5/10/24
1) If cotx = 7/7.5, then cosecx is
a) 7.5/4 b) 8/17 c) 17/15 d) 15/17
2) If 2x = secA and tanA= 2/x then the value of 2(x²- 1/x²)²= ?
a) 1/2 b) 1/4 c) 1/8 d) 1/16
3) The value of (sin43° . cos47°+ cos43° sin47°) is
a) 0 b) 1 c) sin4° d) cos4°
4) If tanx = 4/5, then cosx =
a) 4/5 b) 3/5 c) 3/4 d) 5/√41
5) If sinx = 1/√2, then sec2x =
a) 0 b) 1 c) 2 d) none
6) The value of ( tan35/cot55 + cot78/tan12) is
a) 0 b) 1 c) 2 d) none
7) ABC is a triangle. Then sin{(B+ C)/2}=
a) sin(A/2) b) cos(A/2) c) sinA d) cosA
8) The simplest value of cos53°/sin37° is _____.
9) if tan35° tan55°= sinx, then lowest positive value of x will be_____.
10) If cos²x - sin²x = 1/x (x > 1), then cos⁴x - sin⁴x = ____.
11) The value of (sin 12 . cos 18. sec 78. Cosec72) is___.
12) The value of tan 15 tan 45 tan 60 tan 75 is ____.
13) if tanx = 4/5, then x = ____.
14) If sinx =1/2, then cos2x =_____.
15) cosx= √3/2, then sin2x=_____. √3/2
16) The value of (4/sec²x + 1/(1+ cot²x) + 3 sin²x) is ____.
17) If sinx =1/2, then tan2x =___.
18) If sin(x - 30°)= 1/2, then the value of cosx is_____.
4/10/24
1) A person deposited Rs100 in a bank and gets the amount Rs121 after 2 years. The rate of compound interest is____%.
2) If the simple interest for n years at r% p.a. be Rs Pnr/25, then the principle will be Rs____.
3) At same rate percent per annum, the simple interest and compound interest of same principal are same in ____ year.
4) A person depreciates at a certain rate over time is called____.
5) The person who gives loan is called____.
6) Amount of Rs2P per t years at the rate of simple interest r/2% per annum (2P+ ____) Rs.
7) if the ratio of principle and amount for 1 year is 8:9, then the rate of the simple interest per annum is_____.
8) Fixed amount rupee fixed annual interest rate one year compound interest rate and simple interest rate ____.
9) With the passage of time, someone grows at a certain rate , it is called___.
2/10/24
1) if a principal becomes twice of it in 10 years, then the rate of a simple interest for annum is
a) 5% b) 10% c) 15% d) 20%.
2) Interest on Rs a at the simple interest 10% per annum for b months is
a) ab/100 b) ab/120 c) ab/1200 c) ab/10.
3) If the ratio of principal and yearly amounts be in the ratio 25:28, then the yearly rate of interest is
a) 3% b) 12% c) 75/7% d) 8%
4) If the total interest becomes Rs x for any principal having the rate of simple interest of x% per annum for x years then the principal will be
a) Rsx b) Rs 100x c) Rs 100/x d) Rs 100/x²
5) The total interest of a principal in n years, at the rate of simple interest of r% per annum is one/109, the principle will be
a) Rs2p b) Rs4p c) Rs3p d) 5p.
6) If the interest on Rs p at the rate of simple interest of r% per annum in t years is I, then
a) I= prt b) prt I= 100. I c) prt = 100. I d) none.
7) A principal becomes twice of its amount in 20 years at a certain rate of simple interest. At that same rate of simple interest, that principal becomes thrice of its amount in
a) 30 years b) 35 years c) 40 years d) 45 years
8) A sum of Rs400 amounts to Rs480 in 4 years. What will it amount to if the rate of interest is increased by 2% ?
a) Rs484 b) Rs560 c) Rs512 d) none
9) At what rate of percent per annum will Rs2304 amount to Rs2500 in 2 years at compound interest ?
a) 9/2% b) 21/5% c) 25/6% d) 13/3%
10) An amount doubles itself in 5 years with simple interest. What is the amount of interest percent per annum?
a) 10% b) 20% c) 25% d) 30%
11) A person deposited Rs109 in a bank and got the amount Rs121 for 2 years. The rate of compound interest is
a) 10% b) 20% c) 5% d) 21/2%
12) In case of compound interest, the rate of compound interest per annum is
a) equal b) unequal c) both equal or unequal d) none.
