4/6/22
Compound Interest
1) ₹800 the lent at 5% compound interest per year for 2 years. Find the amount and the compound interest.
2) Calculate the compound interest due in 5/2 years in ₹6000 at 10% compound interest.
3) Calculate the amount due in 3 years on ₹5000, when the rate of compound interest successive years is 6% , 8% and 10% respectively.
4) A man borrows ₹6000 at 5% compound interest. If he repays ₹ 1200 at the end of each year, find the amount of loan outstanding at the beginning of the third year.
5) The population of a town increases at the rate of 7.5% per year. If the present population of that town is 16000; what will be after 2 years ?
6) A manufacturer estimates that the value of his machinery depreciated by 15% of its value at the beginning of the year. Find the original value+cost) of the machine if it depreciated by ₹5355 during the second year.
7) Calculate the amount and the compound interest on:
A) ₹ 3500 at 10% per annum in 2 years.
B) ₹6000 in 3 years at 5% per year.
8) Calculate the amount and the compound interest on:
A) ₹ 3600 in 3/2 years at per annum.
B) ₹ 12000 in 5/2 years at 4% per annum.
C) ₹10000 in 9/4 years at 6% per annum.
9) Calculate the amount and the compound interest on:
A) ₹4600 in 2 years, when the rate of interest for successive years is 10% and 12% respectively.
10) ₹ 16000 in 3 years, when the rate of interest for successive years is 5%, 7% and 10% respectively.
11) A man borrows ₹ 1200 at 5% per annum compounded interest. If he repays ₹250 at the end of each year, find the amount of loan outstanding at the beginning of the fourth year.
12) A man borrows ₹4000 at 6% per annum compound interest. If he ₹ 1500 at the end of the 1st year and ₹1600 at the end of the second year; find the amount of loan outstanding at the beginning of the third year.
13) A borrowed ₹2500 from B at 12% per annum compound interest. After 2 years, A gave ₹ 2936 and a watch to B to clear the account. Find the cost of the watch.
14) What sum will amount to ₹2782.50 in 2 years at compound interest., If the rates are 5% and 6% for the successive years.
15) Calculate the difference between the simple interest and the compound interest on ₹4000 in 2 years at 8% per annum compounded yearly.
16) A man borrows ₹ 4000 at 5% simple interest for 2 years. He immediately invests the entire amount for 2 years in a " re-investment scheme" under which gets interest at the rate of 5% compounded annually. What is his gain at the end of two years, when he repays his loan?
17) A person borrowed ₹ 12000 from a bank at 15/2% per annum and lent the whole amount to a shopkeeper at the same rate but at compound interest. What will be his gain in 2 years.
18) A man saves every year ₹3000 and invests at the end of the year at 10% compound interest. Calculate the total amount of his saving at the end of the third year.
19) Find the compound interest on ₹2400 for 5/2 years at 5% per annum, correct to the nearest rupee.
20) An investment, at compound interest, amounted ₹798.60 after 3 years and ₹878.46 after 4 years. What was the interest rate ?
21) Geeta deposits ₹20000 in a private finance company, at the rate of 16% compounded yearly; whereas Meera deposits an equal sum in PNB Housing Finance Limited. at the rate of 15% compounded half-yearly. If both deposit their money for 3/2 years only; calculate which deposit earns better interest by how much ?
22) The value of a machine depreciated by 10% per year during the first two years and 15% per year during the third year. Express the total depreciation of the machine, as percent during 3 years.
23) During 1994, the population of a village increased by 10% and during 1995, it further increased by 8%. If the increase in population during the year 1995 be 2200; calculate the population of the village:
A) in the beginning of 1994.
B) at the end of 1994.
24) find the sum, invested at 8% compounded annually, on which the interest for 3rd year exceeds the interest for first year by ₹ 199.68.
13/5/22
FACTORISATION
1) 12x² - 7x +1
2) 2x² + 7x +3.
3) 6x² + 5x -6.
4) 3x² - x - 4
5) x³ - 2x² - x + 2
6) x³ - 3x² - 9x -5
7) x³ + 13x² - 32x + 20.
