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
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
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