1) Two equal area of two circles subtended angle 60 and 75 at the centre. Find the ratio of the radio of the two circles. 5:4
2) If cosx - sinx =√2 sinx, prove sinx + coax =√2 coax
3) If 7 coax + 5 sinx= 5, find the value of 5cosx - 7sinx. ±7
4) If secx + tanx = x show you that sinx = (x²-1/(x²+1)
5) If sinx +cosecx = 2 show that sin¹⁰ + cosec¹⁰ = 2
6) If tan⁴x + tan²x= 1 show that cos⁴x + cos²x=1
7) If co⁴x + cos²x =1, show that tan⁴x + tan²x = 1
8) If sinA, cosA,tanA are in G. P prove cot⁶A - cot²A = 1
9) If (secx -1)(secy -1)(secz -1)= (secx+1)(secy+1)(ssecz +1) show that the value of each side is
± tanx tany Tanz
10) If (a² - b²) sinx + 2ab cosx= a²+ b², find the of tanx. (a²-b²)/2ab
27/11/2
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11) If 100 times the 100th term of an A. P with non-zero common difference equals the 50 times it's 50th term, then find 150th term
12) If the product of the roots of the Equation
x² - 2√2 kx + 2e² ˡᵒᵍ ᵏ -1=0 is 31, then find k.
13) Out of 64 students, the number of students taking maths is 45 and the number of students taking both maths and stats is 10. Then the number of students taking only Statistics is ?
14) Let S ᵢ denotes the sum of first n terms of an A. P. and S ₂ᵢ = 3S ᵢ. if S₃ᵢ= kS ᵢ Then find k
15) If A and B have n elements in common, then the number of elements common to AxB and BxA is ?
16) Find the greatest term in (1- x)⁻ⁿ when x= 3/4 and n=10.
17) Write down the fourth and fifth and fifth terms of (x + 1/x)⁸ in the simplified form.
18) Use the principle of Mathematical Induction Induction to prove:
1/(3.6) + 1/(6.9) + 1/(9.12) +... + 1/{3n(3n+2)} = n/{9(n+1)}.
19) Find the Quartile Deviation of the following frequency distribution:
Daily wages No. of workers
10-15 6
15-20 12
20-25 18
25-30 10
30-35 4
What is the interquartile range?
30/11/20
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20) If the pth, qth and rth terms of an AP respectively 1/a, 1/b and 1/c by show that, (q-r)bc + (r-p) ca + (p -q)ab = 0
21) How many terms of the series 1/1+ 1/3+ 1/6+...... must be taken so that the sum may be (-3/2) ?
22) Find the sum of 1-3+5 - 7 + 9 - 11 +.... to n terms.
23) How many even numbers are there between 15 and 150 ? Find the sum of all those numbers.
24) Find the sum of all the numbers between 200 and 300 which are multiples of 7.
25) If (p+1)th term of an AP be a, find the sum of first (2p+1) terms of the AP.
26) If the 11th term of an AP be 25, find the sum of first 21 terms of the AP.
27) There are (2n+1) terms in an AP. Show that the ratio of the sum of odd terms and the sum of even terms is (n+1): n.
28) Find the 99 term of the series 2+7 +14+23+34+ ........
29) How many terms are there in the series1+3+6+10+15+21+ .....+ 5050 ?
30) The sum of four numbers are in AP is and the sum of their squares is 120; find the numbers.
31) The sum of 6 numbers in AP in is 345 and the difference between the first between the first and the sixth is 55; find the numbers.
32) the 4th term of an AP is thrice the first term and the 7th term exceeds twice the third term by 2. Find the sum of first ten terms of the AP.
33) If 3rd, 7th, 12th terms of an A. P are three consecutive terms of a G. P, then find common ratio.
14) From 6 men and 4 women, the number of ways of forming a committee of 5 members, if there is no restriction on its formation, is..
15) If ¹²P ᵣ = ¹¹P₆ + 6 . ¹¹P₅ , then r is
19) If the letters of the word SACHIN are arranged in all possible ways and these words are written in dictionary order, then the word SACHIN appear at serial number ?
20) In a meetingting after every one had shaken hands with everyone else, it was found that 66 handshakes were exchanged. How many members were present at the meetings?
22) From a set of 17 balls marked 1, 2, 3, ....., 16, 17 one is drawn at random. What is the probability that its number is a multiple of 3 or 7 ?
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