JIPMAT 2023 Question Paper

Assertion [A]:-

First 100 even natural numbers that are divisible by 5 are - {10,20,30,......,1000}

$$Sum=\dfrac{n}{2}\left[a+l\right]$$

$$Sum=\dfrac{100}{2}\left[10+1000\right]$$

$$Sum=50\times1010$$

$$Sum=50500$$

Thus, Assertion [A] is FALSE.

Sum of the first n-terms of an Arithmetic Progression is given by $$S=(n/2)*(a+l)$$ where a=first term, l=last term.

This is TRUE, as this is the actual formula for the sum of n terms. 

Thus, Reason (R) is TRUE. 

The diameter of the circle that can be inscribed in the square will be equal to the side of the square.

Thus, diameter of circle = 6 cm

Thus, Radius of circle = 3 cm

Area of circle = $$\pi\left(3\right)^2=9\pi\ cm^2$$

Let the radii of the two cones be 2r and 3r, and their heights be h1 and h2. 

The ratio of volumes of the two cones is 1:3

$$\dfrac{\frac{1}{3}\pi\left(2r\right)^2h_1}{\frac{1}{3}\pi\left(3r\right)^2h_2}=\dfrac{1}{3}$$

$$\dfrac{4r^2h_1}{9r^2h_2}=\dfrac{1}{3}$$

$$\dfrac{h_1}{h_2}=\dfrac{3}{4}$$

$$h_1:h_2=3:4$$

THIS QUESTION WAS DELETED, BECAUSE THEY DIDN'T MENTION THAT THE TABLE CONSISTS OF PERCENTAGES RATHER THAN THE ACTUAL MARKS OF STUDENTS

If solved, the following will be the correct answers.

%age of A $$=\dfrac{70+75+70+65+60+70}{720}\times100=56.94\%$$

%age of B $$=\dfrac{80+70+75+60+50+75}{720}\times100=56.94\%$$

%age of C $$=\dfrac{75+72+71+70+60+65}{720}\times100=57.36\%$$

THIS QUESTION WAS DELETED, BECAUSE THEY DIDN'T MENTION THAT THE TABLE CONSISTS OF PERCENTAGES RATHER THAN THE ACTUAL MARKS OF STUDENTS

If solved, the following will be the correct answers. 

Average marks in Economics $$=\dfrac{70+80+75+60+70+65}{6}=70\%$$

Average marks in Economics $$=\dfrac{60+50+60+60+55+50}{6}=55.84\%$$

THIS QUESTION WAS DELETED, BECAUSE THEY DIDN'T MENTION THAT THE TABLE CONSISTS OF PERCENTAGES RATHER THAN THE ACTUAL MARKS OF STUDENTS

THIS QUESTION WAS DELETED, BECAUSE THEY DIDN'T MENTION THAT THE TABLE CONSISTS OF PERCENTAGES RATHER THAN THE ACTUAL MARKS OF STUDENTS

To find the overall percentage for each subject, we calculate the average of the percentage scores of all the students for that subject:

Physics: $$\dfrac{70+80+75+60+70+65}{6}=\dfrac{420}{6}=70\%$$

Biology: $$\dfrac{75+70+72+70+75+70}{6}=\dfrac{432}{6}=72\%$$

Maths: $$\dfrac{70+75+71+65+65+60}{6}=\dfrac{406}{6}=67.67\%$$

Geology: $$\dfrac{65+60+70+55+50+65​}{6}=\dfrac{365}{6}=60.83\%$$

Economics: $$\dfrac{60+50+60+60+55+50​}{6}=\dfrac{335}{6}=55.83\%$$

English: $$\dfrac{70+75+65+70+60+60​}{6}=\dfrac{400}{6}=66.63\%$$

Biology has the highest score of 72%.

Let the total sales in 2005 be 100x, then we can calculate the shares of each of the 5 computer brands A, B, C ,D and E as follows:

Now, in 2006, sales of A went up by 50%, so sales of A in 2006 = 1.5 times sales of A in 2005 = $$1.5\times\ 45x=67.5x$$

And, sales of E increased by 10% , So sales of E in 2006 = 1.1 times sales of E in 2005 = $$1.1\times\ 22x=24.2x$$ 

The sales of B, C and D remain unchanged, hence we update the table by adding another column for 2006 and filling in the values as:

Now, we have to calculate the percentage by which the sales in 2006 increased compared to the sales in 2005, which is given by $$\dfrac{Sales_{2006}-Sales_{2005}}{Sales_{2005}}\times\ 100\%=\dfrac{124.7x-100x}{100x}\times\ 100\%=24.70\%$$

So, the sales in total increased by 24.70% in 2006 as compared to 2005 .

Let the total sales in 2005 be 100x, then we can calculate the shares of each of the 5 computer brands A, B, C, D and E as follows:

Now, in 2006, sales of A went up by 50%, so sales of A in 2006 = 1.5 times sales of A in 2005 = $$1.5\times\ 45x=67.5x$$

And, sales of E increased by 10% , So sales of E in 2006 = 1.1 times sales of E in 2005 = $$1.1\times\ 22x=24.2x$$

The sales of B, C and D remain unchanged, hence we update the table by adding another column for 2006 and filling in the values as:

The total sales in 2006 is given to be 2,16,000 , which is 124.7x .

So, $$x=\frac{216000}{124.7}$$

We have to calculate the sales of A in 2005 , which is 45x = $$45\times\ \frac{216000}{124.7}=77947.07...\approx\ 77947\ $$.  So the correct answer is option C.

Let the total sales in 2005 be 100x, then we can calculate the shares of each of the 5 computer brands A, B, C, D and E as follows:

Now, in 2006, sales of B went up by 10%, so sales of B in 2006 = 1.1 times sales of B in 2005 = $$1.1\times\ 15x=16.5x$$

And, sales of A decreased by 10% , So sales of E in 2006 = 0.9 times sales of A in 2005 = $$0.9\times\ 45x=20.5x$$

The sales of C, D and E remain unchanged, hence we update the table by adding another column for 2006 and filling in the values as:

So the sales in 2006 decreased compared to 2005 .

The change can be expressed as percentage as $$\frac{Sales_{2006}-Sales_{2005}}{Sales_{2005}}\times\ 100\%=\frac{97x-100x}{100x}\times\ 100\%=-3\%$$

Hence, there was a 3% decrease in sales.