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Ekvij provide mock test paper ca foundation 2021 in Business Mathematics, Business Economics, logical reasoning, Statistics.
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
Correct
x+2y-5=0 ……………( i )
x-3y-7=0 …………….( ii )
to get the point of intersection, by solving equation 1 and 2
we get, x=29/5 and y=-2/5
eqn of a line passing through the point ( 29/5,-2/5 ) and ( 1,0 )
y-0= -2/5-0 / -29/5-1 ( x-1 )
y= -2/5×5/24 (x-1)
y= -1/12 (x-1)
x+12y=1
Incorrect
x+2y-5=0 ……………( i )
x-3y-7=0 …………….( ii )
to get the point of intersection, by solving equation 1 and 2
we get, x=29/5 and y=-2/5
eqn of a line passing through the point ( 29/5,-2/5 ) and ( 1,0 )
y-0= -2/5-0 / -29/5-1 ( x-1 )
y= -2/5×5/24 (x-1)
y= -1/12 (x-1)
x+12y=1
Question 4 of 25
4. Question
1 points
a man sells 6 radios and 4 televisions for Rs 18480. if 14 radios and 2 televisions are sold for the same amount, what is the price of a television?
Correct
let the price of radio be x and television be y
then, 6x+4y= 18480 and 14x+2y= 18480
by solving above eqn we get x=840 and y=3360
therefore, price television = Rs 3360
Incorrect
let the price of radio be x and television be y
then, 6x+4y= 18480 and 14x+2y= 18480
by solving above eqn we get x=840 and y=3360
therefore, price television = Rs 3360
Question 5 of 25
5. Question
1 points
A man starts his job with a certain monthly salary and earns a fixed increment every Yr. if his salary was Rs 1500 after 4 Yr of service and Rs 1800 after 10 Yr of service, what was his starting salary and what is the annual increment in Rs?
Correct
let starting salary be x and annual increment be y
then, x+4y=1500 ……….. 1 and x+10y=1800……… 2
by solving 1&2 we get x=1300=starting salary and y=50= annual increment
Incorrect
let starting salary be x and annual increment be y
then, x+4y=1500 ……….. 1 and x+10y=1800……… 2
by solving 1&2 we get x=1300=starting salary and y=50= annual increment
Question 6 of 25
6. Question
1 points
The equation of a line which is perpendicular to 5x-2y=7 and passes through the mid points of the line joining ( 2,7 ) and ( -4,1 ) is
Correct
the eqn of a line perpendicular to 5x-2y-7=0 is 2x+5y+k=0
mid points of the line joining ( 2,7 ) and ( -4,1 )=2+( -4 )/2,7+1/2=(-1,4)
eqn 1 passes through mid point
2x+5y+k=0
2x-1+5×4+k=0
k=-18
Incorrect
the eqn of a line perpendicular to 5x-2y-7=0 is 2x+5y+k=0
mid points of the line joining ( 2,7 ) and ( -4,1 )=2+( -4 )/2,7+1/2=(-1,4)
eqn 1 passes through mid point
2x+5y+k=0
2x-1+5×4+k=0
k=-18
Question 7 of 25
7. Question
1 points
The area of a triangle with vertices (1,3), (5,6) and (-3,4) in terms of square units is
Correct
Incorrect
Question 8 of 25
8. Question
1 points
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
Correct
Incorrect
Question 9 of 25
9. Question
1 points
The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units and a right angled triangle is formed. the side of the equilateral triangle is
Correct
Incorrect
Question 10 of 25
10. Question
1 points
Correct
Incorrect
Question 11 of 25
11. Question
1 points
Area of a rectangular garden is 8000 sq m. ratio in length and breath is 5:4. a path of uniform width runs all round the inside of the garden. if the path occupies 3200 sq m, what is its width?
Correct
Incorrect
Question 12 of 25
12. Question
1 points
The value of k for which the points (k,1),(5,5) and (10,7) may be collinear is
Correct
Incorrect
Question 13 of 25
13. Question
1 points
A man went to RBI with Rs 1000. 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 received?
Correct
let the no of notes of Rs 5 be x and Rs 10 be y
then, x+y = 175……… 1 and 5x+10y=1000……….. 2
by solving eqn 1&2 we get x = 50 and y=25
therefore, no of notes of Rs 5=150 and Rs 10=25
Incorrect
let the no of notes of Rs 5 be x and Rs 10 be y
then, x+y = 175……… 1 and 5x+10y=1000……….. 2
by solving eqn 1&2 we get x = 50 and y=25
therefore, no of notes of Rs 5=150 and Rs 10=25
Question 14 of 25
14. Question
1 points
The centroid of the triangle ABC is at the point (2,3). A and B are the points (5,6) and (-1,4). the coordinates of C are
Correct
Let coordinates of C be (x,y)
centroid = X1+X2+X3/3,Y1+Y2+Y3/3
then, 5+(-1)+x/3=2,6+4+y/3=3
4+x=6,10+y=9
x=2,y=-1
coordinates of C are (2,-1)
Incorrect
Let coordinates of C be (x,y)
centroid = X1+X2+X3/3,Y1+Y2+Y3/3
then, 5+(-1)+x/3=2,6+4+y/3=3
4+x=6,10+y=9
x=2,y=-1
coordinates of C are (2,-1)
Question 15 of 25
15. Question
1 points
A man rowing at the rate of 5 km in an hour in still water takes thrice as much time in going 40 km up the river as in going 40 km down. find the rate at which the rive flows?