8) 2x³ + x² - 2x - 1
9) x² - 5x + 6
10) x³ - 23x² + 142x + 120
11) 9x² + 6xy + y²
12) 4x² - 4x + 1
13) x² - y²/100
14) 8a³ + b³ + 12a²b + 6ab²
15) 8a³ - b³ - 12a²b + 6ab².
16) 27 - 125a³ - 135a + 225a²
17) 64a³ - 27b³ - 144a²b + 108ab².
18) 27p³ - 1/216 - 9p²/2 + p/4
19) 27y³ + 125z²
20) 64m³ - 34n³
21) x² + 1/x² - 2x - 2/x +2
22) a(a- 1)- b(b- 1)
23) 8x³ - 27y³ + 36x²y +54xy².
24) 8x³ + y³ + 27z³- 18xyz
25) (2x+ 3y)³ - (2x - 3y)³.
26) a³ - b³ + 1 + 3ab
27) (p -q)³ + (q - r)³ + (r - p)³
28) 9x³ - 9y³ + 6x + 1
29) x² - 5x/12 + 1/24
30) x⁶ - y⁶
31) 1 + x³
32) x¹² - y¹²
33) 54a³ - 250b³
34) 8x³ + 27y³ + 36x²y +54xy².
9/5/22
Expand: (3a - 2b +5c)²
25) If x + 1/x = 4, find the value of
A) x²+ 1/x²
B) x⁴ + 1/x⁴
26) If x - 1/2x = 3, find the value of
A) x² + 1/4x²
B) x⁴ + 1/16x⁴
27) If a² + 1/a²= 14, then find
A) a+ 1/a
B) a - 1/a
C) a² - 1/a²
28) If a² - 3a +1= 0 and a≠ 0, find the value of
A) a+ 1/a
B) a² + 1/a²
29) Complete to making it a perfect square
A) 25a²+ 9b²+ _____
B) 16a² - 8ab+ _____
30) If a²+ b²+ c²= 125 and ab+ bc+ ca= 50, find the value of a+ b+ c.
31) multiply:
A) (5x-4y)(5x+ 3y)
B) (2x² + 3/x²)(2x² - 3/x²)
C) (x-5)(2x -1)(2x+3)
32) simplify:
A) (x +1/x)²+ (x - 1/x)²
B) (3x - 1/3x)² - (3x + 1/3x)(3x - 1/3x)
C) (3x + 1)² - (3x +2)(3x - 1)
33) If (a - b)= 0.9 and ab= 0.36, find the value of
A) a+ b
B) a² - b²
34) If x - 2= 1/3x, find the value of
A) x² + 1/9x²
B) x⁴ + 1/81x⁴
35) If x² + 1/x²= 7, find the value of
A) x+ 1/x
B) x - 1/x
C) 2x² - 2/x²
36) If x² + 1/25x² = 47/5, find the value of x - 1/5x
7/5/22
Expansion
1) Product of: (y²+ 3/2)(y² - 3/2).
2) Product of with the help of formula: 95 x 96
3) Product of with the help of formula:104 x 96
4) Expand: (2x - y +z)²
5) Expand: (a/4 - b/2 +1)²
6) Expand: (2a - 3b)³
7) Expand: (3x/2 + 1)³
8) Expand: (x - 2y/3)³
9) Evaluate by formula: 998³
10) Evaluate by formula: 102³
11) If x + y + z= 0 show that x³+ y³+ z³ = 3xyz
12) without actually calculating the cubes, find the value of each:
a) (-12)³+ (7)³+ (5)³
b) (28)³+ (-15)³+ (-13)³
13) Expand: (3a + 4b+ 5c)²
14) without multiplying, find the product of:
a) 105 x 106
b) 98 x 99
15) Expand: (5p - 3q)²
16) If x - 1/x = 1, then x² + 1/x²
17) If x + 1/x = 1, then x² + 1/x²
18) If a+ b + 2= 0, then find a³+ b³+ 8
19) If a= 9 - 4 √5, find the value of a - 1/a
20) If x= 3+ 2 √2, find the value of x² + 1/x²
21) Find the value of x³ + y³ + 15xy - 125 when x + y= 5.
