Revision (Similarity)
1) A vertical stick 12m long casts a shadow 8m long on the ground. At the time a tower casts the shadow 40m long on the ground. Determine the height of the tower. 60m
2) The perimeter of two similar triangles are 30 and 20cm respectively. If one side of the first triangle is 12cm, determine the corresponding side of the second triangle. 8cm
3) The perimeter of two similar triangles ABC and PQR are respectively 36cm and 24cm. If PQ= 10cm, find AB. 15cm.
4) Two triangles BAC and BDC, right angled at A and D respectively, are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P, prove AP x PC= DP x PB.
5) P and Q are points on sides AB and AC respectively of ∆ ABC. If AP= 3cm, PB=6 cm, AQ= 5cm and QC = 10cm, show BC = 3PQ
6) Two poles of height a metres and b metres are p metres apart. Prove that the height of the point of interaction of the lines joining the top of each pole to the foot of the opposite pole is given by ab/(a+b) metres.
7) In trapezium ABCD AB//DC and DC= 2AB. EF drawn parallel to AB cuts AD in F and BC in E such that BE/EC = 3/4, Diagonal DB intersects EF at G. Prove that 7 FE = 10 AB.
8) A vertical stick 10cm long casts a shadow 8cm long. At the same time a tower casts a shadow 30m long. Determine the height of the tower. 37.5m
9) The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of first triangles is 9cm, what is the corresponding side of the other triangle ? 5.4cm
10) in ∆ ABC and DEF, it is being given AB= 5, BC= 4cm and CA= 4.2cm, DE= 10cm, EF= 8cm and FD= 8.4cm. If AL perpendicular to BC and DM perpendicular to EF, find AL : DM. 1:2
11) D and E are the points on the side AB and AC respectively of ∆ ABC such that AD= 8cm, DB= 12cm, AE= 6cm and CE= 9cm. prove that BC=5/2 DE.
12) DE is the midpoint of the side BC of ∆ABC. AD is bisected at the point E and BE produced cuts AC at the point X. prove that BE: EX= 3:1.
Revision Test (November)
SECTION A (Marks 40)
(Attempt all questions)
1)a) Ravi bought a radio for ₹840(GST at 7%) and a watch for ₹825(GST at 10%). Calculate the total amount. Ravi had to pay to settle the bill.
b) Find the eighteenth term of 9,5,1,......
2)a)
3a) solve the inequation: -2 ≤7- 3x < 1; x belongs to R. Represent the solution set on a number line.
b) ABC is a triangle XY|| to BC which is same side of BC, area of∆ AXY= 49cm², area of trapezium BCYX= 24cm², BC= 10cm, find XY.
4a) A girl of height 90cm is walking away from the base of a lamp-post at a speed of 1.2m/s. If the lamp is 3.6m above the ground, find the length of her shadow after 4 seconds.
b) Given A= 2 0
1 3 evaluate A²+2A.
SECTION B (Marks: 40)
6a) Given x belongs to I, solve the inequation 3≥ (x-4)/2 +x/3 ≥2. Graph the solution set a number line.
b) How many terms of the geometric series 1+4+16+64+ ... will make the sum 5461 ?
7)a) A train travels a distance of 300 km constant speed. If the speed of the train is increased by 5 km an hour, the journey would take 2 hours less. find the speed of the train.
b) Ravi opened a Recurring Deposit Account in a bank and deposited ₹500 per month for 3 years. The bank paid him ₹20220 on maturity. Find the rate of interest paid by the bank.
8a) In an AP, the first term is 2 and the sum of first five terms is one-fourth of the next five terms. Show that its 20th term is -112.
b) i)If A= -1 3 & B= a & C= 10
4 k 5 20
And expression AB= C, find the values of a and k.
ii) If P= -3 1 & Q= -3 2
2 0 1 4 , calculate PQ= Q²
9a)Solve for x: 3x²- 2x- 1=0.
------------------------------------------------------
Revision Test (metrices)
1) If A= 3 2 & B= 5/3 -2/3
6 5 -2 1 then AB= ?
A) BA B) O C) I D) none
2) If A= 4 1
-1 2 then A² - 6A= ?