13) In case of compound interest
a) The principals remains unchanged each year
b) principal changes in each year
c) principal may be equal or unequal in each year d) none
27/8/24
1) On What sum of money, the difference be
tween the simple interest and compound interest in 2 years at 5% per annum is Rs15 ?
2) A certain sum of money invested at 5% intrest, compounded annually, for 3 years. If the interest computes to Rs2522, determine the principal.
3) In how many years will a sum of Rs800 at 10% per annum compounded semi-annually become Rs926.10 ?
4) Suraj has a fixed deposit in Bank of India of Rs40000 for a period of 3 years. The bank allows a compound interest of 13% compounded half yearly. Find the maturity value.
Day- 8
1) A bar graph is drawn to the scale 1cm= k units, then a bar of length k cm represents
a) 1 unit b) k units c) 2k units d) k² units
2) A bar graph is drawn to the scale of 1 cm = x units. If the length of a bar representing a quantity of 702 units is 3.6cm, then x=
a) 165 b) 175 c) 185 d) 195
3) In figure
bar graph represents sales of two wheelers and four wheelers in a mega city from 2013 to 2016. In which year the difference between the sales of two wheelers and four wheelers is less ?
a) 2013 b) 2014 c) 2015 d) 2016
4) In the figure, the total number of vehicles (two wheelers and four wheelers ) sold in the year 2013 and 2014 is
a) 26100 b) 28500 c) 25100 d) 27500
5) In figure, the maximum difference between sales of two wheelers and that of four wheelers, in any year, in the given period is :
a) 1500 b) 1700 c) 1800 d) 2000
6) In figure, the total number of two wheelers sold in four years is
a) 26000 b) 27000 c) 31000 d) 32000
7) in a bar graph, the height of a bar is 5cm and it represent 40 units . The height of the bar representing 56 units is:
a) 11.2cm b) 5.6cm c) 7cm d) 8cm
8) in a bar graph, length of a bar is 6.4cm and it represent 256 units. The number of units represented by a bar of length 5.3cm is
a) 228 b) 196 c) 212 d) 224
9) In a bar graph, the height of a bar is proportional to the
a) width of the bar b) range of the data c) value of the component d) number of observation in the data.
10) Which one of the following is not the graphical representation of statistical data ?
a) bar graph b)?histogram c) frequency polygon d) cumulative frequency distribution
11) In a frequency distribution, ogives are graphical representation of
a) frequency b) relative frequency c) cumulative frequency d) raw data.
12) A frequency polygon is constructed by plotting frequency of the class interval and the
a) upper limit of the class b) lower limit of the class c) mid value of the class d) any values of the class
13) In a Instagram the area of each rectangle is proportional to
a) the class marks of the corresponding class interval.
b) the class size of the corresponding class interval
c) frequency of the corresponding class interval.
d) cumulative frequency of the corresponding class interval .
14) In the 'less than' type of ogive the cumulative frequency is plotted against
a) the lower limit of the concerned class interval.
b) the upper limit of the concerned class interval .
c) the mid value of the concerned class interval.
d) any value of the concerned class interval.
15) In a histogram the class interval or the groups are taken along
a) y-axis b) x-axis c) both of x-axis and y-axis d) in between x and y-axis .
16) A histogram is a pictorial representation of the grouped data in which class intervals and frequency are represpectively taken along
a) vertical axis and horizontal Axis
b)!vertical access only
c) horizontal Axis only
d) horizontal axis and vertical axis.
17) In a histogram, each class rectangle is constructed with base as
a) frequency b) class intervals c) range d) size of the class
18) Consider the following frequency distribution :
Class interval Frequency
5-10 6
10-15 12
15-25 10
25-45 8
45-75 15
To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-44 is
a) 6 b) 5 c) 3 d) 2
19) Figure shows the bar graph of number of boys and number of girls in a school from 2014 to 2017.