22) If a+ b + c= 6 find the value of (2- a)³ + (2- b)³ + (2- c)³ - 3(2- a)(2- b)(2- c).
23) If x + y= -1, then find x³+ y³- 3xy
22/4/22
1) The compound interest on a certain sum of money at 5% per annum for 2 years is ₹246. calculate the simple interest on the same sum for 3 years at 6% per annum. 432
2) what sum of money amount to ₹3630 in two years at 10% p.a compound interest. 3000
3) If a² + 1/a² = 14, find the values of:
A) a + 1/a. ±4
B) a - 1/a . ±2√3
C) a² - 1/a². ±8√3
4) If x - 1/2x = 3, find the value of
a) x² + 1/4x². 10
b) x⁴ + 1/16x⁴. 199/2
3) on a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is ₹180. Find the sum left out, if the rate of interest in both the cases is 10% p.a. 72000
4) A man borrows ₹ 5000 at 12% compound interest p.a, interest payable every six months. He pays back ₹1800 at the end of every six months. calculate the third payment he had to make at the end of eight months in order to clear the entire loan. 2024.60
5) Calculate the compound interest for the second year on ₹800 invested for 3 years at 10% p.a. 880
6) A man invests ₹5000 for 3 years at a certain rate of interest compounded annually. At the end of one year amounts ₹5600, calculate,
a) the rate of interest per annum.
b) the interest accrued in the second year.
c) the amount at the end of the third year. 12%, 672, 7024.64
7) A man invests ₹46875 4% per annum compound interest for 3 years. Calculate
a)the interest for the first year.
b) The amount standing to his credit at the end of second year.
c) the interest for the third year. 1875, 50700, 2028
8) A person invests ₹5600 at 14% p.a. compound interest for two years. calculate:
a) the interest for the first year.
b) the amount at the end of 1st year.
c) The interest for the second year, correct to nearest rupees. 784, 6384, 894
9) the compound interest, calculated yearly, on a certain sum of money for the second year is 880 and for the third year ₹968. calculate the rate of interest and the sum of money. 10%, 8000
10) A certain sum of money amounts ₹5292 in two years and to ₹5556.60 in three years, interest being compounded annually. find the rate%. 5%
11) At what rate percent, per annum compound interest, would 80000 amounts to ₹ 88200 in 2 years; interest being compounded half yearly ? 5%
12) A sum of money is lent out at compound interest for 2 years at 20% p.a, C. I being reckoned yearly. If the same sum of money was lent out at compound interest at the same rate per annum, C. I being reckoned half yearly. It would have fetched ₹482 more by the way of interest. calculate the sum of money lent out. 200000
1/8/21
*** Find the distance
1)a) (3,6),(0,2). 5 unit
b) (-4,-6) and (6,4). 10√2
c) (11,-9), and (-9,12). 29
d) (-a, -b) and (a,b). 2√(a²+b²)
e) (3)5,2) and (-1/5, 7/5). 1
f) (√3+1, 1) and (0,√3). 2√2
2) Find the co-ordinates of points on x-axis which are at a distance of 5 units from the point (6,-3). (2,0),(10,0)
3) Show that the points A(8,3), B(0,9) and C(14,11) are the vertices of an isosceles right angled triangle.
4) Show that A(3,1), B(0,-2), C(1,1) and D(4,4) from a parallelogram ABCD.
5) A point A is at a distance of √10 from the point (4,3). Find the co-ordinates of point A, if it's ordinate is twice of its abscissa. (3,6),(1,2)
6) The distance between the points (3,1) and (0,x) is 5. Find x. 5,-3
7) A point P(2,-1) is equidistant from the points (a,7) and (-3,a). Find a. 7
8) Find the co-ordinates of points on x-axis which are at a distance of 17 units from the point (11,-8). (26,0).