A) I B) 9 C) -9 D) none
3) If I= 1 0
0 1 then I³ is
A) I B) O C) 2 D) none
4) If A= 2 B= -3 C= 1
3 1 2 and the relation X+A - B= 0. Then matrix X is
A) O B) 2I C) -3I D) none
5) If each element of a matrix is zero, it is called
A) null matrix
B) Unit matrix
C) Identity matrix
D) none
6) If A= 1 2 x & B= 1 -2 y
0 1 0 0 1 0
0 0 1 0 0 1 and AB= I, then x+y is
A) 0 B) -1 C) 2 D) none
7) If A= 1 -1 & B= a 1
2 -1 b -1 and (A+ B)²= A² + B², values of a, b are
A) 4,1 B) 1,4 C) 0,4 D) 2,4
8) If A= a b
c - a is such that A² = I, then
A) 1+ a²+ bc= 0
B) 1- a²+ bc= 0
C) 1- a²- bc= 0
D) 1+ a²- bc= 0
9) 3x+7 5 = 0 y-2
y+1 2- 3x 8 4 then find the values of x, y
A) -1/3, 7 B) 7, -2/3 C) -1/3, -2/5 D) not possible to find.
10) If A= 0 2 and kA= 0 3a
3 -4 2b 24 then the values of k, a, b are
A)-6,-12,-18 B) -6,4,9 C) -6,-4,-9 D)6,12,18
Revision (Metrices)
1) a+2 b -3 = 2a -3 4b+1
-1 3+c -1. 5c-7 then find the value of a, b, c, d
2) If A= 2 x & B= y 0 & C= 8 -6
1 5 3 -1 6 14 and the 3A + B= C then find x, y
3) If A= 1 4 & B= -4 -1
2 2 -3 -2
A) find the matrix 2A+ B
B) find the matrix C such that: C+ B= O
4) If M- 2I= -3 0
12 3 and
5M + 3I= 8 -20
0 -12 Find the matrix M
5) If A= 1 3 & B= 1 2 & C= 4 3
2 4 4 3 1 2 then find
A) (AB)C
B) A(BC)
6) IF A= -2 1 & B= m & C= 5
0 -3 1 n and AB= C then find the value of m, n.
7) If A= -1 1
a b and A² = I, find a, b
8) If A= 0 1 & B= 0 1
1 -2 1 -1 then
Is A² - B²= (A+B)(A-B)
9) If A= 1 1 & B= 1 2
0 2
And the relation MA = B where M is a matrix
A) state the order of matrix M
B) Find the matrix M.
10) If A= p q & B= p
q
The relation AB= 25 then the value of p, q
11) If A= 1 4 & B= 2 1
1 0 3 -1 verify if IA² + IB² = A²I + B²I.
___________________________________
Write down the first five terms of the sequence, whose nth term is (-1)ⁿ⁻¹. 5ⁿ⁺¹. 25,-125,625,-3125, 15625
2) If the 3rd and 6th terms of an AP are 7 and 13 respectively, find the first term and the common difference. 3 and 2
3) find the sum of all natural numbers between 100 and 1000 which are multiple of 5. 98450
4) how many terms of the AP -6, -11/2, -5,.... are needed to give the sum -25 ? 5 or 20.
5) Determine the sum of the first 35 terms of an AP if a₂ = 2 and a₇ = 22. 2310
6) If the first term of an AP is 2 and the sum of first five terms is equal to one fourth of the sum of the next five terms, show that the 20th term is --112
7) Insert 3 arithmetic mean between 2 and 10. 4,6,8
8) The sum of three decreasing numbers in AP is 27. If -1, -1, 3 are added to them respectively, the resulting series is in GP. The numbers are
A) 5,8,13 B)15,9,3 C)13,9,5 D) 17,9,1
9) The sum of all odd numbers between 1 and 100 which are divisible by 3, is..
A) 83667 B) 90000 C) 83660 D) n
10) If 7th and 13th terms of an AP be 34 and 64 respectively, then its 18th term is.
A) 87 B) 88 C) 89 D) 90
11) If the sum of p terms of an AP is q and the sum of q terms is q, then the sum of the p + q terms will be..
A) 0 B) p-q C) p+q D) -(p +q)
12) If the sum of n terms of AP be n² - n and its common difference is 6, then its first term is..
A) 2 B) 3 C) 1 D) 4
13) Sum of all two digit numbers which when divided by 4 yield Unity as reminder is..
A) 1200 B) 1210. C)1250. D) n
14) In n AM's introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3:1, then the value of n is..
A) 6 B) 8 C) 4 D) n
15) The 1st and last terms of an AP are 1 and 11. If the sum of its terms is 36, then the number of terms will be.
A) 5 B) 6 C) 7 D) 8
16) Find the sum of all odd integers from 1 to 1001. 251001
17) If the ratio between the sums of n terms of two AP is (7n+1):(4n+27) find the ratio of their 11th term. 148: 111
18) If the sum of m terms of an AP be n and the sum of n terms be m, show that the sum of m+n terms is -(m+n).
19) If the sum of n terms of an AP is (pn+ qn²), where p and q are constants, find the common difference. 2q
20) In an AP, the first term is 2 and the sum of first five terms is one-fourth of the sum of next terms. Show that the 20th term is - 112 and the sum of first 20 term is -1100.
