27/11/20
8) Evaluate without consulting tables:
3 cos18/sin72. + Cosec61/sec29
9) Find the value of k given that
3x³ + 4x² -6x +k is divisible by x+1
10 )Use graph for this question. Take 1cm= 1 unit on both axes.
i) Plot point P(2,3) and Q(3, 1)
ii) Reflect P in x-axis to P'. Reflect P' in y-axis axis to P". Write coordinates of P'' and P".
iii) Reflect Q in y-axis to Q' and reflect Q' in the origin to Q". write coordinates of Q' and Q".
iv) write the geometrical name of PQQ"P'.
11) Given A= 2 0 and B= p q
0 5 o r
i) Compute A+B
ii) AB
iii) Given A+B= AB, find the value of p, q, r.
12) Solve the inequation
- 1/3 < x/2 -4/3≤ 1/6 , x belongs to R . Graph the solution set on a number line.
13). Simplify:
(cos 0°+ sin²45° - sin30°) ( sin90 - cos²45 + cos²60)
14) a cylindrical water tank, base radius 1.4 metre and height 2.1 metre is filled with with the help of a pipe of radius 7cm. calculate the time(in minutes) required to fill the tank, given that water flows at the rate of 2m/s in the pipe.
15) use graph paper for this question.
Monthly wages of some factory workers are given in the following table .
with 2cm= Rs 400 starting the origin at Rs4000 and to 2cm=10 workers on the y-axis, draw the Ogive. estimate the median from the graph.
Wages in Rs. No. Of workers.
4000-4400 8
4400-4800 12
4800-5200 20
5200-5600 25
5600-6000 17
6000-6400 10
16) A point P(3,-4) is reflected in X-axis..
I) write the coordinates of P'', the image of P..
ii) PP' is joined. To which coordinates axis PP' parallel to?
17) When expression ax²+bx-6 is divided by x-1, x+1, the remainder are -10, 4. Find a,b.
18) Given a/b= c/d, prove (2a-c)/(2a+c) = (2b-d)/(2b+d)
19) Calculate i) the Arithmetic mean ii) median iii) mode for
11,10,,11,13,13,12,15,17,14,12,13,14
20) 2/5≤ x - (1+ 2x/5)< 4/5, x belongs to R and show the number line.
21) A bus moving at its usual speed covers distance between town X and Y, which are 550km apart, in 1 hour less than it takes to cover the same distance, when it is raining and the bus has to reduce the speed by 5km/hr. Calculate the time taken to cover the distance between X and Y, when it is raining.
30/11/20
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22) If A= -2 1 and B= 2 4
0 3 -3 1
Find 2x2 matrix X, given that 2A-X= 3B.
23) Marks Students
0-8 5
8-16 3
16-24 10
24-32 16
32-40 4
40-48 2
Find mean
24) Find the value of k given that
3x³ + 4x² -6x +k is divisible by x+1
25)Use graph for this question. Take 1cm= 1 unit on both axes.
i) Plot point P(2,3) and Q(3, 1)
ii) Reflect P in x-axis to P'. Reflect P' in y-axis axis to P". Write coordinates of P'' and P".
iii) Reflect Q in y-axis to Q' and reflect Q' in the origin to Q". write coordinates of Q' and Q".
iv) write the geometrical name of PQQ"P'.
26) Given A= 2 0 and B= p q
0 5 0 r
i) Compute A+B
ii) AB
iii) Given A+B= AB, find the value of p, q, r.
27) Solve the inequation
- 1/3 < x/2 -4/3≤ 1/6 , x belongs to R . Graph the solution set on a number line.
28). Simplify:
(cos 0°+ sin²45° - sin30°) ( sin90 - cos²45 + cos²60)
29) a cylindrical water tank, base radius 1.4 metre and height 2.1 metre is filled with with the help of a pipe of radius 7cm. calculate the time(in minutes) required to fill the tank, given that water flows at the rate of 2m/s in the pipe.
30) use graph paper for this question.
Monthly wages of some factory workers are given in the following table .
with 2cm= Rs 400 starting the origin at Rs4000 and to 2cm=10 workers on the y-axis, draw the Ogive. estimate the median from the graph.
Wages in Rs. No. Of workers.
4000-4400 8
4400-4800 12
4800-5200 20
5200-5600 25
5600-6000 17
6000-6400 10
31) Using the Remainder Theorem, find the remainder when 7x²-3x+8 is divided by (x- 4).
32) If x²,4 and 9 are in Continued Proportion, find x.
33) Given A = 1 -2 B = 0
-3 4 1 find
a) matrix C such that A+C is zero metrix. b) find metrix D such that
A+D =A. c) Find AB
34) (i) If 7 is the mean of
5,3,0.5,4.5,b,8.5,9.5 find b.
(ii) if each observation is decreased in value by 1 unit,what would the new mean be ?
35) solve by formula
(x+3)/(2x+3) =(x+1)/(3x+2).
36) From the following table, find:
(i) The average wage of a worker, give your answer, correct to the nearest paise.
(ii) The modal class.
Wages in Rs. No of workers
Below 10 15
Below 20 35
Below 30 60
Below 40. 80
Below 50 96
Below 60. 127
Below 70 190
Below 80 200.
37) prove.√{(1+cos x)/(1-cos x)} =
Codec x + Cot x.
9/12/200
1) If a: b :: c:d then prove
(a²+ac+c²)/(a²-ac+c²)= (b²+bd+d²)/(b²- bd+d²)
2) Use the proportion to solve
(2x³+6x)/(12x²+4)= 682/364
3) If x= 2ab/(a+b) then prove that [(x+a)/(x-a). + (x+b)/(x-b)]
4) Solve for x:
{√(x+4) + √(x-10)}/{√(x+4)-√(x-10) = 5/2
5) If x= {√(b+3a)+√(b-3a)}/{√(b+3a) - √(b-5a)} then prove 3ax² - 2bx + 3a = 0
6) What least number must be added to each of the numbers 16, 7, 79 and 43, so that the resulting numbers are in proportion?
7) Using the remainder theorem, find the remainder when 7x² - 3x +8 is divided by (x -4).
8) If x², 4 and 9 are in continued proportion, find x.
9) If x belongs to Z, find the solution set for the ineqution
5 < 2x - 3 ≤ 14 and graph it on a number line.
10) Find the values of p and q if g(x)= x+2 is a factor of
f(x)= x³ - px + x +q and f(2)= 4.
11) Given A = 1 -2 B = 0
-3 4 1
i) Find a matrix C such that A + C is a zero matrix.
ii) Find the matrix D such that
A+D = A
iii) Find AB
12) If 7th and 13th terms of an A. P be 34 and 64. Then 18th term is
13) If the sum of pth terms of an A. P. is q and the sum of qth term is p, then sum of p+q terms will be
14) If the sum of nth terms of an A. P. be 3n²- n and its common difference is 6, then it's first term is.
15) Sum of all two digit numbers which when divided by 4 yield as reminder is -
16) In n A. M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3:1, the value of n is.
17) The first and last terms of an A. P are 1 and 11. If the sum of its terms is 36, then the number of terms will be-
18) If the sum of n terms of an A. P is 3n²+5n then which terms is 164 ?
19) If the sum of n terms of an A. P is 2n²+5n, then find nth term.
20) In the A. P whose common difference is non-zero, the sum of first 3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n terms to the next 2n terms is-
21) If four numbers in A. P are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are-
22) If n arithmetic means are inserted between 1 and 31 such that the ratio of the first mean and nth mean is 3:29, then the value of n is-
23) The first and last term of an A. P are a and l respectively. If S is the sum of all the terms of the A. P. and the common difference is given by
(l²-a²)/{k - (l+a)}, then find k
24) If the sum of first n even natural numbers equals to k times the sum of first n odd natural numbers, then k is
25) If the first, second and last term of A. P are a, b and 2a .Then it's sum is
26) If the first term of an A. P is 2 and common difference is 4, then the sum of its 49 terms is.
27) The number of terms of the A. P 3,7,11,15,...to be taken so that the sum is 406 is.
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