Correct
let the rate of flow of river be x km/hr
speed of a man up stream = 5-x km/hr
speed of a man down stream = 5+x km/hr
distance covered = 40 km
time taken to go up stream = distance/time = 40/x-5
down stream = 40/ x+5
then, 40/x-5=3×40/x+5
x=10 km/hr= speed of the river
Incorrect
let the rate of flow of river be x km/hr
speed of a man up stream = 5-x km/hr
speed of a man down stream = 5+x km/hr
distance covered = 40 km
time taken to go up stream = distance/time = 40/x-5
down stream = 40/ x+5
then, 40/x-5=3×40/x+5
x=10 km/hr= speed of the river
Question 16 of 25
16. Question
1 points
Correct
Incorrect
Question 17 of 25
17. Question
1 points
If area and perimeter of a rectangle is 6000 cm and 340 cm, then the length rectangle is
Correct
Incorrect
Question 18 of 25
18. Question
1 points
A straight line passes through the point (3,2). find the equation of the straight line
Correct
If the line passes through a point, then the coordinates of the point satisfies the equation of that line
similarly, (3,2) should satisfy the equation which passes through it. so, from the given options C viz.x+y=5 is satisfied at the point 3,2
Incorrect
If the line passes through a point, then the coordinates of the point satisfies the equation of that line
similarly, (3,2) should satisfy the equation which passes through it. so, from the given options C viz.x+y=5 is satisfied at the point 3,2
Question 19 of 25
19. Question
1 points
Correct
Incorrect
Question 20 of 25
20. Question
1 points
A straight line of x=15 is
Correct
Incorrect
Question 21 of 25
21. Question
1 points
If the length of a rectangle is 5 cm more than the breath and if the perimeters of the rectangle is 40 cm, then the length and breath of rectangle will be
Correct
Let breath=x cm and length= x+5 cm
perimeter = 2(l+b)
40=2[(x+5)+x]
20=x+5+x
x=15/2=7.5=breath
length=x+5=7.5+5=12.5 cm
Incorrect
Let breath=x cm and length= x+5 cm
perimeter = 2(l+b)
40=2[(x+5)+x]
20=x+5+x
x=15/2=7.5=breath
length=x+5=7.5+5=12.5 cm
Question 22 of 25
22. Question
1 points
The point of intersection of the lines 2x-5y=6 and x+y=3 is
Correct
2x-5y=6………. 1 and x+y=3……….. 2
by solving 1&2 we get x=3 and y=0
point of intersection is (3,0)
Incorrect
2x-5y=6………. 1 and x+y=3……….. 2
by solving 1&2 we get x=3 and y=0
point of intersection is (3,0)
Question 23 of 25
23. Question
1 points
Find the equation of the line passing through the point (1,1) and parallel to the line 3x+5y+17=0
Correct
Let the eqn be 3x+5y+k=0 passes through point (1,1)
3x+5y+k=0
3×1+5×1+k=0
3+5+k=0
k= -8
Incorrect
Let the eqn be 3x+5y+k=0 passes through point (1,1)
3x+5y+k=0
3×1+5×1+k=0
3+5+k=0
k= -8
Question 24 of 25
24. Question
1 points
The graph of straight line x=5 will be
Correct
Incorrect
Question 25 of 25
25. Question
1 points
Find the equation of the line joining the point (3,5) with point of intersection 2x+3y-5=0 and 3x+5y-7=0
Correct
Incorrect
Mock test in equation Business Mathematics, CA Foundation
CA Foundation Equation
Time limit: 0
Quiz-summary
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Subject :- Quantitative Aptitude
Chapter :- Equations-Test 2
Questions :- 25
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If the ratio of (5x-3y) and (5y-3x) is 3:4, then the value of x:y is
Correct
Given, 5x-3y/5y-3x=3/4
4(5x-3y)=3(5y-3x)
20x+9x=15y+12y
x/y=27/29=27:29
Incorrect
Given, 5x-3y/5y-3x=3/4
4(5x-3y)=3(5y-3x)
20x+9x=15y+12y
x/y=27/29=27:29
Question 5 of 25
5. Question
1 points
Correct
Incorrect
Question 6 of 25
6. Question
1 points
Correct
Incorrect
Question 7 of 25
7. Question
1 points
Correct
Incorrect
Question 8 of 25
8. Question
1 points
The equation of the straight line passing through the intersection of 4x-3y-1=0 and 2x-5y+3=0 and parallel to 4x+5y=6 is
Correct
Incorrect
Question 9 of 25
9. Question
1 points
Correct
Incorrect
Question 10 of 25
10. Question
1 points
Find the point which divides the line joining the points(2,-2) and (-4,1) in the ratio 5:2 externally
Correct
Incorrect
Question 11 of 25
11. Question
1 points
Correct
Incorrect
Question 12 of 25
12. Question
1 points
State the type of quadrilateral formed by the vertices (1,1),(4,4),(4,8) and (1,5)
Correct
Incorrect
Question 13 of 25
13. Question
1 points
Correct
Incorrect
Question 14 of 25
14. Question
1 points
A seller makes an offer of selling certain articles that can be described by the equation x=25-2y where x is the price per unit and y denotes of the number of units. the cost price of the article is Rs 10 per unit. the maximum quantity that can be offered in a single deal to avoid loss is
Correct
Given x=25-2y
10=25-2y(for at par)
2y=15
y=7.5
Incorrect
Given x=25-2y
10=25-2y(for at par)
2y=15
y=7.5
Question 15 of 25
15. Question
1 points
If kx-4=(k-1)x, then which of the following is true?