21) If the sum of n terms of an AP is given by (3n²+ 4n), find its rth term. 6r +1
22) The digits of a three-digit numbers are in AP and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. 852
23) Between 1 and 31, m numbers have been inserted in such a way that the ratio of 7th and (m-1)th numbers is 5:9. Find the value of m. 14
24) In the arithmetic progression whose common difference is non zero, the sum of the first 3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n terms the next to 2n terms is
A) 1/5. B) 2/3 C) 3/4 D) none
25) If four numbers in AP are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are:
A) 5,10,15,20 B) 4,10,16,22
C) 3,7,11,15 D) none
26) The first and the last term of an AP are a and l respectively. if S is the sum of all the terms of the AP. and the common difference is given by (l²-a²)/{k -(l+a)}, then k is
A) S B) 2S C) 3S D) none
27) If the sum of the first n even natural number is equal to K times the sum of the first n odd natural numbers, then k is..
A) 1/n B) (n-1)/n C)(n+1)/2n D)(n+1)/n
28) If the first, second and last term of an AP are a,b and 2a respectively, then its sum is
A) ab/{2(b-a)} B) ab/(b-a)
C) 3ab/{2(b-a)} D) none
29) If x is the sum of an arithmetic progression of n odd number of terms and y the sum of the terms of the series in odd places, then x/y is
A) 2n/(n+1) B) n/(n+1)
C) (n+1)/2n D) (n+1)/n
30) If the first term of an AP is 2 and common difference is 4, then the sum of its 40 terms is
A) 3200 B) 1600 C) 200 D) 2800
31) The number of terms of the AP 3, 7, 11, 15, ... to be so that the sum is 406 is...
A) 5 B) 10 C) 12 D) 14 E) 20
32) If a(1/b+ 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP , then
A) a, b, c are in AP
B) 1/a, 1/b, 1/c are in AP
C) a, b, c are in HP
D) 1/a, 1/b, 1/c are in GP.
33) If the sum of the three numbers in AP be 18 then what is the middle term ? 6
34) The fifth term and the 11th term of an AP are 41 and 20 respectively. Find the first term. What will be the sum of first 11 terms of the AP. ? 825/2
35) The n-th term of an AP is p. Show that sum of first (2n-1) terms is (2n-1)p.
36) The middle term, of an AP having 11th term is 12. Find the sum of the 11 terms of that progression. 132
37) There are n arithmetic means between 4 and 31. If the second mean : last mean=5: 14 then find the value of n. 8
38) If the sum of the first P terms of an AP be equal to the sum of the first Q terms then show that the sum of the first P +Q terms is zero.
39) Find the sum upto n terms of the series 1²- 2²+ 3²- 4²+ 5²- 6²+.. .. -n/2 (n+1) (n= 2r)
40) if the sum of p terms of an AP is to the sum of q terms as p²:q², show that (pth term)/(qth term)= (2p-1)/(2q-1).
40) The first term of an AP is a, the second term is b and the last term is c. Show that the sum is {(a+c)(b+c-2a)}/{2(b-a)}.
41) The sides of a right angled triangle are in AP. if the smallest side is 5cm then find the largest side. 25/3
42) find the sum of natural numbers from 1 to 200 excluding those divisible by 5. 16000
43) Show that the sum of all odd numbers between 2 and 1000 which are divisible by 3 is 83667 and of those not divisible by 3 is 166332.
44) Find the 14 A. M which can be inserted between 5 and 8 and show that their sum is 14 times the Arithmetic mean between 5 and 8.
45) Divide 25/2 into five parts in AP, such that the first and the last parts are in the ratio 2: 3. 2,9/4,5/2, 11/3, 3.
46) For what value of m, the sequence 2(4m+7), 6m + 1/2, 12m-7 forms an AP. -3/4
47) Find the 20th term of the AP 80, 75, 70,... Calculate the number of terms required to make the sum equal to zero. 33
48) Prove that if unity is added to the sum of any number of terms of the AP 3, 5,7,9...the resulting sum is a perfect square.
