Quantitative Aptitude - Equations
Exam Duration: 45 Mins Total Questions : 30
If 6 = 2x+4y, what is the value of x+2y is
- (a)
2
- (b)
3
- (c)
6
- (d)
8
Solve for y in the equation \(\frac { y+11 }{ 6 } -\frac { y+1 }{ 9 } =\frac { y+7 }{ 4 } \)and the value of y is -
- (a)
-1
- (b)
7
- (c)
1
- (d)
\(-\frac{1}{7}\)
Solving equation x2 - (a+ b)x + ab = 0 we find value(s) of x
- (a)
a, b
- (b)
a
- (c)
b
- (d)
None
Solving equation x2 - 24x + 135 = 0 we find value(s) of x
- (a)
9,6
- (b)
9,15
- (c)
15, 6
- (d)
None
Solving equation z + \(\sqrt { z } =\frac { 6 }{ 25 } \) the value of z works out to
- (a)
1/5
- (b)
2/5
- (c)
1/25
- (d)
2/25
If \(\frac { x-bc }{ b+c } +\frac { x-ca }{ c+a } +\frac { x-ab }{ a+b } \)=a+b+c the value of x is
- (a)
a2 + b2 + c2
- (b)
a(a+b+c)
- (c)
(a+b)(b+c)
- (d)
ab + bc + ca
If \(\frac { x+2 }{ x-2 } +\frac { x-2 }{ x+2 } =\frac { x-3 }{ x+3 } - \frac { x+3 }{ x-3 }\)then the values of x are
- (a)
\(0,±\sqrt { 6 } \)
- (b)
\(0,±\sqrt { 3 } \)
- (c)
\(0,±2\sqrt { 3 } \)
- (d)
None
Solve \(\left( x-\frac { 1 }{ x } \right) ^{ 2 }+2\left( x+\frac { 1 }{ x } \right) =7\frac { 1 }{ 4 } \) .
- (a)
\(x=\frac { -9\pm \sqrt { 65 } }{ 4 } \) or \(x=2\frac { 1 }{ 2 } \)
- (b)
\(x=\frac { -9\pm \sqrt { 55 } }{ 4 } \) or \(x=3\frac { 1 }{ 2 } \)
- (c)
\(x=\frac { -9\pm \sqrt { 45 } }{ 4 } \) or \(x=4\frac { 1 }{ 2 } \)
- (d)
\(x=\frac { -9\pm \sqrt { 35 } }{ 4 } \) or \(x=2\frac { 1 }{ 2 } \)
The solution of the equation x -\(\sqrt { 25-{ x }^{ 2 } } \)=1, is
- (a)
x = -3
- (b)
x = \(\pm\)5
- (c)
x = 1
- (d)
x = 4
Solving equation \(\frac { 6x+2 }{ 4 } +\frac { 2{ x }^{ 2 }-1 }{ 2{ x }^{ 2 }+2 } =\frac { 10x-1 }{ 4x } \) we get roots as
- (a)
\(\pm\)1
- (b)
+1
- (c)
-1
- (d)
0
Solving \(\sqrt { { y }^{ 2 }+4y-21 } +\sqrt { { y }^{ 2 }-y-6 } =\sqrt { 6{ y }^{ 2 }-5y-39 } \) following roots are obtained -
- (a)
2 3 \(\frac { 5 }{ 3 } \)
- (b)
2 3 -\(\frac { 5 }{ 3 } \)
- (c)
-2 -3 \(\frac { 5 }{ 3 } \)
- (d)
-2 -3 -\(\frac { 5 }{ 3 } \)
Solving \(\sqrt { \frac { x }{ y } } +\sqrt { \frac { y }{ x } } -\frac { 5 }{ 2 } =0\)and x + y - 5 = 0 we get the roots as under
- (a)
1, 4
- (b)
1, 2
- (c)
1, 3
- (d)
1, 5
The roots of a x2 + bx + c = 0, are real and unequal if
- (a)
b 2< 4ac
- (b)
b2 - 4ac
- (c)
b 2> 4ac
- (d)
b2 = 4ac
If \(\alpha \ \beta \) are the roots of equation x2 - 5x + 6 = 0 the equation with the roots (\(\alpha \beta +\alpha +\beta \)) and (\(\alpha \beta -\alpha -\beta\)) is
- (a)
x2 -12x +11 = 0
- (b)
2x2 - 6x + 12 = 0
- (c)
x2 -12x + 12 = 0
- (d)
None
If \(p\neq q\) and p2 = 5p - 3 and q2 = 5q - 3 the equation having roots as \(\frac { p }{ q } \) and \(\frac { p }{ q } \) is
- (a)
x2 -19x + 3 = a
- (b)
3x2-19x-3=0
- (c)
3x2 -19x +3=0
- (d)
3x2+19x+3=0
