.
The value of q if x = 2 is a solution of 8x2 + qx – 4 = 0 is _____- a)14
- b)-28
- c)-14
- d)28
Correct answer is option 'C'. Can you explain this answer?
The value of q if x = 2 is a solution of 8x2 + qx – 4 = 0 is _____
a)
14
b)
-28
c)
-14
d)
28
|
|
Kuldeep Raj answered |
Let us place 2 in the place of "x" for 8x² + qx - 4 = 0 (According to the question).
8(2)² + q(2) - 4 = 0.
8(4) + 2q - 4 = 0.
32 + 2q - 4 = 0.
Shift (32) to the right side.
2q - 4 = -32.
Shift (-4) to the right side. Then,
2q = -32 + 4.
2q = -28.
q = -28/2.
q = -14.
Therefore, the value of q if x = 2 is a solution of 8x² + qx - 4 = 0 is -14.
Hence, option (c) is correct friend...
8(2)² + q(2) - 4 = 0.
8(4) + 2q - 4 = 0.
32 + 2q - 4 = 0.
Shift (32) to the right side.
2q - 4 = -32.
Shift (-4) to the right side. Then,
2q = -32 + 4.
2q = -28.
q = -28/2.
q = -14.
Therefore, the value of q if x = 2 is a solution of 8x² + qx - 4 = 0 is -14.
Hence, option (c) is correct friend...
The solution of x2 + 4x + 4 = 0 is- a)2
- b)-2
- c)0
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The solution of x2 + 4x + 4 = 0 is
a)
2
b)
-2
c)
0
d)
None of these
|
|
Priyanshu Intelligent answered |
(-2)^2 + 4(-2) + 4
= 4 - 8 + 4
=8-8
=0.
Hence , option b) is the right answer.
= 4 - 8 + 4
=8-8
=0.
Hence , option b) is the right answer.
In elimination method _____________ is an important condition.- a)Equating either of the coefficients
- b)Equating only the y coefficient.
- c)Equating only the x co-efficient.
- d)Equating both the coefficients.
Correct answer is option 'A'. Can you explain this answer?
In elimination method _____________ is an important condition.
a)
Equating either of the coefficients
b)
Equating only the y coefficient.
c)
Equating only the x co-efficient.
d)
Equating both the coefficients.
|
|
Rajiv Gupta answered |
Elimination Method (by Equating Coefficients)
There is another method of eliminating a variable, than often used method i. e --------Suppose you are to solve
23x - 17y + 11=0 ------(1)
and 31x + 13y - 57 = 0 -------(2)
Now expressing x in terms of y would involve division by 23 or 31. Express y in terms of x, it would involve division by 17 or 13. You know that multiplication is more convenient than division, better to convert the division process into a multiplication process.
Multiplying the first equation by 13 viz., coefficient of y in (2), and second by 17 viz., coefficient of y in (1), you will get an equivalent system of equations. The new system has the advantage that y has the same numerical coefficient 17x13 in both the equations. When you add these new equations, the terms containing y would cancel out as these have opposite signs and the same numerical coefficient. Thus, y has been eliminated. Now proceed as before, and solve the system. This method of elimination is also called elimination by equating coefficients for obvious reasons.
Example: Solve the following system of equations using the elimination method by equating coefficients:
11x - 5y + 61 = 0 (1)
3x - 20y - 2 = 0 (2)
Solution: Let us multiply equation (1) by 3 and equation (2) by 11. This gives
33x - 15y + 183 = 0 (3)
and 33x - 220y - 22 = 0 (4)
Subtracting (4) from (3), you will get 205y + 205 = 0
, or y = - 1
Substituting this value of y in equation (2), you will get
3x - 20 * (- 1) - 2 = 0
or 3x = -18
or x = - 6
Thus, the required solution is
x = - 6 and y = -1.
Now you should verify; substitute x = - 6 and y = -1 in the given equations, you will notice both the equations are satisfied. Hence, the solution is correct
The value of x in mx + ny = c; nx – ny = c + 1 is
- a)x = (m + n) / (c + 1)
- b)x = (2c + 1) / (m + n)
- c)x = m + n
- d)x = 2c + 1
Correct answer is option 'B'. Can you explain this answer?