49) The sum of n terms of the series 25, 22, 19, 16,.. is 116. Find the number of terms and the last term. The given series is AP. 18405
50) Find the sum of all natural numbers from 100 to 300:
a) which is divisible by 4. 10200
b) excluding those which are divisible by 4. 30000
c) which are exactly divisible by 5.
d) which are exactly divisible by 4 and 5. 8200, 2200
e) which are exactly divisible by 4 or 5. 16200
1/8/21
1) Amit deposited ₹150 per month in a bank for 8 months under the recurring deposit scheme. What will be the maturity value of his deposits, if the rate of interest is 8% p.a and interest is calculated at the end of every month ? ₹1236
2) Lakshmi took a Cumulative time deposit account of ₹240 per month at 10% p.a. she received ₹3840 on maturity. Find the period for this account. 15 months
3) Manoj opened a recurring deposit account in a bank and deposited ₹500 per month for 3 years the band paid him ₹20220 on maturity. Find the rate of interest paid by the bank. 8%
4) Rajeev opens a Recurring deposit account with the bank of Rajasthan and deposited ₹600 per month for 20 months. calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum. ₹13050
5) Miss Anshu Pandey deposited ₹350 per month for 20 months under recurring deposit scheme. Find the total amount payable by the bank on maturity of the account if the rate of interest is 11 % per annum. ₹7673.75
6) Mrs. Matthew opened a recurring deposit account in a bank with ₹500 per month for 5/2 years. find the amount she will get on maturity if the interest is paid on monthly balance at 12.5% per annum. 17421.87
7) calculate the amount received on maturity of a recurring deposit of ₹150 per month for 1 year 6 months, if the rate of interest is 11% per annum. 2935.13
8) Amar deposits ₹1600 per month in a Recurring deposit for 3 years at the rate of 9% p.a. simple interest, find the amount Amar will get at the time of maturity. 65592
9) A Recurring deposit account of ₹1200 per month has a maturity value of ₹12440. If the rate of interest is 8% interest and the intrest is calculated at the end of every month, find the time (in months) of the Recurring deposit account. 10 months
10) Sujata deposited a certain sum of money, every month, for 5/2 years in cumulative time deposit account. At the time of maturity She collected ₹4965. if the rate of interest was 8% p.a. find the monthly deposit. 150
11) Sumit paid ₹300 per month in cumulative time deposit account for two years. he received ₹7875 as the maturity amount. find the rate of interest. 9%
12) Meena has cumulative time deposit account of ₹340 per month at 6% per annum. if she gets ₹7157 at the time of a maturity, find the total time for which the account was held. 20 months
13) on depositing ₹200, every month in a cumulative time deposit account, paying 9% p.a. interest, a person collected ₹2517 at maturity. find the period. 12 months.
14) Mr. Desai opens a recurring deposit of ₹2000 per month for 30 months paying simple interest of 12%p a. Calculate the amount he received at the time of maturity. 69300
15) Calculate the amount receivable on maturity of a recurring deposit of ₹800 every month for 5 years at 11 % per annum.
16)
27/7/21
1) Roots of a quadratic equation are 1/2 and -14. Find the equation. 2x²+ 27x -14= 0
Solve::
2) √(3x²+x+5)= x-3. -4, 1/2
3) 8(t²+1/t²)- 42(t- 1/t)+29=0. 15/4, 3/2
4) 5ˣ⁺¹ + 5²⁻ˣ = 126.
5) 3²ˣ - 10.3ˣ+ 9=0. 2,0
6) 2²ˣ⁻¹ - 9. 2ˣ⁻²+1 = 0. 2, -1
7) 6x² - x -14= 0.
8) x² -8x -1280 = 0
9) 1/(2y-9) = 1/(y-3) + 4/5.
10) x⁵ +242= 243/x⁵. -3,1
**Correct up to 2 decimal places.
11) x² -6x -16 = 0. -1.90, 7.90
12) 2x² +11x -10 = 0.
13) The bill of a party for a certain number of people is ₹19200. If there were 10 more persons, the bill each person had to pay would have reduced by ₹160. Find the number of people at the party. 30
14) A two digit number is such that the product of digits is 12. When 9 is added to the number the digits are interchanged. Find the number.
15) The sides of a right angled triangle are x cm, 4(x+1)cm, (4x+5) cm. Find x.
16) A man purchased some sheep for ₹4500. Three sheep were lost and the rest he sold for ₹30 more per sheep than he had paid. If his gain on the whole transaction is 8%, how many sheep did he buy?
17) the sum of the ages of a man and his son is 46 years and the product of their ages is 168 years. find the age of the Son.
