SRCC GBO 2021

On cross-multiplying, we get the equation: $$x^2$$ = $$2^{\frac{7}{2}}$$*$$2^{\frac{1}{2}}$$*$$3^{\frac{4}{2}}$$ 

On solving the same, $$x^2$$ = $$2^4$$*$$3^2$$

This gives the value of x as $$4\times3$$ which is 12. 

Rearranging the inequation, we get 16y>-32, or y>-2

This means the solution set for this inequation is $$(-2, \infty)$$

Out of the ten books, we need to have a case where a specific pair of two books is always there. 

To solve this, the best way is to assume the two books as a single element. This leaves us with nine different elements, where one of them has two books in it. 

To arrange nine different elements, we have 9! ways.

Now, it is important to note that the two books considered as a single element can be arranged within themselves as XY or YX (2 ways). 

Therefore, we shall multiply the initial result by 2, which makes the total number of ways as 9!$$\times\ $$2.

The shortest method to solve this question is by finding the remainder when 315654 is divided by 11. 

By doing so, we find that the remainder is 9, and adding 2 would make it divisible by 11. 

Let us assume the lengths of the larger part of the bridge and the smaller part as mx and nx.

As per the question, $$\ \frac{mx+nx}{nx}$$ = 6$$\times\ $$ $$\ \frac{\ mx}{mx+nx}$$

This means, $$\left(m+n\right)^2$$ = 6mn

Or, $$m^2+n^2$$ = 4mn

Hence, the value of $$m^2+n^2$$ - 4mn = 0, thereby making the value of $$\sqrt{25 + mn(m^2 - 4mn + n^2)}$$ as 5.

Here, the height of the parallelogram and the triangle are the same, and also the base is the same. This is because the question states that the PE divided SR into half.

The area of triangle is 1/2*b*h=1/2*x*h=37 $$\Rightarrow$$ xh=74.

Area of the PQRE is b*h=x*h=74

The total area is 37+74=111 $$cm^2$$.

The line in question (slope 'a') is perpendicular to a straight line (slope 'b') joining (2, -3) and (4, 2). Hence, a$$\times\ $$b= -1

b= $$\ \frac{\ 5}{2}$$, which makes a= $$\ \frac{\ -2}{5}$$

Hence, the equation of line with slope $$\ \frac{\ -2}{5}$$ is y= $$\ \frac{\ -2}{5}$$x + 5

Let 'a' be the radius of the bigger circle where A is its center, while 'b' is the radius of the smaller circle and B is its center.

's' is the distance between their circumference, and D is the distance between the two centers.

Hence, D = a - (b+s)

Let us assume that the total is 8 units (LCM of 2,4,8).

This means Tom does 4 units/hour, Suresh does 2 units/hour, and Adil does 1 unit/hour.

Now, Suresh's efficiency is increased and becomes 2n units/hour.

Due to this, they all complete the 8 units of work in less than 1 hour. 

This means, $$\ \ \frac{\ 8}{5+2n}<1\ $$, or n>1.5

The nearest integer is 2, making the value of $$n^2 + 2$$ as 6

To solve the equation, we shall first shift the 'x' in the base to RHS, which makes $$x^0$$ or 1. 

Now, we will shift the '5' in the base to RHS, which becomes $$5^1$$ or 5 as the value in RHS. Meanwhile, the LHS becomes $$\sqrt{\ x+5}$$+$$\sqrt{\ x}$$.

Now, $$\sqrt{\ x+5}$$+$$\sqrt{\ x}$$ = 5.

The best way to proceed ahead is going through the options and substituting them in the equation. On doing so, we find out that x=4 would satisfy the equation and hence it is the correct answer.