SRCC GBO 2021

Cos(x) is an even function, because Cos(-x) has the same points that overlap with Cos(x).

Let's designate x  cm as the length of each side of rhombus ABCD. Its perimeter is  4x cm.

Thus, 4x = 40, which leads to x = $$x=\dfrac{40}{4}$$ = 10  cm.

In triangle ABC, L is the midpoint of side AB, and M is the midpoint of side BC, resulting in LM measuring 6 cm.

Applying the similarity criterion in triangles BLM and BAC, we get $$\dfrac{BL}{BA}=\frac{LM}{AC}$$

This simplifies to $$\dfrac{BA}{2BA}=\frac{LM}{AC}$$ , which further simplifies to 1/2 = 6/AC , leading to  AC = 12 cm.

Hence, in triangle ABC, the sides are a = 10cm,  b = 12cm, and  c = 10cm.

The semi-perimeter, s, is calculated as (10+12+10)/2 = 16

The area of triangle ABC is given by $$\sqrt{𝑠(𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)\ }$$, which equals$$\sqrt{16\times(16−10)\times(16−12)\times(16−10)\ }$$​, which further simplifies to $$\sqrt{16\times6\times4\times6\ }=48cm^2$$

As the rhombus ABCD consists of two congruent triangles ABC, its area equals 2×area of triangle ABC=2×48 cm², resulting in 96cm².

Since the two persons are traveling toward each other, their relative speed will be (36+27)kmph, which is 63kmph. 

Now, they will meet at t= $$\ \frac{\ 84}{63}$$ hours, which is $$\ \frac{\ 4}{3}$$ hours.

Now, in $$\frac{CA\ }{(CA‒CB)\ }$$, CA is the distance traveled at a speed of 36 kmph in 't' hours and CB is (84-CA)

In 't' hours, CA= $$36\times\frac{\ 4}{3}$$, which is 48 km. 

Similarly, CB= 84-48= 36 km

Putting these values in (CA/(CA ‒ CB), we get the answer as 4.

This is a special property with respect to an equilateral triangle, where its orthocentre and centroid coincide with each other. 

Also, we know that the centroid divides the median in a ratio 2:1. Hence, the orthocentre shall divide the median in the same ratio. 

This is a direct relation: If the numbers are m and n, their product will equal the product of their LCM and HCF.

Applying the same in this question, m$$\times\ $$n = 196$$\times\ $$7

Putting this in the required expression, we get the answer as $$\sqrt{\ 196}$$, which is 14.

The direct method to solve the questions for non-negative integral solution is finding the value of

Here, n= 14 r=3

Substituting the values, we get $$\ 16_{C_2}$$which is 120.

Let us assume that the area under maize and barley in the larger plot is 8x and 9x. 

Similarly, the area under maize and barley in the smaller part is 13y and 15y. 

It is given that the total area under maize and barley (taking both the plots) is in the ratio 29:33.

By this, we get that $$\ \frac{\ 8x+13y}{9x+15y}$$= $$\ \frac{\ 29}{33}$$

This is, 264x+429y=261x+435y, making this as 3x=6y, or x=2y

For the ratio of area under maize (larger plot) to area under barley in smaller plot, we shall substitute the values in 8x:15y

The final ratio is 16y:15y, or 16:15.

Assume that the cost price of each of the articles as Rs.100. So, the total cost price is Rs.200.

The first article is sold at a profit of 30%, which makes its selling price as Rs.130.

The second article is sold at a loss of 20%, which makes its selling price as Rs.80. 

The total selling price is Rs.210, while the total cost price is Rs.200.

Hence, profit% = (10/200) * 100, which is 5%.