18) The total surfaces area of a cylinder is 75.24cm² and its height is 3.6 cm. If its radius is x cm, find x
***Find the nature of the roots.
19) 4x² - 4x+1=0
20) If m,n are roots of x²- px+q= 0, find
a) m²+n². p²-2q
b) m³+ n². p³ -3pq
c) m-n. -√(p²-4q).
d) m⁴+ n⁴. p⁴- 4p²q+2q²
*** Solve:
21) 3x² - x- 7 = 0. 1.70, -1.37
22) 1/(x+1) + 2/(x+2)= 4/(x+4). 2± 2√3
23) 2x² + √7x -7= 0. √7/2, -√7
24) √3 x²+ 10x - 8√3= 0. 2√3/3, -4√3
25) (x+3)/(2x+3)= (x+1)/(3x+2). -3± √6
26) (x-2)/(x+2)+ (x+3)/(x -2)= 4. ±2√3
27) /(x+1)+ 2/(x+2)= 4/(x+4). 2± 2√3
28) a(x²+1)= (a²+1)x, a≠ 0. a, 1/a
29) 4x² - 4ax +(a² - b²)= 0. (a±b)/2
30) x/(x+1)- 4/(x+2)=0 3.24,-1.24
31) 5/(x -1)+ 2x/(x- 2)=0 1.61,-3.11
32) 2x - 1/x= 7. 3.64, -0.138
33) 2/(x -1)+ 3/(x+2)= 4/(x+2). 0.23, -8.77
34) (x+3)/(x-3) - (1-x)/x = 17/4. 4, -2/9
1) (x+3)/(x-3) - (1-x)/x = 17/4. 4, -2/9
35) a/(ax-1) + b/(bx-1)= a+ b, a+b≠0, ab≠0. (a+b)/ab, 2/(a+b)
Form the Quadratic equations whose roots are:
36) a) -2, 1. x²+x-2= 0
b) -3, -4. x²+7x +12=0
c) a,-b. x²-(a-b)x -ab=0
d) -2/3, 4/5. 15x²-2x -8=0
e) -3, 2/5. 5x²+13x -6=0
f) 2/5, -1/2. 10x²+x - 2=0
37) An Aeroplane travelled a distance of 480 km at an average speed of x kmhr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for
a) the onward journey
b) the return journey
If the return journey took 30 minutes less than the onward journey, write an equation in x and find the value of x. 160
38) Car A travels x km for every litres of petrol, while car B travels (x+5) km for every litres of petrol.
a) write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
b) If car A uses 4 litres of petrol more than car B in covering the 400 km, write down an equation in terms of x and solve it to determine the number of litres of petrol used by car B for the journey. 16 litres
39) In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. when the number of rows was doubled and the number of seats in each row reduced by 10, The total number of seats increased by 300. Find
a) the number of rows in the original arrangement.
b) the number of seats in the auditorium after rearrangement. 30, 1200
40) A Hotel bill for a number of people for overnight stay is ₹4800. If there were four people more, the bill each person had to pay would have reduced by ₹200. find the number of people staying overnight. 8
41) A trader boy x articles for a total cost of ₹600.
a) write down the cost of one article in terms of x.
if the cost per article were ₹5 more, the number of articles that can be bought for ₹600 would be 4 less.
b) Write down the equation in x for the above situation and solve it for x. 24
42) The distance by road between two towns A and B is 216 km, and by rail it is 200 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. calculate:
a) the time taken by the car to reach town B from A, in terms of x
b) If the train takes two hours than the car, to reach town B, obtain an equation in terms of x, and solve it.
c) Hence, find the speed of the train. 52 km/hr
43) A train covers a distance 600 km/hr. Had the speed been (x+20) km/hr, the time taken to cover the distance would have been reduced by 5 hours. write down an equation in terms of x and solve it to evaluate x. 40
44) x/(x+1) + (x+1)/x= 34/15, x≠ 0, x≠ -1. 3/2, -5/2
45) (x+3)/(x -2) - (1- x)/x= 17/4, 4, -2/9
46) 4/x - 3 = 5/(2x+3) -2, 1
47) 2x/(x -3)+ 1/(2x+3)+ (3x+9)/{(x-3)(2x+3) =0. -1
TEST PAPER
-----------------
Section - A
___________
(Answer all the questions from this section). (40 marks)
1) (1x10)
a) Amarnath purchased a cycle for ₹1664 including GST. If the list price of the cycle is ₹1600, then the rate of sales tax is..
A) 4% B) 5%. C) 6%. D) 7%
c) the Quadratic equations whose roots are -3, -4
A) x²+7x+12=0 B) x²-7x+12=0
C) x²+7x-12=0 D) x²-7x-12=0
d)
f) Sum of the roots of the Equation x² - 5x +6
A) 5. B) -5 C) 6 D) -6
g) Number of roots in Quadratic equations are
A) 1 B) 2 C) 3 D) 4
h) a is less than b, written as a< b, if and only if b - a is
A) positive B) negative C) both positive D) both negative.
i) A dealer from West Bengal sells goods worth ₹50000 to a dealer in Bihar at 18% GST. Then seller collect ₹9000 as IGST and the entire amount will go to the..
