1. If the roots, \[x_{1}\] and \[x_{2}\] , of the quadratic
equation \[x^{2}-2x+c=0\] also satisfy the equation \[7x_{2}-4x_{1}=47\] , then which of the following
is true?
a) c = – 15
b) \[x_{1}=-5 , x_{2}=3\]
c) \[x_{1}=4.5 , x_{2}=-2.5\]
d) None of these
Explanation:
2. One year payment to a servant is Rs 90 plus one turban. The servant leaves after 9 months and receives Rs 65 and a turban. Then
find the price of the turban
a) Rs 10
b) Rs 15
c) Rs 7.5
d) Cannot be determined
Explanation:
3. You can collect Rubies and Emeralds as many as you can. Each Ruby is worth Rs 4crores and each Emerald is worth of Rs 5crore.
Each Ruby weights 0.3 kg. and each Emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What you should collect to get
the maximum wealth?
a) 20 Rubies and 15 Emeralds
b) 40 Rubies
c) 28 Rubies and 9 Emeralds
d) None of these
Explanation:
4. \[\mid r-6\mid =11\] and \[\mid 2q-12\mid =8\] , then what is the minimum value of q / r?
a) -2
b) \[\frac{17}{10}\]
c) \[-\frac{1}{5}\]
d) \[\frac{2}{5}\]
Explanation:
5. The expenses of a boarding school depends upon the fixed cost and variable cost. Variable cost varies directly as the number of
students. If the expenses per student were Rs 600 for 50 students and Rs 700 for 25 students then what are the expenses for 100
students?
a) 50000
b) 60000
c) 57500
d) 55000
Explanation:
6. x > 2, y > -1 then which of the following holds good ?
a) xy > -2
b) xy < -2
c) \[x>-\frac{2}{y}\]
d) None of these
Explanation: Given, y > – 1 i.e. if y is positive no. then product of x and y also positive.
But any option does not give xy is +ve.
By putting different values of x and y we see that none of these three hold good.
7. A, B and C are 3 cities that form a triangle and where every city is connected to every other one by at least one direct roots. There
are 33 routes direct & indirect from A to C and there are 23 direct routes from B to A. How many direct routes are there from A to
C ?
a) 15
b) 10
c) 20
d) 25
Explanation: Let the no. of direct routes from A to B be x, from A to C be z and that from C to B be y
Then the total no. of routes from A to C are = xy + z = 33
Since the no. of direct routes from A to B are 23,
x = 23
Therefore, 23y + z = 33
Then y must take value 1 and then z = 10
Hence, 10 routes are direct from A to C
8. If the equation \[x^{3}-ax^{2}+bx-a=0\] has three real roots then which of the following is true?
a) a = 11
b) \[ a \neq 1\]
c) b = 1
d) \[ b \neq 1\]
Explanation:
9. \[\mid x^{2}+y^{2}\mid =0.1\] and \[\mid x-y\mid =0.2\] , then the value
of \[\mid x\mid +\mid y\mid \] is
a) 0.6
b) 0.4
c) 0.36
d) 0.2
Explanation:
10. If x > 5 and y < – 1, then which of the following statements is true?
a) (x + 4y) > 1
b) x > – 4y
c) – 4x < 5y
d) None of these
Explanation:
