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This mock test of Test: Equations- 3 for CA Foundation helps you for every CA Foundation entrance exam.
This contains 40 Multiple Choice Questions for CA Foundation Test: Equations- 3 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Test: Equations- 3 quiz give you a good mix of easy questions and tough questions. CA Foundation
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QUESTION: 1

A man went to the Reserve Bank of India with Rs. 1, 000. He asked the cashier to give him Rs. 5 and Rs.10 notes only in return. The man got 175 notes in all. Find how many notes of Rs. 5 and Rs. 10 did he receive?

Solution:

QUESTION: 2

The area of a triangle with vertices (1,3), (5, 6) and (-3, 4) in terms of square units is:

Solution:

QUESTION: 3

The equation of the straight line through the point of intersection of x+2y-5=0 and x-3y-7=0 and passing through the point (1, 0) is :

Solution:

QUESTION: 4

A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1,500 after 4 years of service and Rs. 1,800 after 10 years of service, what was his starting salary and what is the annual increment in rupees?

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QUESTION: 5

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QUESTION: 6

Find the positive value of k for which the equations: x^{2}+kx+64=0 and x^{2}-8x+k=0 will have real roots

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QUESTION: 7

The value of k for which the points (k,1), (5, 5) and (10,7) may be collinear is:

Solution:

QUESTION: 8

A man sells 6 radios and 4 televisions for Rs. 18,480. If 14 radios and 2 televisions are sold for the same amount, what is the price of a televisions?

Solution:

QUESTION: 9

The value of k for which the points (k,1), (5, 5) and (10,7) may be collinear is:

Solution:

QUESTION: 10

The centroid of the triangle ABC is at the point (2,3). A and B are the points (5, 6) and (-1, 4) respectively. The coordinates of C are:

Solution:

QUESTION: 11

The line joining (-1,1) and (2,-2) and the line joining (1,2) and (2, k) are perpendicular to each other for the following value of k:

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QUESTION: 12

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QUESTION: 13

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QUESTION: 14

Root of the equation 3x^{2}-14x+k=0 will be reciprocal of each other if:

Solution:

QUESTION: 15

If (2+√3)is a root of a quadratic equation x^{2}+p_{x}+q=0 then find the value of p and q.

Solution:

QUESTION: 16

The value of

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QUESTION: 17

The point of intersection of the lines 2x-5y=6 and x+y=3 is

Solution:

QUESTION: 18

The graph of straight line x=5 will be:

Solution:

QUESTION: 19

One root of the equation:

X^{2}-2(5+m)x+3(7+m)=0 is reciprocal of the other.

Find the value of M.

Solution:

QUESTION: 20

A straight line of x=15 is

Solution:

QUESTION: 21

If area and perimeter of a rectangle is 6000 cm^{2} and 340 cm respectively, then the length of rectangle is:

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QUESTION: 22

The lines 3x+4y+10=0 and 4x-3y+5=0 are ________

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QUESTION: 23

Find the equation of the line joining the point (3, 5) with the point of intersection 2x+3y-5=0 and 3x+5y-7=0.

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QUESTION: 24

A straight line passes through the point (3, 2). Find the equation of the straight line.

Solution:

QUESTION: 25

If the length of a rectangle is 5 cm more than the breadth and if the perimeter of the rectangle is 40cm, then the length & breadth of the rectangle with be:

Solution:

QUESTION: 26

If x^{3} - 6x^{2 }+ 11x - 6 = 0 then find the value of (3x-4).

Solution:

Let p(x) = x^{3 }- 6x^{2} + 11x - 6

By trial, we find that

p(1) = (1)^{3} - 6(1)^{2} + 11(1) - 6 = 0

∴ By converse of factor theorem, (x - 1) is a factor of p(x).

Now, x^{3} - 6x^{2} + 11x - 6

= x^{2} (x - 1)- 5x (x - 1) + 6 (x - 1)

= (x - 1) (x2 - 5x + 6)

= (x - 1) {x2 - 2x - 3x + 6}

= (x - 1) {x(x - 2)-3 (x - 2)}

= (x - 1)(x - 2)(x - 3)

When x=1, 3x-4 = -1

When x=2, 3x--4 = 2

when x=3, 3x-4 = 5

QUESTION: 27

A man rowing at the rate of 5km in an hour in still water takes thrice as much time in going 40km up the river as in going 40km down. Find the rate at which the river flows:

Solution:

Speed of the boat in water =.5 km/hr

Let the speed of the stream be x km/hr

So, the speed of the boat upstream will be (5-x) km / hr

So, the speed of the boat downstream is (5+x) k/hr

Time given to cover 40 km upstream = 3(time taken to cover dowmstream)

⇒40/ (5-x) km/hr = 3(5+x)

⇒1/(5-x)=3(5+x)

⇒5+x=15-3x

⇒x+3x=15-5

⇒4x=10

⇒X=10/4

⇒X=5/2

∴x=2.5 km/hr

QUESTION: 28

Find the equation of the line passing through the point (1, 1) and parallel to the line 3x+5y+17=0

Solution:

QUESTION: 29

The equation -7x+1=5-3x will be satisfied for x equal to:

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QUESTION: 30

The sum of two numbers is 52 and their difference is 2. The numbers are

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QUESTION: 31

Divide 56 into two parts such that three times the first part exceeds one third of the second by 48 the parts are.

Solution:

QUESTION: 32

The diagonal of a rectangle is 5 cm and one of at sides is 4 cm. Its area is

Solution:

QUESTION: 33

On the average an experienced person does 7 units of work while a fresh one work 5 units of work daily but the employer has to maintain an output of atleast 35 units of work per day. The situation can be expressed as:

Solution:

QUESTION: 34

If one root of the equation x^{2}-3x+k=0 is 2, then value of k will be

Solution:

QUESTION: 35

The solution of the equation (p+2) (p+3) + (p+3) (P-4) = p(2p-5) is

Solution:

(p+2)(p-3)+(p+3)(p-4)=p(2p-5)

p²-3p+2p-6+p²-4p+3p-12=2p²-5p

2p²-2p-18=2p²-5p

-2p+5p=18

3p=18

p=6

QUESTION: 36

The product of two numbers is 3200 and the quotient when the larger number is divided by the smaller is 2. The number are

Solution:

QUESTION: 37

The solution of the set of equations 3x+4y=7, 4x-y=3 is

Solution:

QUESTION: 38

Ten years ago the age of a father was four times of his son. Ten years hence the age of the father will be twice that of his son. The present ages of the father and the son are.

Solution:

QUESTION: 39

Solve for x and y : x-3y=0, x+2y=20.

Solution:

QUESTION: 40

The fourth part of a number exceeds the sixth part by 4. The number is

Solution:

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