The value of x in mx + ny = c; nx – ny = c + 1 is
a)
x = (m + n) / (c + 1)
b)
x = (2c + 1) / (m + n)
c)
x = m + n
d)
x = 2c + 1
|
|
Mansi desai answered |
To find the value of x in the equation mx + ny = c, we need more information or another equation. The equation nx = 0 does not provide enough information to solve for x.
If b2 - 4ac = 0 then The roots of the Quadratic equation ax2 + bx + c = 0 are given by :- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
If b2 - 4ac = 0 then The roots of the Quadratic equation ax2 + bx + c = 0 are given by :
a)
b)
c)
d)
|
Udexy Coaching Center answered |
Formula for finding the roots of a quadratic equation is
So since
b2 - 4ac = 0, putting this value in the equation
So there are repeated roots
So since
b2 - 4ac = 0, putting this value in the equation
So there are repeated rootsThe nature of the roots of the equation x2 – 5x + 7 = 0 is –- a)No real roots
- b)1 real root
- c)Can't be determined
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The nature of the roots of the equation x2 – 5x + 7 = 0 is –
a)
No real roots
b)
1 real root
c)
Can't be determined
d)
None of these
|
|
Krishna Iyer answered |
Given equation is x2-5x+7=0
We have discriminant as b2-4ac=(-5)2-4*1*7= -3
And x =
, Since we do not have any real number which is a root of a negative number, the roots are not real.
We have discriminant as b2-4ac=(-5)2-4*1*7= -3
And x =
, Since we do not have any real number which is a root of a negative number, the roots are not real.The value/s of x when (x – 4) (3x + 2) = 0 ________- a)4, -2/3
- b)-4, – 2/ 3
- c)4, 2/3
- d)-4, 2/3
Correct answer is option 'A'. Can you explain this answer?
The value/s of x when (x – 4) (3x + 2) = 0 ________
a)
4, -2/3
b)
-4, – 2/ 3
c)
4, 2/3
d)
-4, 2/3
|
|
Drishti Kumari answered |
( x - 4 ) ( 3x + 2 ) = 0
x - 4 = 0
x = 4
3x + 2 = 0
3x = -2
x = -2 / 3
Therefore option (A) is correct.
x - 4 = 0
x = 4
3x + 2 = 0
3x = -2
x = -2 / 3
Therefore option (A) is correct.
If one root of a Quadratic equation is m + , then the other root is- a)m – √n
- b)m +√n
- c)Can not be determined
- d)√m + n
Correct answer is option 'A'. Can you explain this answer?
If one root of a Quadratic equation is m + , then the other root is
a)
m – √n
b)
m +√n
c)
Can not be determined
d)
√m + n
|
|
Arun Sharma answered |
In a quadratic equation with rational coefficients has an irrational root α + √β, then it has a conjugate root α - √β.
So if the root is m+ √n the other root will be m- √n
So if the root is m+ √n the other root will be m- √n
The Index of Coincidence for English language is approximately- a)0.068
- b)0.038
- c)0.065
- d)0.048
Correct answer is option 'C'. Can you explain this answer?
The Index of Coincidence for English language is approximately
a)
0.068
b)
0.038
c)
0.065
d)
0.048
|
Hariteja Patnala answered |
Yes actually you said option C is correct it is actually correct but the actual answer is different
actual answer for index of coincide of English language is 0.0 667
index of coincide is a technique to find the probability of the repeating letters in an encrypted text
the index of coincide value is calculated on the basis of the probability of occurrence of a specified letter and the probability of comparing it to the same letter from the second text
so this is my answer for index of coincide of English language is 0.0667 but you have given that C is correct option
actual answer for index of coincide of English language is 0.0 667
index of coincide is a technique to find the probability of the repeating letters in an encrypted text
the index of coincide value is calculated on the basis of the probability of occurrence of a specified letter and the probability of comparing it to the same letter from the second text
so this is my answer for index of coincide of English language is 0.0667 but you have given that C is correct option
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Quadratic Equations" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths) Q. Which of the following quadratic expression can be expressed as a product of real linear factors?- a)x2 – 2x + 3
- b)3x2 – √2x – √3
- c)√2x2 – √5x + 3
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Practice Test/Quiz or MCQ (Multiple Choice Questions) with Solutions of Chapter "Quadratic Equations" are available for CBSE Class 10 Mathematics (Maths) and have been compiled as per the syllabus of CBSE Class 10 Mathematics (Maths)
Q. Which of the following quadratic expression can be expressed as a product of real linear factors?
a)
x2 – 2x + 3
b)
3x2 – √2x – √3
c)
√2x2 – √5x + 3
d)
None of these
|
|
Amit Kumar answered |
Thus, it can be expressed as product of linear factors.
