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Test: Equations- 3 - CA Foundation MCQ


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30 Questions MCQ Test - Test: Equations- 3

Test: Equations- 3 for CA Foundation 2024 is part of CA Foundation preparation. The Test: Equations- 3 questions and answers have been prepared according to the CA Foundation exam syllabus.The Test: Equations- 3 MCQs are made for CA Foundation 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Equations- 3 below.
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Test: Equations- 3 - 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?

Test: Equations- 3 - Question 2

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

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Test: Equations- 3 - 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 : 

Test: Equations- 3 - 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?

Test: Equations- 3 - Question 5

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 : 

Test: Equations- 3 - Question 6

Find the positive value of k for which the equations: x2+kx+64=0 and x2-8x+k=0 will have real roots 

Test: Equations- 3 - Question 7

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

Test: Equations- 3 - 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?

Test: Equations- 3 - Question 9

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

Test: Equations- 3 - 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: 

Test: Equations- 3 - 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: 

Test: Equations- 3 - Question 12

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?

Test: Equations- 3 - Question 13

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?

Test: Equations- 3 - Question 14

Root of the equation 3x2-14x+k=0 will be reciprocal of each other if:

Test: Equations- 3 - Question 15

If (2+√3)is a root of a quadratic equation x2+px+q=0 then find the value of p and q. 

Test: Equations- 3 - Question 16

Calculate the length of the diagonal of a square sheet if its sides are 4 cm each.

Detailed Solution for Test: Equations- 3 - Question 16

Side of the square sheet ‘ a’ = 4 cm.

By applying Pythagoras theorem, the diagonal of the square

=√2 x a

=√2 x 4

= 5.656 cm

Therefore, the diagonal of the square sheet is 5.656 cm.

Test: Equations- 3 - Question 17

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

Test: Equations- 3 - Question 18

 The graph of straight line x=5 will be:

Test: Equations- 3 - Question 19

One root of the equation:
X2-2(5+m)x+3(7+m)=0 is reciprocal of the other.
Find the value of M.

Test: Equations- 3 - Question 20

A straight line of x=15 is

Test: Equations- 3 - Question 21

If area and perimeter of a rectangle is 6000 cm2 and 340 cm respectively, then the length of rectangle is: 

Test: Equations- 3 - Question 22

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

Test: Equations- 3 - 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. 

Test: Equations- 3 - Question 24

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

Test: Equations- 3 - 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: 

Test: Equations- 3 - Question 26

If x3 - 6x2 + 11x - 6 = 0 then find the value of (3x-4).

Detailed Solution for Test: Equations- 3 - Question 26

Let p(x) = x3 - 6x2 + 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, x3 - 6x2 + 11x - 6
= x2 (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

Test: Equations- 3 - 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:

Detailed Solution for Test: Equations- 3 - Question 27

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

Test: Equations- 3 - Question 28

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

Test: Equations- 3 - Question 29

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

Test: Equations- 3 - Question 30

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

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