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Business Mathematics equation

Mock test in equation Business Mathematics, CA Foundation

CA Foundation Equation

Subject :- Quantitative Aptitude

Chapter :- Equations-Test 2

Questions :- 25

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Question 1 of 25

1. Question
1 points
$r o o t s o f t h e e q u a t i o n 3 x^{2} - 14 x + k = 0 w i l l b e r e s i p r o c a l t o e a c h o t h e r i f$
- k=-3
- k=0
- k=3
- k=14
Correct

since roots are reciprocal to each other
$r o o t s o f e q n w i l l b e α, 1 / \infty$
product of roots will be 1=+c/a

k/3=1

therefore,k=3

Incorrect

since roots are reciprocal to each other
$r o o t s o f e q n w i l l b e α, 1 / \infty$
product of roots will be 1=+c/a

k/3=1

therefore,k=3
Question 2 of 25

2. Question
1 points
The line 3x+4y+10=0 and 4x-3y+5=0 are
- parallel
- perpendicular to each other
- bisect each other
- concide with each other
Correct

Incorrect
Question 3 of 25

3. Question
1 points
$i f o n e r o o t o f t h e e q u a t i o n x^{2} - 3 x + k = 0 i s 2, t h e n v a l u e o f k w i l l b e$
- -10
- 0
- 2
- 10
Correct

$x^{2} - 3 x + k = 0 s u b x = 2 2^{2} - 3 x 2 + k = 0 4 - 6 + k = 0 k = 2$

Incorrect

$x^{2} - 3 x + k = 0 s u b x = 2 2^{2} - 3 x 2 + k = 0 4 - 6 + k = 0 k = 2$
Question 4 of 25

4. Question
1 points
If the ratio of (5x-3y) and (5y-3x) is 3:4, then the value of x:y is
- 27:29
- 29:27
- 3:4
- 4:3
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
$i f r o o t s o f e q u a t i o n x^{2} + x + r = 0 a r e α a n d β a n d α^{3} + β^{3} = - 6 . f i n d t h e v a l u e o f r$
- -5/3
- 7/3
- -4/3
- 1
Correct

Incorrect
Question 6 of 25

6. Question
1 points
$i f o n e r o o t o f t h e e q u a t i o n p x^{2} + q x + r = 0 t h e n o t h e r r o o t o f e q u a t i o n w i l l b e$
- 1/q
- 1/r
- 1/p
- 1/p+q
Correct

Incorrect
Question 7 of 25

7. Question
1 points
$I f t h e r a t i o o f t h e r o o t o f e q u a t i o n 4 x^{2} - 6 x + p = 0 i s 1 : 2 t h e n t h e v a l u e o f p i s$
- 1
- 2
- -2
- -1
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
- 4x+5y-12=0
- 4x+5y-16=0
- 4x+5y-9=0
- 4x+5y-4=0
Correct

Incorrect
Question 9 of 25

9. Question
1 points
$T h e m i n i m u m v a l u e o f t h e f u n c t i o n x^{2} - 6 x + 10 = 0 i s$
- 1
- 2
- 3
- 10
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
- -5,8
- -8,3
- -5,4
- -8,5
Correct

Incorrect
Question 11 of 25

11. Question
1 points
$I f t h e p o i n t (k, 3) i s a t a d i s t e n c e o f \sqrt{5} u n i t s f r o m t h e p o i n t s (2, k) t h e n v a l u e k i s$
- 1
- 4
- 1 and 4 both
- none
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)
- parallel ogram
- squares
- rhombus
- rectangle
Correct

Incorrect
Question 13 of 25

13. Question
1 points
$i f b^{2} - 4 a c i s a p e r f e c t s q u a r e b u t n o t e q u a l t o z e r o t h e n t h e r o o t s a r e$
- real and equal
- real, irrational and equal
- real, rational and unequal
- imaginary
Correct

$i f b^{2} - 4 a c i s a p e r f e c t s q u a e b u t n o t e q u a l t o z e r o i . e . D > 0 a n d h a v e p e r f e c t s q u a r e s o, r o o t s a r e r e a l u n e q u a l a n d r a t i o n a l$

Incorrect

$i f b^{2} - 4 a c i s a p e r f e c t s q u a e b u t n o t e q u a l t o z e r o i . e . D > 0 a n d h a v e p e r f e c t s q u a r e s o, r o o t s a r e r e a l u n e q u a l a n d r a t i o n a l$
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
- 6
- 7
- 8
- 9
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?
- x=5
- x= -4
- x= -3
- x=4
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
- 2,1
- 1,2
- -1,2
- -2,1
Correct

3/x+y + 2/x-y = -1……… 1 and 1/x+y – 1/x-y = 4/3…….. 2

solving 1&2 we get (1,2) by (trial method)

Incorrect

3/x+y + 2/x-y = -1……… 1 and 1/x+y – 1/x-y = 4/3…….. 2

solving 1&2 we get (1,2) by (trial method)
Question 17 of 25

17. Question
1 points
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
- 14
- 16
- 12
- 18
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
- right angled
- equilateral
- isosceles
- none
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
- 6 units
- 7 units
- 8 units
- 10 units
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
- concurrent
- parallel
- not concurrent
- none
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
- 2x-y+9=0
- 2x-y-9=0
- x-2y+9=0
- x+2y-9=0
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
- -1
- -2
- 2
- 3
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
- 6
- 10
- 14
- 18
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
- 4,8
- 8,5
- 4,16
- 16,4
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
- 5
- 2/3
- 6
- 3/2
Correct

Incorrect

Business Mathematics equation

CA Foundation Equation

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