Ruhi’s mother is 26 years older than her. The product of their ages (in years) 3 years from now will be 360. Form a Quadratic equation so as to find Ruhi’s age- a)x 2 + 32 x – 273 = 0
- b)x 2 -32 x – 273=0
- c)x 2 + 32 x + 273 = 0
- d)x 2 – 32 x +273 = 0
Correct answer is option 'A'. Can you explain this answer?
Ruhi’s mother is 26 years older than her. The product of their ages (in years) 3 years from now will be 360. Form a Quadratic equation so as to find Ruhi’s age
a)
x 2 + 32 x – 273 = 0
b)
x 2 -32 x – 273=0
c)
x 2 + 32 x + 273 = 0
d)
x 2 – 32 x +273 = 0
|
|
Amit Sharma answered |
Ruhi’s mother is 26 years older than her
So let Ruhi’s age is x
So mother’s age is x+26
The product of their ages 3 years from now will be 360
So After three years , Ruhi’s age will be x+3
Mother’s age will be x+26+3=x+29
Product of their ages =(x + 3)(x + 29)=360
x2+(3+29)x+87=360
x2+32x-273=0
So let Ruhi’s age is x
So mother’s age is x+26
The product of their ages 3 years from now will be 360
So After three years , Ruhi’s age will be x+3
Mother’s age will be x+26+3=x+29
Product of their ages =(x + 3)(x + 29)=360
x2+(3+29)x+87=360
x2+32x-273=0
The two positive numbers differ by 5 and square of their sum is 169 are
- a)2,4
- b)5,6
- c)4,9
- d)3,7
Correct answer is option 'C'. Can you explain this answer?
The two positive numbers differ by 5 and square of their sum is 169 are
a)
2,4
b)
5,6
c)
4,9
d)
3,7
|
Apoorv khanna answered |
Explanation:
Let the two numbers be x and y, where x is greater than y.
Given, x - y = 5
=> x = y + 5
Also, (x+y)^2 = 169
=> (y+5+y)^2 = 169 (Substituting x = y + 5)
=> (2y+5)^2 = 169
=> 4y^2 + 20y + 25 = 169 (Expanding the square)
=> 4y^2 + 20y - 144 = 0
=> y^2 + 5y - 36 = 0
=> (y + 9)(y - 4) = 0
=> y = -9 or y = 4
Since the numbers are positive, y = 4
Therefore, x = y + 5 = 9
Hence, the two numbers are 4 and 9.
Therefore, option C is the correct answer.
Let the two numbers be x and y, where x is greater than y.
Given, x - y = 5
=> x = y + 5
Also, (x+y)^2 = 169
=> (y+5+y)^2 = 169 (Substituting x = y + 5)
=> (2y+5)^2 = 169
=> 4y^2 + 20y + 25 = 169 (Expanding the square)
=> 4y^2 + 20y - 144 = 0
=> y^2 + 5y - 36 = 0
=> (y + 9)(y - 4) = 0
=> y = -9 or y = 4
Since the numbers are positive, y = 4
Therefore, x = y + 5 = 9
Hence, the two numbers are 4 and 9.
Therefore, option C is the correct answer.
The solution of 5z2 = 3z is- a)0, 3/5
- b)0, -3/5
- c)3/5
- d)0
Correct answer is option 'A'. Can you explain this answer?
The solution of 5z2 = 3z is
a)
0, 3/5
b)
0, -3/5
c)
3/5
d)
0
|
|
Vikram Kapoor answered |
We have 5z2=3z
5z2-3z=0
z(5z-3)=0
So either z=0
Or 5z-3 =0 = z=⅗. So there are two solutions
5z2-3z=0
z(5z-3)=0
So either z=0
Or 5z-3 =0 = z=⅗. So there are two solutions
The condition for equation ax2 + bx + c = 0 to be linear is- a)a > 0, b = 0
- b)a ≠ 0, b = 0
- c)a < 0, b = 0
- d)a = 0, b ≠ 0
Correct answer is option 'D'. Can you explain this answer?
The condition for equation ax2 + bx + c = 0 to be linear is
a)
a > 0, b = 0
b)
a ≠ 0, b = 0
c)
a < 0, b = 0
d)
a = 0, b ≠ 0
|
|
Tanisha answered |
Answer is d...bcoz to make ax^2 +bx+c=0,linear equation.
we need to eliminate ax^2.
So, we will put a=0 ,to make the degree of this equation 1 ...and b should not be equal to 0,bcoz if b will be 0 ,then it will be a constant equation,instead of a linear equation.
we need to eliminate ax^2.
So, we will put a=0 ,to make the degree of this equation 1 ...and b should not be equal to 0,bcoz if b will be 0 ,then it will be a constant equation,instead of a linear equation.
Find the solution to the following system of linear equations: 2x-y+6=0 4x+5y-16=0- a)(2,-3)
- b)(-1,4)
- c)(2,3)
- d)(1,4)
Correct answer is option 'B'. Can you explain this answer?
Find the solution to the following system of linear equations: 2x-y+6=0 4x+5y-16=0
a)
(2,-3)
b)
(-1,4)
c)
(2,3)
d)
(1,4)
|
Pooja Shah answered |
2x-y+6=0
y=2x+6 ….(1)
4x+5y-16=0
Substituting the values
4x+5(2x+6)-16=0
14x+14=0
x=-1
y=4
y=2x+6 ….(1)
4x+5y-16=0
Substituting the values
4x+5(2x+6)-16=0
14x+14=0
x=-1
y=4
If -3 is a root of both the Quadratic equations 2x2 + px – 15 = 0, and p(x2 + x) + q = 0, then the value of q if the equation containing it has equal roots is- a)1/2
- b)1/4
- c)14
- d)2
Correct answer is option 'B'. Can you explain this answer?
If -3 is a root of both the Quadratic equations 2x2 + px – 15 = 0, and p(x2 + x) + q = 0, then the value of q if the equation containing it has equal roots is
a)
1/2
b)
1/4
c)
14
d)
2
|
|
Ananya Das answered |
-3 is root of both
2(9) -3p -15 = 0
p = 1
and
second equation has two equal roots so,
b2-4ac = 0
p2 = 4pq
p = 4q
q = 1/4
The equation 
in standard form ax2 + bx + c = 0 is written as :- a)x2 - 4x + 1 = 0
- b)x2 + 4x + 1 = 0
- c)x2 - 4x - 1 = 0
- d)x2 + 4x - 1 = 0
Correct answer is option 'A'. Can you explain this answer?
The equation in standard form ax2 + bx + c = 0 is written as :
in standard form ax2 + bx + c = 0 is written as :a)
x2 - 4x + 1 = 0
b)
x2 + 4x + 1 = 0
c)
x2 - 4x - 1 = 0
d)
x2 + 4x - 1 = 0
|
|
Naina Sharma answered |
We have 
Taking LCM,
Multiplying LHS and RHS by x
x2+1=4x
x2-4x+1=0
Which is the required equation.
Taking LCM,
Multiplying LHS and RHS by x
x2+1=4x
x2-4x+1=0
Which is the required equation.
If a,b,c are real and b2-4ac >0 then roots of equation are- a)real roots
- b)real and equal
- c)real and unequal
- d)No real roots
Correct answer is option 'C'. Can you explain this answer?
If a,b,c are real and b2-4ac >0 then roots of equation are
a)
real roots
b)
real and equal
c)
real and unequal
d)
No real roots
|
Ram trivedi answered |
The expression b^2 - 4ac is the discriminant of a quadratic equation of the form ax^2 + bx + c = 0. It determines the nature of the solutions of the equation.
If b^2 - 4ac > 0, then the quadratic equation has two distinct real solutions.
If b^2 - 4ac = 0, then the quadratic equation has one real solution (also known as a double root).
If b^2 - 4ac < 0,="" then="" the="" quadratic="" equation="" has="" no="" real="" solutions.="" however,="" it="" may="" have="" two="" complex="" />
So, in summary, if b^2 - 4ac > 0, there are two real solutions.
If b^2 - 4ac > 0, then the quadratic equation has two distinct real solutions.