A) Central Government only
B) State Government only
C) both A and B
D) none
3) Solve: 3x²- x-7= 0. Correct upto 2 decimals. (6)
4) A shopkeeper buys an article whose printed price is ₹4000 from a wholesaler at a discount of 20% and sells it to a consumer at the printed price. If the sales are intrastate and the rate of GST is 12%, find
A) the price of the article inclusive of GST at which the shopkeeper bought it
B) the amount of Tax (under GST) paid by the shopkeeper to the State government.
C) the amount of Tax(under GST) received by the Central Government.
D) the amount which the consumer pays for the article. (6)
5) Given A={x: 5x-4≥6, x∈ R} and B={x:5-x > 1, x ∈ R}
Represent A and B on the number line.
Find a) A∩ B b) A' ∩ B. (6)
SECTION -- B
Attempt any 4 (40 marks)
b)
7) a) using Quadratic formula, solve: 5 + 11x - 5x². (5)
8) a) Kriss goes to a shop to buy a leather coat costing ₹654. The rate of GST is 9%. He tells the shopkeeper to reduce the price to such an extent that he has to pay ₹654, inclusive of GST. Find the reduction needed in the price of the coat. (5)
b) a(x²+1)= (a²+1)x, a≠0. (5)
b) Find the smallest value of x which satisfies the inequation 2x + 7/2 > 5x/3 +3, x ∈I. (5)
10a) Ram paid ₹345.60 as GST on purchase of ₹3840. Find the rate of GST. (2)
c) 2x - 1/x= 7. (2)
d
11)a)
b) 2/(x-1) + 3/(x+1) = 4/(x+2). (5)
8/7/21
1)
7/7/21
1) The catalogue price of a colour T. V is ₹24000. The shopkeeper gives a discount of 8% on the listed price. He gives a further off-season discount of 5% on the balance. But GST at 10% is charged on the remaining amount. Find:
A) the GST a customer has to pay.
B) the financial price he has to pay for the colour TV. 2097.60, 23073.60
2)
3) 2x -5≤ 5x+4<11, x belongs to R.
4) find the remainder if 4x³ - 6x²+7x -2 is divided by x - 1/2. 1/2
5) X: 13 15 18 20 22 24 25
F:. 6 4 11 9 16 12 2 find a) median b) lower quartile c) upper quartile d) semi-interquartile. 21, 18, 22, 2
6) If the m th term of an AP is a and its n th term is b, Show that the sum of its m+ n terms.
6/7/21
1) By remainder theorem show that 5x³+2x²-13x+6 is divisible by x+2.
2) Given A= 30 and B= 60 verify sin(B-A)= sin B cos A - cos B sin A.
3) Given 2 tanx= 5 find (3sinx - 4 cosx)/(sinx + 4cosx). 7/13
4) The sum of the three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms. 4,7,10
5) If the sum of n terms of an AP is 3n²+ 4n, find its rth term. 6r+1
6) Following table gives the basic salaries of person employed in an office.
Salary no. Of employees
200-300 11
300-400 10
400-500 15
500-600 8
600-700 4
A) using above information Calculate cumulative frequencies of the employees.
B) draw the ogive
C) estimate the median. 420
7) Mr. X purchased a cycle for ₹25488, which includes 10% rebate on the marked price and 18% tax on the remaining price. Find the marked price of the cycle. 24000
5/6/21
1) find the sum of all numbers between 100 to 300 which are divisible by 8. 5000
2) Find the remainder when 3x³ - 9x +4 is divided by x-1. -2
3) Find the mean, median and mode of 3,7,10, 6,9, 5, 7, 5, 16, 7. 7.5, 7, 7
4) solve: x + 1/5< 4x/3+ 8/15≤ x/5 + 5/3, x belongs to R.
5) find median
Class Frequency
00-10 7
10-20 9
20-30 13
30-40 25
40-50 16
50-60 10
6) class frequency
0-5 4
5-10 a
10-15 8
15-20 5
20-25 3 if mean is 34/3 find a.
4/6/21
1) A V. C. R is marked for sale ₹ 14280 inclusive of GST at 12%. Calculate GST in rupees. 765,765
2) Find the remainder when 2x³+ 3x² - 2x +3 is divided by x+2 with the help of factor theorem. 3
3) Solve: -8/3≤ x + 1/3< 10/3; x belongs to R. -3≤ x < 3
4) √{(1-sinA)/(1+ sinA)}= cosA/(1+ sinA)
5) class frequency
0-8 3
8-16 5
16-24 7
24-32 4
32-40 2 find mode. 19.2
6) If the 10th, 28th and last term of an AP are respectively 29, 83, 122. Find its first term, common difference and number of terms. 2,3,41
1/7/21
1) Draw the histogram and hence the mode for the following:
Class frequency
00-10 2
10-20 8
20-30 10
30-40 5
40-50 4
50-60 3. 23
2) calculate the mean, the median and mode of 6,3,6,5,4,6,8,4,5,3.
