List of top Mathematics Questions asked in CBSE Class XI

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the center. Find the height of the arch at a point 1.5 m from one end.

Solve the given inequality for real\(x:\frac{ x}{3} > \frac{x}{2} +1\).

The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Subject	Mathematics	Physics	Chemistry
Mean	42	32	40.9
Standard deviation	12	15	20

Which of the three subjects shows the highest variability in marks and which shows the lowest?

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

(i) If wrong item is omitted.

(ii) If it is replaced by 12.

Given that \(\bar{x}\) is the mean and \(Ïƒ2\) is the variance of n observations x₁,x₂,...,x_n. Prove that the mean and variance of the observations ax₁,ax₂,ax₃,...,ax_n are \(a\bar{x}\) and \(a^2Ïƒ2\), respectively,\((a ≠ 0).\)

The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12 and 14. Find the remaining two observations.

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:

\(\sum_{i=1}^{50}x_i=212,\sum_{i=1}^{50}x_i^2=902.8,\sum_{i=1}^{50}y_i=261,\sum_{i=1}^{50}y_{i=1}^2=1457.6\)

Which is more varying, the length or weight?

The following is the record of goals scored by team A in a football session:

No. of goals scored	0	1	2	3	4
No. of matches	1	9	7	5	3

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

-	Firm A	Firm B
No. of wage earners	586	648
Mean of monthly wages	Rs 5253	Rs 5253
Variance of the distribution of wages	100	121

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

From the data given below state which group is more variable, A or B?

X	35	54	52	53	56	58	52	50	51	49
Y	108	107	105	105	106	107	104	103	104	101

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Find the distance between P(x₁,y₁) and Q(x₂,y₂) when: (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis

The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin.Find vertices of the triangle.

Draw a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2). Also, find its area.

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8^th set of letter is mailed.

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

Find the 20th term of the series 2×4+4×6+6×8+ ... + n terms.