9) Find the co-ordinates of points on x-axis, which are at a distance of 10 units from the point (-8,4). (0,10) and (0,-2).
10)
28/7/21
** Solve:
1) (x+3)(x-3)= 40. -7, 7
2) 8x² + 15x= 26x. 5/2, 3/4
3) x(2x+5)= 25. -5, 5/2
4) 3x²-14x+8=0,
a) x belongs to N. 4
b) x belongs to Q. 2/3
5) x² +(3-2a)x -64=0. -3, 2a
6) 3x3x² - 2√6 x +2= 0. √(2/3)
7) (7x+1)/(7x+5) = (3x+1)/(5x+1). 1, -2/7
8) (x-1)/(x-2) + (x-3)/(x-4)= 10/3. 5, 5/2
9) 5x²= 3x. 0, 3/4
10) (x²- 5x)/2= 0. 0,5
11) (x-3)(2x+5)= 0. 3, -5/2
12) x(2x+1)= 6. -2, 3/2
13) x² -3x-10= 0. -2,5
14) x(2x+5)= 3. -3, 1/2.
15) 3x² - 5x -12= 0. 3, -4/3
16) (x-3)(2x+5)= 0. 3,-5/2
16) x² - 7x+10= 0. 2,5
17) -2x² +3x+ 35 = 0. 5, 7/2
18) 6x² +x- 35= 0. -5/2,7/3
19) 9x² + 9x - 4= 0. -4/3,1/3
20) 15x² - 2x - 8 = 0. 4/5,-2/3
21) 3x² - x - 4= 0. -1,4/3
22) 16x² = 25. 5/4,-5/4
23) 3x² - 10x+8 = 0. 2, 4/3
24) x(6x-11)= 35. 7/2,-5/3
25) 6x(3x-7)= 7(7- 3x). 7/3,-7/6
26) a²x²+ 2ax+1= 0, a≠0. -1aa, -1/a
27) x²+6x +5=0. -5,1
28) 8x²-22x - 21=0. 7/2, -3/4
29) x² - 9=0. -3,3
30) x²- 8x +16=0. 4,4
31) x/(x+1) + (x+1)/x= 34/15, x≠ 0, x≠ -1. 3/2, -5/2
32) (x+3)/(x -2) - (1- x)/x= 17/4, 4, -2/9
33) 4/x - 3 = 5/(2x+3) -2, 1
34) 2x/(x -3)+ 1/(2x+3)+ (3x+9)/{(x-3)(2x+3) =0. -1
35) (x-4)(x+2)=0. 4,-2
36) (2x +3)(3x -7)=0. -3/2, 7/3
37) 4x²+ 5x =0. 0, -5/4
38) 9x²- 3x - 3=0. 2/3, -1/3
39) 6x²- x - 2 =0. 2/3, -1/2
40) 6x² + 11x + 3=0. -3/2,-1/3
41) 5x²- 3x - 2=0. -2/5, 1
42) 48x² -13x -1=0. -1/16, 1/3
43) 3x²- 3x -2 =0. -2/5, 1
44) 3x²= -11x- 10. -5/3, -2
45) 25x(x+1)= -4. -4/5, -1/5
46) 10x - 1/x= 3. 1/2,-1/5
47) 2/x² - 5/x +2= 0. 2,1/2
48) a²x² - 3abx + 2b²= 0. 2b/a,b/a
49) 2x/(x-4)+ (2x-5)/(x-3)= 25/3. 6, 40/13.
50) (x+3)/(x-2) -(1-x)x=17/4. 4, -2/9
13/7/21
1) The compound interest on a certain sum of money at 5% p.a for 2 years is 246. Find the simple interest on the same sum for 3years at 6% p.a. 432
2) What sum of money will amount to ₹ 3630 in two years at 10% p.a. compound interest? 5160
3) Show that the points (3,3),(9,0) and (12,21) are the vertices of a right angled triangle.
4) Find the mean of first five prime numbers. 5.6
5) Expand (2x + 1/3x)².
