Q1:
Hard
$2^{122}+4^{62}+8^{42}+4^{64}+2^{130}$ is divisible by which one of the following integers?
Hard
$2^{122}+4^{62}+8^{42}+4^{64}+2^{130}$ is divisible by which one of the following integers?
Hard
Find the maximum value of $n$ such that $61 \times 42 \times 26 \times 81 \times 64 \times 49 \times 47 \times 51 \times 63 \times 16 \times 67$ is perfectly divisible by $56^n$
Medium
Three rings complete 60, 36 and 24 revolutions in a minute. They start from a certain point in their circumference down wards. By what time they come together again in the same position?
Medium
Arrange the following in descending order: A. $\sqrt{401}-\sqrt{399}$ B. $\sqrt{301}-\sqrt{299}$ C. $\sqrt{101}-\sqrt{99}$ D. $\sqrt{201}-\sqrt{199}$ Choose the correct answer from the options given below:
Medium
If $\frac{p}{q}=\frac{3}{7}$ and $\frac{r}{s}=\frac{5}{9}$, the value of $\frac{7pr-qs}{6qs-21pr}$ is
Easy
The average age of 8 men increases by 4 years when one of them whose age is 30 years is replaced by a new man. What is the age of new man?
Medium
Let $a, b, c, d, e, f, g$ be seven consecutive even numbers and $j, k, l, m, n$ be five consecutive odd numbers. What is the average of all numbers?
Easy
Two number are in the ratio of 2:3. If 9 (Nine) is added to each number, they will be in ratio 3:4. What is the product of the two numbers?
Easy
Seeta got married 6 years ago. Today her age is $1\frac{1}{4}$ times her age at the time of her marriage. Her son's age is $\frac{1}{10}$ times her present age. What is the present age of her son?
Medium
Match the LIST-I with LIST-II | | LIST-I (Expression) | | LIST-II (Value) | |---|---|---|---| | A. | $(550\%\text{ of }250) \div 275$ | I. | 129.58 | | B. | $38\%\text{ of }341$ | II. | 231.6 | | C. | $15\%\text{ of }578+22.5\%\text{ of }644$ | III. | 156.8 | | D. | $140\%\text{ of }56+56\%\text{ of }140$ | IV. | 5 | Choose the correct answer from the options given below:
Easy
Which of the following multipliers will cause a number to increase by 29.7%?
Easy
If the difference between 62% and 80% of a number is 198, then the difference between 92% and 56% of the same number will be :-
Easy
Successive discounts of $p\%$ and $q\%$ on an invoice is the same as a single discount of
Medium
Given below is the data pertaining to four movies which have collected gross revenues in domestic and international markets in Million USD ($). Arrange them in ascending order based on the ratios of their international versus domestic gross revenues. | | | | | |---|---|---|---| | A. | Avengers - | Domestic 623.4 | International 888.4 | | B. | The Darknight - | Domestic 448.1 | International 632.9 | | C. | Skyfall - | Domestic 304.2 | International 804.1 | | D. | Ice Age CD - | Domestic 161.3 | International 714.0 | Choose the correct answer from the options given below:
Easy
If P : Q = 5 : 2, then (2P - 3Q) : (3P - 5Q) is equal to:
Hard
The simple interest on a sum of money for 3 years is ₹240 and the compound interest on the same sum, at the same rate for 2 years is ₹170. The rate of interest is:
Medium
'A' started a business with investment of ₹5000. After 2 months, 'B' & 'C' joined with ₹2500 and ₹3500, respectively. If total annual profit was ₹4800, what was B's share in annual profit?
Medium
A solid cone and a solid cylinder have equal base and equal height. If the radius and height be in the ratio of 12 : 5, the ratio of the total surface area of cone to that of the cylinder is
Medium
A Merchant had 50 kg of pulse. He sold one part at 10% profit and other remaining part at 5% loss. The overall gain he had was 7%. Then the quantities of pulse, which he sold at 10% profit and 5% loss, respectively, are
Medium
A and B can do a piece of work in 40 days and 50 days, respectively. Both begin doing the work together but after certain time A leaves. Then, B finishes the remaining work in 20 days. After how many days did A leave?
Medium
A student walks from his house at speed of $2\frac{1}{2}$ km/hour and reaches his school late by 6 min. Next day, he increases his speed by 1 km/hour and reaches 6 min before school time. How far is the school from his house?
Hard
If $x+y+z=7$, $x^2+y^2+z^2=85$ and $x^3+y^3+z^3=913$, then value of $\sqrt[3]{xyz}$ is
Easy
For which value of $k$, lines $x+2y=9$ and $kx+4y=-5$ are parallel?
Medium
The product of two positive integers $x$ and $y$ is 6760 and their HCF is 13. How many such pairs $(x, y)$ can be formed?
Easy
If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of other, then which of the following is correct?
Hard
Let $p$ and $q$ be the roots of the quadratic equation $ax^2+bx+c=0$, $a\ne0$. If $a$, $b$ and $c$ are in arithmetic progression and $\frac{1}{p}+\frac{1}{q}=4$, then the value of $(p-q)^2$ is
Medium
An aluminum sheet 25 cm long, 20 cm broad and 2 cm thick is melted into a cube. The difference in the surface area of the two solids would be
Medium
The value of $3+\frac{1}{\sqrt3}+\frac{1}{3+\sqrt3}+\frac{1}{\sqrt3-3}$ is
Medium
A box contains 2 blue caps, 4 red caps, 5 green caps and 1 yellow cap. If three caps are picked at random without replacement, what is the probability that two are red and one is green?
Medium
Sam can hit a target 1 time in 4 shots, Jack can hit the target 2 times in 4 shots and Raj can hit the target 6 times in 6 shots. What is the probability that at least 2 shots hit the target?
Easy
A cube has each edge 2 cm and cuboid is 1 cm long, 2 cm wide and 3 cm high. The paint in a certain container is sufficient to paint area equal to 54 cm². Which of the following is correct?
Medium
The sum of length, breadth and height of a cuboid is 22 cm and the length of its body diagonal is 14 cm. What is the surface area of the cuboid?
Hard
The sum of length, breadth and height of a cuboid is 22 cm and length of its body diagonal is 14 cm. if S is the sum of cubes of dimensions of the cuboid and V is the volume, the (S−3V) will be equal to
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