When $3^{333}$ is divided by 11 , the remainder is
a.
1
b.
10
c.
6
d.
5
Correct Answer
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Q2mcq
If $x$ and $y$ satisfy the equations $|x|+x+y=15$ and $x+|y|-y=20$, then $(x-y)$ equals
a.
10
b.
5
c.
20
d.
15
Correct Answer
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Q3mcq
If $m$ and $n$ are natural numbers such that $n>1$, and $m^n=2^{25} \times 3^{40}$, then $m-n$ equals
a.
209932
b.
209937
c.
209947
Correct Answer
d.
209942
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Q4mcq
A function $f$ maps the set of natural numbers to whole numbers, such that $f(x y)=f(x) f(y)+f(x)+f(y)$ for all $x, y$ and $f(p)=1$ for every prime number $p$. Then, the value of $f(160000)$ is
a.
1023
b.
4095
Correct Answer
c.
2047
d.
8191
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Q5mcq
$A B C D$ is a trapezium in which $A B$ is parallel to $C D$. The sides $A D$ and $B C$ when extended, intersect at point $E$. If $A B=2 \mathrm{~cm}, C D=1 \mathrm{~cm}$, and perimeter of $A B C D$ is 6 cm , then the perimeter, in cm , of $\triangle A E B$ is
a.
10
b.
9
c.
8
Correct Answer
d.
7
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Q6nat
Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil
together can complete the same task in 100 days. Amal starts working on the task and
works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes
over and completes the remaining task in 45 days. If Amal had started the task alone and
worked on all days, Vimal had worked on every second day, and Sunil had worked on every
third day, then the number of days required to complete the task would have been
✓ Accepted Answer:139
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Q7nat
Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells
this product to Hari. If Bina would have sold this product to Shyam at the purchase
price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by
Shyam is
✓ Accepted Answer:2160
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Q8mcq
The sum of the infinite series $\frac{1}{5}\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{5}\right)^2\left(\left(\frac{1}{5}\right)^2-\left(\frac{1}{7}\right)^2\right)+\left(\frac{1}{5}\right)^3\left(\left(\frac{1}{5}\right)^3-\left(\frac{1}{7}\right)^3\right)+\cdots$ is equal to
a.
$\frac{5}{408}$
Correct Answer
b.
$\frac{7}{816}$
c.
$\frac{7}{408}$
d.
$\frac{5}{816}$
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Q9nat
If $a, b$ and $c$ are positive real numbers such that $a>10 \geq b \geq c$ and $\frac{\log _8(a+b)}{\log _2 c}+\frac{\log _{27}(a-b)}{\log _3 c}=\frac{2}{3}$, then the greatest possible integer value of $a$ is
✓ Accepted Answer:14
No explanation saved for this question yet.
Q10mcq
A company has 40 employees whose names are listed in a certain order. In the year 2022,
the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was
Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year,
the average bonus of the first 10 employees increased by 100%, of the last 10 employees
increased by 200% and of the remaining employees was unchanged. Then, the average bonus,
in rupees, of all the 40 employees together in the year 2023 was
a.
90000
b.
95000
Correct Answer
c.
80000
d.
85000
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P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths,
between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is
no direct path between P and S, while there are few direct paths between Q and R, and
between R and S. One can travel from P to S either via Q, or via R, or via Q followed by
R, respectively, in exactly 62 possible ways. One can also travel from Q to R either
directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct
paths between Q and R is
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A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each
type. At the beginning of a day, the number of mangoes make up 40% of his stock. That
day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the
day, he ends up selling 50% of the fruits. The smallest possible total number of fruits
in the stock at the beginning of the day is
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Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded
half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years,
and then reinvests the entire amount he receives at the end of 5 years, for one year at
10% simple interest. If the amounts received by both at the end of 6 years are equal,
then the initial investment, in rupees, made by Sunil is
a.
20480
b.
20808
c.
20640
d.
20860
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The roots $\alpha, \beta$ of the equation $3 x^2+\lambda x-1=0$, satisfy $\frac{1}{\alpha^2}+\frac{1}{\beta^2}=15$. The value of $\left(\alpha^3+\beta^3\right)^2$, is
a.
9
b.
16
c.
4
d.
1
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A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a
constant speed of 60 km per hour and reached its destination 3.5 hours later than its
scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of
its total scheduled travel time, and the remaining part of the route at 40 km per hour
to reach just on time. The scheduled arrival time of the bus is
a.
10 : 30 pm
b.
7 : 00 pm
c.
7 : 30 pm
d.
9 : 00 pm
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Three circles of equal radii touch (but not cross) each other externally. Two other circles, $X$ and $Y$, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of $X$ is more than that of $Y$, the ratio of the radii of $X$ and $Y$ is
a.
$2+\sqrt{3}: 1$
b.
$4+\sqrt{3}: 1$
c.
$7+4 \sqrt{3}: 1$
d.
$4+2 \sqrt{3}: 1$
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A vessel contained a certain amount of a solution of acid and water. When 2 litres of
water was added to it, the new solution had 50% acid concentration. When 15 litres of
acid was further added to this new solution, the final solution had 80% acid
concentration. The ratio of water and acid in the original solution was
a.
5 : 3
b.
4 : 5
c.
5 : 4
d.
3 : 5
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When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3
: 2. When Garima's age becomes the same as the present age of Rajesh,
the ratio of the ages of Rajesh and Garima will become
a.
4 : 3
b.
2 : 1
c.
3 : 2
d.
5 : 4
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