A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The
number of apples and
mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the
oranges, the ratio of
number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of
unsold fruits is
✓ Accepted Answer:66
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Q2mcq
If $(a+b \sqrt{n})$ is the positive square root of
$(29-12 \sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then
the maximum possible value of $(a+b+n)$ is
a.
22
b.
6
c.
18
Correct Answer
d.
4
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Q3mcq
The sum of all real values of $k$ for which
$\left(\frac{1}{8}\right)^k \times\left(\frac{1}{32768}\right)^{\frac{1}{3}}=\frac{1}{8} \times\left(\frac{1}{32768}\right)^{\frac{1}{k}}$, is
a.
$\frac{2}{3}$
b.
$-\frac{2}{3}$
Correct Answer
c.
$\frac{4}{3}$
d.
$-\frac{4}{3}$
No explanation saved for this question yet.
Q4mcq
In the $X Y$-plane, the area, in sq. units, of the region
defined by the inequalities $y \geq x+4$ and $-4 \leq x^2+y^2+4(x-y) \leq 0$ is
a.
$4 \pi$
b.
$2 \pi$
Correct Answer
c.
$\pi$
d.
$3 \pi$
No explanation saved for this question yet.
Q5nat
Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema
would take 8 days
working 5 hours per day to complete the same task. They decide to work together to
complete this task. Seema
agrees to work for double the number of hours per day as Renu, while Renu agrees to work
for double the
number of days as Seema. If Renu works 2 hours per day, then the number of days Seema
will work, is
✓ Accepted Answer:6
No explanation saved for this question yet.
Q6mcq
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a
house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective
incomes to cover
the total house rent in that month. In October, the house rent remains unchanged while
their incomes
increase by 10%, 12% and 15%, respectively. In October, the percentage of their total
income that will be
paid as house rent, is nearest to
a.
14.84
b.
12.75
c.
13.26
Correct Answer
d.
15.18
No explanation saved for this question yet.
Q7mcq
Consider two sets $A=\{2,3,5,7,11,13\}$ and
$B=\{1,8,27\}$. Let $f$ be a function from $A$ to $B$ such that for every element $b$
in $B$, there is at least one element $a$ in $A$ such that $f(a)=b$. Then, the total
number of such functions $f$ is
a.
540
Correct Answer
b.
537
c.
665
d.
667
No explanation saved for this question yet.
Q8mcq
Let $x, y$, and $z$ be real numbers satisfying
$$
\begin{aligned}
& 4\left(x^2+y^2+z^2\right)=a \\
& 4(x-y-z)=3+a
\end{aligned}
$$
Then $a$ equals
a.
3
Correct Answer
b.
1 $\frac{1}{3}$
c.
1
d.
4
No explanation saved for this question yet.
Q9nat
The sum of all four-digit numbers that can be formed with
the distinct non-zero digits $a, b, c$, and $d$, with each digit appearing exactly once in
every number, is $153310+n$, where $n$ is a single digit natural number. Then, the value of
$(a+b+c+d+n)$ is
✓ Accepted Answer:31
No explanation saved for this question yet.
Q10mcq
When $10^{100}$ is divided by 7 , the remainder is
a.
3
b.
6
c.
1
d.
4
Correct Answer
No explanation saved for this question yet.
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There are four numbers such that average of first two numbers is 1 more than the first
number, average of
first three numbers is 2 more than average of first two numbers, and average of first
four numbers is 3 more
than average of first three numbers. Then, the difference between the largest and the
smallest numbers, is
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An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple
interest of 5% per
annum. On maturity, the total amount received is deposited in bank B for another 5 years
at a simple
interest of 6% per annum. If the interests received from bank A and bank B are in the
ratio 10 : 13, then
the investment period, in years, in bank A is
a.
4
b.
3
c.
6
d.
5
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A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and
an additional 3 kg
of these grains to the first customer. Then, it sells half of the remaining quantity and
an additional 3 kg
of these grains to the second customer. Finally, when the shop sells half of the
remaining quantity and an
additional 3 kg of these grains to the third customer, there are no grains left. The
initial quantity, in
kg, of grains is
a.
18
b.
36
c.
50
d.
42
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Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to
B while Sunil goes
from B to A. Starting at the same time, they cross each other in exactly 1 hour 30
minutes. If Anil reaches
B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
a.
16
b.
14
c.
12
d.
18
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The surface area of a closed rectangular box, which is
inscribed in a sphere, is 846 sq cm , and the sum of the lengths of all its edges is 144 cm .
The volume, in cubic cm , of the sphere is
a.
$750 \pi$
b.
$1125 \pi \sqrt{2}$
c.
$1125 \pi$
d.
$750 \pi \sqrt{2}$
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A glass is filled with milk. Two-thirds of its content is poured out and replaced with
water. If this process
of pouring out two-thirds the content and replacing with water is repeated three more
times, then the final
ratio of milk to water in the glass, is
a.
1 : 27
b.
1 : 81
c.
1 : 26
d.
1 : 80
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ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side
CD. Then, the length,
in cm, of radius of incircle of $\triangle A D E$ is
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The selling price of a product is fixed to ensure 40% profit. If the product had cost 40%
less and had been
sold for 5 rupees less, then the resulting profit would have been 50%. The original
selling price, in
rupees, of the product is
a.
10
b.
15
c.
20
d.
14
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