9/7/21
1) A man invests ₹ 5000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to ₹5600. Find
A) the rate of interest. 12%
B) interest in the 2nd year. 672
C) The mount at the end of 3rd year. 7024.64
2) using formula find the value of 124 x 116. 14384
3) expand: (√2 m + √3 n)².
4) Show that (_1,1),(2,3) and (8,11) are collinear.
5) Find the mean of all the factors of 20. 7
8/7/21
1) Find the mean of 144, 152, 151, 158, 155. 152
2) Find the AM of first 6 natural numbers. 3.5
3) Find the AM of first 10 odd natural numbers. 10
4) Find the sum of the deviation of the variable values 3,4,6,8,14 from their mean. 0
5) The mean of 40 observations was 160. It was detected on reaching that the value of 165 was wrongly copied as 125 for computation of mean. Find the correct mean. 161
6) The mean of 100 items was found to be 30. If at the time of calculation two items were wrongly copied as 32, 12 instead of 23, 11. Find the correct mean. 29.9
7/7/21
1) Find the difference the simple interest and compound interest on ₹16000 at 8% p.a at the end of 1 year, if the interest is compounded quarterly. 38.92
2) Rationalise: (3√2+2√3)/(3√2-2√3). 5+ 2√6.
4) Prove that the points P(-3,-4), Q(2,6) and R(-6,10) are the vertices of a right angled triangle.
5) 4,8,10,x, 15,15,19,20 are in ascending order. Given that the median is 13, find x. 11
6/7/21
1) If ₹20000, amounts to₹21200 after a year, at CI. Calculated yrly. Find
A) the rate of interest. 6%
B) the amount to which it would amount to at the end of the second year. 22472
2) If x+1/x= 3, find x³+1/x³= 3. 18
3) find the product of (6-x)(x+5).
4) Name the triangle formed by the coordinates (-3,4),(2,-5),(0,3).
5) The mean weight of 60 students of a class is 52.75kg. if the mean weight of 25 of them is 51kg. Find the mean weight of the remaining students. 54kg
6) The simple interest in 3years and the compound interest in 2 years on a certain sum at the same rate are ₹1200 and ₹832. Find
A) the rate of interest p.a. 8%
B) the principal. 5000
C) the difference between the CI and SI for 3 years. 98.56
5/7/21
1) On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is ₹180. Find the sum lent out, if the rate of interest in both the cases is 10%. 72000
2) The marks of 20 students in a test were as follows: 5,6,8,9,10, 11, 11,12,13,13,14,14,15,15,15, 16, 16, 18,19,20. Find
A) mean. 20
B) median 13.5
c) mode. 15
3) The coordinates of A(0,0), B(3,-4), C(6,0), D(3,4). Respectively. With the help of distance formula name the type of quadrilateral.
4) What sum of money will amount to₹3630 in two years at 10% p.a compound interest? 123005
1) The compound interest, calculated yrly, on a certain sum of money for the second year is ₹ 880 and for the third year it is ₹968. Calculate the rate of interest and the sum of money. 10%, 8000
2) A sum of₹9600 is invested for 3years at 10% p.a at compound interest.
A) find the sum due at the end of first year. 10560
B) sum at the end of 2nd yr. 11616
C) C. I in 2 years. 2016
D) find the difference between the answer in B and A and find the interest on this sum(obtained as difference to B & A) for 1 yr. 1056
E) C. I for 3rd year. 1161.60
3) A man invests₹46875 at 4% p.a compound interest for 3yrs. Calculate
A) Interest for the 1st year. 1875
B) the amount standing to his credit at the end of the 2nd yr. 50700
C) the interest for the 3rd yr. 2028
4) A man invests ₹5000, for 3 years at a certain rate of interest, compounded annually. At the end of 1year it amounts to ₹5000. Find
A) the rate of interest. 12%
B) the interest in 2nd year. 672
C) amount at the end of 3rd yr. 7024.64
5) A man borrows₹5000 at 12% compound interest p.a-- interest payable every six months. He pays back ₹1800 at the end of every six months. Calculate the third payment he has to make at the end of 18 months in order to clear the entire loan. 2024.60
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