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If the Federal Research and Development Budget in 2002 increases by 10% over that of 2001, by what percentage will the budget for Basic Research by Defence increase?

How many steps will be required for getting the final output for the following input?

Input: 101 85 66 49 73 39 142 25 115 74

There are 15 chocolates be distributed among 3 children subject to condition that child can take any number of chocolates. Find the required number of ways to do this if chocolates are identical.

What is the distance between the points of tangency of a common tangent AB to two circles I and II which are externally tangent to each other. The radii of the two circles are 9 and 16 units.

On which date in October was Sibal born ?

Statement I. Sibal's friend remembers that he was born before the 19${}^{th}$ but after 15${}^{th}$ .

Statement II. Sibal's brother remembers that he was born before the 17${}^{th}$ but after 12${}^{th}$ .

Study the following information carefully and answer the given questions:

A word and number arrangement machine when given an input line of words and numbers rearrange them following a particular rule in each step. The following is an illustration of input and rearrangement.

Input: gain 96 63 forest 38 78 deep house
Step I: deep gain 96 63 forest 38 78 house
Step II: deep 38 gain 96 63 forest 78 house
Step III: deep 38 forest gain 96 63 78 house
Step IV: deep 38 forest 63 gain 96 78 house
Step V: deep 38 forest 63 gain 78 96 house
Step VI: deep 38 forest 63 gain 78 house 96

And Step VI is the last step of the rearrangement of the above input.
As per the rules of followed in the above steps, find out in each of the following questions the appropriate step for the given input

Step II of an input is : cold 17 wave 69 never desk 52 43
How many more steps will be required to complete the rearrangement?

Given that P is a natural number. Is P > $(10{)}^{10}$ ?

Statement A: P > $2^{34}$

Statement B: P > 50!

Given that a_i $>$ 0 and i belongs to a set of natural numbers. If $a_1,a_2,a_3.....a_{2n}$ are in AP, then find the value of $\frac{a_1+a_{2n}}{\sqrt{a_1}+\sqrt{a_2}}+\frac{a_2+a_{2n}-1}{{\sqrt{a}}_2+\sqrt{a_3}}............+\frac{a_n+a_{n+1}}{\sqrt{a_n}+\sqrt{a_{n+1}}}$

If it is known that South Africa won a match against Australia, then New Zealand tied their match with which of the following teams?

Find the number of ways in which 128 can be written as a sum of two or more consecutive natural numbers.

If a, b, c are sides of a triangle such that $a^2+b^2+c^2$=ab+bc+ac. Then the triangles are:

A rectangle is divided into four rectangles, and their respective areas are shown in the figure. (Figure is not drawn to scale). What is the missing area 'X' of the fourth rectangle?

$\begin{array}{cc}25& 20\\ 5& x\end{array}$

Find the value of 1-2-3+2-3-4+...+ upto 100 terms.

Suppose f(x) = (x+1)${}^3$. If g(x) is the function whose graph is reflection of the graph of f(x) with respect to the line x = 3 and h(x) is the reflection of g(x) with respect to the x-axis, then h(8) equals:

Q17. Consider the following statements:

1. Mumbai to Ahmedabad High Speed Rail (MAHSR) is scheduled for completion in December 2023.

2. The Japan International Cooperation Agency (JICA) will fund it at a low rate of interest.

Which of the above statements are correct?

In the given figure, O is the center of the circle.
If $\angle AOD={140}^{\circ }and\angle CAB={50}^{\circ },find\angle EDB.$

Who among A, B, C, D and E teaches History?

Statements:

I: Each one of them teaches only one subject. B teaches Mathematics while E teaches Science. A or C does not teach Geography. A or D does not teach English.

II: C and E are teachers of English and Science respectively and A is the teacher of Mathematics.

If $x^2-gx+3=0$ and $2x^2-6x+g=0$ have a common root, then find the value(s) of the common root.

Which of the following is the factor of f(x) = x${}^5$ - 2x${}^4$ + 3x${}^3$ - 6x${}^2$ - 4x + 8.

If a cone is cut into two parts by a horizontal plane through the mid-point of its axis, the ratio of the volumes of the upper and lower parts is _____.

Q61. Complete the given series: 25 : 37 : : 49 : ?

In an office party, 24 employees ate non veg dinner, and 28 employees ate veg dinner. 7 employees ate both non veg and veg dinner. What is the strength of the office?

Jax and Jane are stuck in a room. The door of the room has a code. Jax thinks that if he deciphers the code, the door will open. Help them find what will come in place of '?' to open the door.

In the figure given, a person can move either towards right or in upward direction only.



The number of different ways to reach the point $B$ from point $A$ is

If a sphere of the maximum volume is placed inside a hollow right circular cone with radius 'r' and slant height 'l' such that the base of the cone touches the sphere, then the volume of the sphere is

Find the missing term : 6, 13, 22, 33, 46, 61, _

How many small cubes are there in the above shown figure. [2 MARKS]

If the excess/shortfall in production with respect to the sales in any year is exported/imported in the same year, then in 1993 the imports form what percentage of the sales?