3) Student English maths
A 30 26
B 60 80
C 35 33
D 62 68
E 47 44
F 60 85
G 47 44
H 28 72
I 64 65 find median.
4) Given x belongs to I, Solve the inequation 3≥ (x-4)/2 + x/3 ≥ 2.
5) Class Frequency
00-05 2
05-10 7
10-15 18
15-20 10
20-25 8
25-30 5 find mode
6) Class Frequency
05-10 10
10-15 6
15-20 4
20-25 12
25-30 8
30-35 4
35-40 2
40-45 1
45-50 3 find median
7)
30/6/21
1) cosA/(1- tanA) + sinA/(1- cotA) = cosA + sinA.
2) Find the value of k, given that 3x³ + 4x³ - 6x + k is divisible by x+1.
3) When ax²+ bx - 6 is divided by (x-1), (x+1), the remainder are -10, 4. Find a,b.
4) find: sin48/cos42 + (sin29 + cos61)(sin29- cos61).
5) Simplify: 2/5 ≤x - (1+2/5)<4/5, x belongs to R and graph the solution set on a real number line.
6) Find the remainder when 5x³+ 8x² -2x-9 is divided by x+2.
7) simplify: (sin63 + cos17)(sin50 - cos 40).
8) solve: -2≤7- 3x<1: x belongs to R
9) √{(1-cosx)/(1+cosx)}= cosecx- cotx
29/6/21
1) If tanx= 5/4, find the value of sin²x - cos²x. 9/41
2) Kamta purchased a cycle for₹1664 including GST. If the list price of the cycle is ₹1600, find the rate of GST. 4%
3) Find the values of m if (x-m) is a factor of x² + my -18. ±3
4) Solve: 3 ≥ (x-4)/2 + x/3 ≥2, x belongs to R. 4.8≤x ≤ 6
5) Find the remainder when 2x³ - 6x +4 is divided by x+3. 40
6) Find the mean, the median and the mode of the following data: 7,4,6,4,5,8,9,11,10,15,4,3. 7,6.5,4
7)
8) Find the mode
Class interval frequency
0-5 2
5-10 2
10-15 18
15-20 10
20-25 8
25-30 5 16
9) Salary (₹) no.of people
400 10
600 8
800 6
1000 10
1200 10
1500 6
Find the mean salary. ₹892
28/6/21
1) Simplify: -31/3 < 5y/3+ 3 ≤ y/2+ 16/3, y belongs to R. -8<y≤2
2) prove x+1 is a factor of 3x³+5x² - 6x -8.
3) If the mean of 10 Observation is 20 and that of another 15 observation is 16, find the mean of all 15 observation. 17.6
4) Shikha bought a calculator for ₹1026, which includes 5% rebate on the marked price and then 20% GST on the remaining price. Find the marked price of the calculator. 900
5) Show that 3x -1 is a factor of 6x² + 7x -3. 1
6) Solve: 21/x² - 29/x -10= 0. -7/2,3/5
7) weight No.of students
30-35 4
35-40 16
40-45 40
45-50 22
50-55 10
55-60 8
Find median. 44
8) Prove: cotx - tanx= (2cos²x -1)/(sinx cosx).
9) Class Frequency
00-10 12
10-20 16
20-30 6
30-40 7
40-50 9
Find mean. 22
27/6/21
1) Prove: (cotx -1)/(2-sec²x)= cotx/(1+tanx)
2) Manisha has a recurring deposit account for 2 years at 10% p.a. if she receives ₹1900 as intrest, find the value of the monthly installment paid by her. 760
3) Find the mean of 25 observation, if the mean of 15 of them is 18 and the mean of remaining ones is 13. 16
4) Find the smallest value of x, which satisfies the inequation 2x+ 7/2> 5x/3 + 3, x belongs to I. -1
5) Find the remainder when 2x³+7x²-x+1 is divided by x+1. 7
6) What is the rate of GST levied on an article that was sold at a price two and half times its marked price? 150%
7)
9) Find the median
Wages No of workers
4000-4400 8
4400-4800 12
4800-5200 20
5200-5600 25
5600-6000 17
6000-6400 10. 4800
10) calculate the mean, the median and mode of the numbers:
3,2,5,4,1,7,2,5,4,2. 3.5, 3.5, 2
11) Prove: (1-sinA)/(1+sinA)= (secA- tanA)².
26/6/21
1)
Marks No. Of students
0-9 5
10-19 9
20-29 16
30-39 22
40-49 26
50-59 18
60-69 11
70-79 6
80-89 4
90-99 3
A) find median. 42.6, 10
B) the number of students who obtained more than 75% marks.
