 ## TMA Questions

Q1. Answer any one of the following questions in about 40-60 words:

(i) If the ∠ A, ∠B and ∠C of a triangle are in an arithmetic progression, and if a, b and c denote the lengths of the sides opposite to ∠ A, ∠B and ∠C respectively. Then, find the value of the expression a/c𝑠𝑖𝑛2𝐶 +a/c𝑠𝑖𝑛2𝐴.

(ii) Each side of an equilateral triangle subtends an angle of 60° at the top of a towerof height h meter located at the centre of the triangle. If ‘a’ is the length of side ofthe triangle, then establish the relation between ‘a’ and ‘h’.

(i) Given that p and q are roots of the equation x2 – 2x + A = 0 and r and s be rootsof the equation x2 – 18 x + B = 0. If p < q < r < s and are in A.P. Then find A andB.
(ii) In a class of 100 students, 55 students have passed in Mathematics, and 67students have passed in Physics. If no student fails, then identify the number ofstudents passed in Physics only.

Q3. Answer any one of the following questions in about 40-60 words:

(i) If a, b, c in A.P. and x =∑∞n=0 an, y =∑∞n=0 bn, z = ∑∞n=0cnthenfind the relation between x, y and z.

(ii) Calculate the greatest integer which divides 101100 – 1.

Q4. Answer any one of the following questions in about 40-60 words:

(i) How many five-letter words containing 3 vowels and 2 consonants can be formedusing the letters of the word ‘EQUATION’ so that the two consonants occurtogether?

(ii) Two students solve a quadratic equation x2+bx+c = 0. One student solves theequation by taking wrong value of b and gets the roots as 2 and 5, while secondstudent solves it by taking wrong value of c and gets the roots as – 3 and – 4. Findthe correct roots of the equation.

Q5. Answer any one of the following questions in about 40-60 words.

(i) Find the sum of the series1+ (1 + a)/2! + (1 + a + a2)/3! + (1 + a + a2 + a3)/4!… … … … …

(ii) A survey was conducted in 1000 families of a city, from which the followinginformation was obtained.

i. 40% of families read newspaper A.
ii. 20% of families read newspaper B.
iii. 10% of families read newspaper C.
iv. 5% of families study both newspaper A and newspaper B.
v. 3% of families study both newspaper B and newspaper C.
vi. 4% of families study newspaper A and newspaper C.
vii. 2% of the families read all the three newspapers.
On the basis of the above information, identify the number of families who readonly newspaper A.

Q6. Prepare any one of the projects out of two given below.

(i) 10 students appeared in a unit test of a school. The maximum marks of the testwere 20. Collect the marks obtained by the students. On perusal of the mark sheet,it was found that one question was out of syllabus. It was decided that 5 bonusmarks would be given to each student for each wrong question. Compare thevariance and standard deviation in both the cases.

(ii) Puneet tosses two dice randomly. The number appearing on the faces of both thedice are different. Calculate the probability of the following event if –
i. The sum of the numbers on the dice is 4.
ii. The sum of the numbers on the dice is 8.
iii. The sum of the numbers on the dice is 12.
iv. The sum of the numbers on the dice is a multiple of 4.
v. The sum of the numbers on the dice is an odd number.
vi. The sum of the numbers on the dice is a prime number.