Correct
if kx-4=(k-1)x
kx-4=kx-x
x=4
Incorrect
if kx-4=(k-1)x
kx-4=kx-x
x=4
Question 16 of 25
16. Question
1 points
If 3/x+y + 2/x-y = -1 and 1/ x+y – 1/x-5 = 4/3 then x,y is
A cottage industry produces a certain no. of pottery articles in a day. it was observed on a particular day that the cost of each article was two more than thrice the no. of articles produced on that day. if total cost of production on that day was Rs 800 the no. of articles produced was
Correct
Incorrect
Question 18 of 25
18. Question
1 points
The triangle formed by line x + 2 y = 3, 2x – y = 1 and y=0 is
Correct
Incorrect
Question 19 of 25
19. Question
1 points
If the sides of an equilateral triangle are shortened by 3 units, 4 units and 5 units and a right triangle is formed, then the sides of an equilateral triangle is
Correct
Incorrect
Question 20 of 25
20. Question
1 points
The lines 3x-4y+5=0, 7x-8y+5=0, 4x+5y-45=0 are
Correct
Given, 3x-4y+5=0…….. 1
7x-8y+5=0……… 2
4x+5y-45=0…….. 3
by solving 1&2 we get x=5,y=5
which satisfy the 3rd eqn
so lines are concurrent
Incorrect
Given, 3x-4y+5=0…….. 1
7x-8y+5=0……… 2
4x+5y-45=0…….. 3
by solving 1&2 we get x=5,y=5
which satisfy the 3rd eqn
so lines are concurrent
Question 21 of 25
21. Question
1 points
The equation of line passing through the point of intersection of the lines y=3 and x+y =0 and parallel to the 2x-y=4 is
Correct
Given, y=3……… 1 and x+y=0………. 2
by solving 1&2 we get x= -3 and y= 3
intersection points of lines is (-3,3)
given lines 2x-y=4
it parallel line eqn 2x-y=k……..A
it passes through (-3,3)
2x -3 – 3 = k
k = -9= substitute in eqn A
then, 2x-y+9 = 0
Incorrect
Given, y=3……… 1 and x+y=0………. 2
by solving 1&2 we get x= -3 and y= 3
intersection points of lines is (-3,3)
given lines 2x-y=4
it parallel line eqn 2x-y=k……..A
it passes through (-3,3)
2x -3 – 3 = k
k = -9= substitute in eqn A
then, 2x-y+9 = 0
Question 22 of 25
22. Question
1 points
If 3 x-y = 2, 5x+ay=3 and 2x+y=3 are concurrent lines, then the value of a is
Correct
If 3 x-y = 2…….. 1
5x+ay=3…….. 2
and 2x+y=3…….. 3
by solving 1&3 we get x=1, y=1
intersection points of line is (1,1)
then, 5x+ay=3
5×1 + ax1 = 3
a = -2
Incorrect
If 3 x-y = 2…….. 1
5x+ay=3…….. 2
and 2x+y=3…….. 3
by solving 1&3 we get x=1, y=1
intersection points of line is (1,1)
then, 5x+ay=3
5×1 + ax1 = 3
a = -2
Question 23 of 25
23. Question
1 points
The no. of students in each section of a school is 36. after admitting 12 new students, 4 sections were started. if total no. of students in each section now is 30, than the no. of sections initially were
Correct
Incorrect
Question 24 of 25
24. Question
1 points
The equation x+5y = 33, x+y/x-y=13/3 has the solution x,y is
Correct
Incorrect
Question 25 of 25
25. Question
1 points
The value of k for which the system of equations kx+2y=5 and 3x+y=1 has no solution is