2) Find the mean of the following:
X: 200 300 400 500 600 700
F: 5 11 10 10 8 6 446
3) The price of a washing machine inclusive of GST at 9% is ₹10028. Find its marked price. If the sales tax is increased to 14%, How much more does the customer pay for the washing machine? 9200
4) Using remainder theorem, find the remainder when 5x² - 4x -1 is divided by (2x-1). -7/4
5) If 12 tanx= 5, then 13sinx-5 is. 0
6) Show that (x-5) is a factor of x³- x² -17x-15.
7) The mean of five numbers is 18. On excluding one number, the mean becomes 16. Find the excluded number. 26
25/6/21
1) The marks scored by 40 pupils of a class in a test were as follows:
X: 0 1 2 3 4 5
F: 2 4 5 14 11 4
Calculate mean mark. 3
3) Using the Step-deviation method, find mean:
Class frequency
50-60 9
60-70 11
60-70 10
80-90 14
90-100 8
100-110 12
110-120 11 85.8
4) Draw the histogram and hence the mode for the following:
Class frequency
00-10 2
10-20 8
20-30 10
30-40 5
40-50 4
50-60 3 23
5) Find the remainder when 7x² - 3x +8 is divided by x-4. 108
6) If x belongs to integer, find the solution set for the inequation 5<2x - 3 ≤ 14 and graph it
24/6/21
1) Mamta has a cumulative time deposit account in a bank. She deposits₹800 p.m and gets ₹15198 as maturity value. If the rate of interest be 7% p.s. find the total time for which the account was held. 18 months
2) The marks scored by 40 pupils of a class in a test were as follows:
X: 0 1 2 3 4 5
F: 2 4 5 14 11 4
Calculate mean mark. 3
3) solve: 2 ≤ 2x -3 < 5, x belongs to R and mark it on the number line. 5/2≤x< 4
5) Using the remainder theorem, find the remainder when 7x³+ 5x² - 4x - 1 is divided by x+1. 1
6) If the price of an Almirah including GST is 7884. If its marked price is₹7300, find the rate of GST. 8%
8) Using the Step-deviation method, find mean:
Class frequency
50-60 9
60-70 11
60-70 10
80-90 14
90-100 8
100-110 12
110-120 11 85.8
9) Prove: (1+cosA)/(1-cosA)= (cosecA + cotA)².
23/6/21
1) Find the remainder when 7x² - 3x +8 is divided by x-4. 108
2) If x belongs to integer, find the solution set for the inequation 5<2x - 3 ≤ 14 and graph it on a number line.
3) 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. 9/2, 2
4) From the following, find
A) The average wage of a worker, Give your answer, correct to the nearest paise.
B) Medain
Wages in ₹. 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. 44.85
6) Prove: √{(1+cost)/(1-cost)= cosect + cot t
22/6/21
1) Find the remainder when 2x³ - 3x² + 7x -8 is divided by x-1. -1
2) Find the value of the constants a and b, If (x-2) and (x-3) are both factors of x³ + ax² + bx - 12. 3,-4
3) The catalogue price of a colour TV is ₹24000. The shopkeeper gives a discount of 8% on the listed price. He gives a further off-season discount of 5% on the balance. But, GST at 10% is charged on the remaining amount. Find:
A) GST amount a customer has to pay. 2097.60
B) The final price he has to pay for the TV. 23073.60
4) x² - 10x +6= 0 Correct to decimal places. .. 9.36, 0.64
5) The distance by road between two towns A and B is 216Km, and by rail it is 208 km. A car travels at a speed of x km/hr, and the train travels at a speed which is 16km/hr faster than the car. calculate:
A) time taken by the car to reach town B from A. in terms of x.
B) time taken by the train to reach town B from A, in terms of x.
C) If the train takes 2 hours less than the car to reach Town B, obtain an equation in x and solve it. 36
D) Hence find the speed of the train. 52 km/hr
6) A trader buys x articles for a total cost of ₹600.
A) write down the cost of one article in terms of x.
If the cost for article were ₹5 more, the number of article that can be bought for ₹600 would be four less.
B) write down the equation in x for their work situation and solve it for x. 24
7) An aeroplane travelled a distance of 400km at an average speed of x km/hr. On the return journey, the speed was increased by 40km/hr. Write down expression for the time taken for:
A) The onward journey
B) The return journey if the return journey to 30 minutes less than the onward journey
If the journey took 30 minute less than the onward journey, write down an equation in x and find its value. 160
8) The work done by (x-3) men (2x-1) days and the work done by (2x+1) men in x+4 days are in the ratio of 3:10. Find the value of x. 6