If b^2 - 4ac = 0, then the quadratic equation has one real solution (also known as a double root).
If b^2 - 4ac < 0,="" then="" the="" quadratic="" equation="" has="" no="" real="" solutions.="" however,="" it="" may="" have="" two="" complex="" />
So, in summary, if b^2 - 4ac > 0, there are two real solutions.
If x + 2y = 5 & x – 2y = 7, then the value of x & y is: -- a)x = 6 & y = 3
- b)x = 12 & y = -1/2
- c)x = 6 & y = -1/2
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
If x + 2y = 5 & x – 2y = 7, then the value of x & y is: -
a)
x = 6 & y = 3
b)
x = 12 & y = -1/2
c)
x = 6 & y = -1/2
d)
None of the above
|
Roshni jain answered |
Solution:
Given, x + 2y = 5 ...(1)
and x + 2y = 7 ...(2)
Subtracting Equation (1) from Equation (2), we get
( x + 2y ) - ( x + 2y ) = 7 - 5
⇒ 0 = 2
The above equation is not satisfied for any value of x and y. Therefore, such values of x and y do not exist.
Hence, the correct option is (d) None of the above.
Given, x + 2y = 5 ...(1)
and x + 2y = 7 ...(2)
Subtracting Equation (1) from Equation (2), we get
( x + 2y ) - ( x + 2y ) = 7 - 5
⇒ 0 = 2
The above equation is not satisfied for any value of x and y. Therefore, such values of x and y do not exist.
Hence, the correct option is (d) None of the above.
Find the value of p for which the quadratic equation x2 + p(4x + p – 1) + 2 = 0 has equal roots :- a)- 1, 2/3
- b)3, 5
- c)1, -(4/3)
- d)3/4, 2
Correct answer is option 'A'. Can you explain this answer?
Find the value of p for which the quadratic equation x2 + p(4x + p – 1) + 2 = 0 has equal roots :
a)
- 1, 2/3
b)
3, 5
c)
1, -(4/3)
d)
3/4, 2
|
Nk Classes answered |
expand the given quadratic equation: x2 + p(4x + p – 1) + 2 = 0
So, the quadratic equation becomes:
The discriminant is :
Which of the following is not a quadratic equation ?- a)5x + 3y2 = 0
- b)z2 - 2z = 0
- c)3x + 4 - 7x2 = 0
- d)5x2 - 125 = 0
Correct answer is option 'A'. Can you explain this answer?
Which of the following is not a quadratic equation ?
a)
5x + 3y2 = 0
b)
z2 - 2z = 0
c)
3x + 4 - 7x2 = 0
d)
5x2 - 125 = 0
|
|
Priyanshu Intelligent answered |
In equation first there are two variables.
That's why it is not a quadratic equation.
That's why it is not a quadratic equation.
If x = -2 is a root of equation x2 – 4x + K = 0 then value of K is
- a)8
- b)-8
- c)-12
- d)12
Correct answer is option 'C'. Can you explain this answer?
If x = -2 is a root of equation x2 – 4x + K = 0 then value of K is
a)
8
b)
-8
c)
-12
d)
12
|
|
Mahi Rastogi answered |
(-2)²-4×-2+k=0
4+8+k=0
12+k=0
k=-12} ans
4+8+k=0
12+k=0
k=-12} ans
If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively.- a)3 and 1
- b)-1 and -3
- c)3 and 5
- d)5 and 3
Correct answer is option 'A'. Can you explain this answer?
If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively.
a)
3 and 1
b)
-1 and -3
c)
3 and 5
d)
5 and 3
|
|
Arun Yadav answered |
Since, x = a and y = b is the solution of the equations x – y = 2 and x+ y = 4, then these values will satisfy that equations
a-b= 2 ,..(i)
and a + b = 4 … (ii)
On adding Eqs. (i) and (ii), we get
2a = 6
a = 3 and b = 1
Chapter doubts & questions for Chapter 2: Equations - Quantitative Aptitude for CA Foundation 2025 is part of CA Foundation exam preparation. The chapters have been prepared according to the CA Foundation exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CA Foundation 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
Chapter doubts & questions of Chapter 2: Equations - Quantitative Aptitude for CA Foundation in English & Hindi are available as part of CA Foundation exam.
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