The roots of the equation (q - r) x x2 + (r - p) x x + (p - q) = 0 are
- (a)
(r - p) / (q - r), 1
- (b)
(p-q)/(q-r),1
- (c)
(q - r) / (p - q), 1
- (d)
(r-p)/(p-q),l
Two numbers are such that thrice the smaller number exceeds twice the greater one by 18 and 1/3 of the smaller and 1/5 of the greater number are together 21. The numbers are -
- (a)
(45,36)
- (b)
(50, 38)
- (c)
(54,45)
- (d)
(55,41)
The number of kilograms of corn needed to feed 5,000 chickens is 30 less than twice the number of kilograms needed to feed 2,800 chickens. How many kilograms of corn are needed to feed 2800 chickens?
- (a)
70
- (b)
110
- (c)
140
- (d)
190
The hypotenuse of a right-angled triangle is 20 cm. The difference between its other two sides is 4cm. The sides are
- (a)
(11cm, 15cm)
- (b)
(12cm, 16cm)
- (c)
(20cm, 24cm)
- (d)
None of these
One machine can seal 360 packages per hour, and an older machine can seal 140 packages per hour. How many minutes will the two machines working together take to seal a total of 700 packages?
- (a)
48
- (b)
72
- (c)
84
- (d)
90
The age of a person is 8 years more than thrice the age of the sum of his two grandsons who were twins. After 8 years his age will be 10 years more then twice the sum of the ages of his grandsons. Then the age of the person when twins born is _______:
- (a)
86 years
- (b)
73 years
- (c)
68 years
- (d)
63 years
Solving x3 + 9x2 - X - 9 = 0 we get the following roots
- (a)
± 1,-9
- (b)
±1, ±9
- (c)
±1, 9
- (d)
None
The solution of the cubic equation x3 - 6x2 + 11 x - 6 = 0 is given by the triplet
- (a)
(-1,1,-2)
- (b)
(1, 2, 3)
- (c)
(-2, 2, 3)
- (d)
(0,4, -5)
If the graphs of both the equations are same, every point on the graph is a point of intersection then there will be
- (a)
Finite number of solutions
- (b)
Infinite number of solutions
- (c)
No solution
- (d)
None
The equation of line passing through the points (1, -1) and (3, -2) is given by
- (a)
2x + y + 1 = 0
- (b)
2x + y + 2 = 0
- (c)
x + y + 1 = 0
- (d)
x + 2 y + 1 = 0
Find the distance between the pair of points p (-5, 2) and q (-3, -4)
- (a)
\(2\sqrt { 10 } \)
- (b)
\(10\sqrt { 2 } \)
- (c)
2
- (d)
10
The co-ordinates of the circumcentre of a triangle with vertices (3, -2) (-6, 5) and (4, 3) are
- (a)
\(\left( -\frac { 3 }{ 2 } ,\frac { 3 }{ 2 } \right) \)
- (b)
\(\left( \frac { 3 }{ 2 } ,\frac { -3 }{ 2 } \right) \)
- (c)
(-3,3)
- (d)
(3,-3)
The area of the triangle bounded by the lines 4x + 3y + 8 = 0 , x - y + 2 = 0, 9x - 2y -17 = 0
- (a)
18
- (b)
17.5
- (c)
17
- (d)
None
The area of the triangle with vertices (-1, 1) (-3, 2) and (-5, 4) is
- (a)
0
- (b)
1
- (c)
-1
- (d)
None
The orthocenter of the triangle bound by lines 3x - y = 9 x - y = 5 and 2x - y = 8
- (a)
(0, 0)
- (b)
(-6, 1)
- (c)
(6,-1)
- (d)
(-6, -1)