In which year the difference between the number of boys and the number of girls was more ?
a) 2014 b) 2015 c) 2016 d) 2017
20) In figure, total number of students in the year 2015 was
a) 1160 b) 1270 c) 1380 d) 1490
21) In figure , the minimum difference between the number of boys and girls in any year in the given period was
a) 90 b) 70 c) 50 d) 30
22) In figure, in which year the number of girls more than the number of boys?
a) 2014 b) 2015 c) 2016 d) 2017
23) In figure , the ratio between the number of student in the year 2016 and 2017 was
a) 107 :145 b) 127 : 145 c) 29 :36 d) 107: 127
CASE STUDY
1) Following bar graph represents the sales of the cold drinks of two companies A and B from 2015 to 2018.
Read the above bar graph and answer the following questions :
i) The year in which the difference between the sells of two companies was highest, was
a) 2018 b) 2015 c) 2016 d) 2017
ii) Total sales of A and B in the year 2016 was
a) 1160000 b) 1270000 c) 1380000 d) 1490000
iii) The minimum difference between the sales of company A and B in any year in the given period was
a) 90000 b) 70000 c) 50000 d) 300000
iv) In which year was the sales of company B more than the sales of company A?
a) 2015 b) 2016 c) 2017 d) 2018
v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107 :145 b) 29:36 c) 127: 145 d) 107: 127
2) Read the following bar graph and answer the following questions:
i) In the which year was the difference between sales of the scooters and the sales of cars the least ?
a) 2015 b) 2016 c) 2017 d) 2018
ii) Total number of the vehicles (scooters and cars) sold in the year 2015 and 2016 was
a) 26100 b) 28500 c) 25100 d) 27500
iii) The maximum difference between the sales of scooters and cars , in the given period was
a) 1500 b) 1700 c) 1800 d) 2000
iv) The total number of scooters sold in the 4 years was
a) 26000 b) 27000 c)!31000 d) 32000
v) The ratio between the total number of vehicles sold (scooters and cars) in the year 2016 that in the year 2018.
a) 41: 46 b) 69: 91 c) 147 :182 d) 46: 49
3) Population census in India is conducted every 10 years. The first complete census was taken in 1881 and 15th decennial census taken in 2011. The 16th decennial census was to be conducted in 2021 but due to the COVID it will be taken in 2022. The data obtained from the census of a town has been represented by a bar graph shown in figure. It represents the number of persons living in various age groups in the town. Observe the bar graph and answer the following questions:
i) What is the total of persons living in the town in the age-groups 10-15 and 60-65 ?
a) 2000 b) 2200 c) 2100 d) 1900
ii) How many persons are more in the age group 10 to 15 than in the age group 30 to 35 ?
a) 200 b) 250 c) 300 d) 350
iii) What is the total population of the town ?
a) 6700 b) 6400 c) 7700 d) 6600
iv) What is the number of persons in the age-group of 60-65 ?
a) 900 b) 750 c) 850 d) 800
v) What is the age group of exactly 1200 persons living in the town ?
a) 10 to 15 b) 20-25 c) 30-35 d) 40-45
4) A healthcare survey was done by the State Health and Family Welfare Care Board of the State of Punjab. The data is collected by forming age groups i.e.,10 - 15, 20 -25, 30 -35, 40 -45, 50 -55, 60- 65, 70-75. The overall data from a town is the given below in the form of a bar graph. Read the data carefully and answer the question that follow :
i) How many persons are more in the age group 10 - 15 than the age group 30-35?
ii) What is the age group of exactly 1200 persons living in the town?
iii) What is the percentage of the youngest age group persons over those in the oldest age group?
iv) What is the total population of the town ?
Assertion- Reason
Each of the following examples contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c), and (d) only one of which is the correct answer. Mark the correct choice.
a) Statement -1 and Statement -2 are true Statement-2 is a correct explanation for statement-1.
b) Statement-1 and statement-2 are true; Statement-2 is not a currect explanation for statement-1.
c) Statement -1 is true, Statement -2 is false.
d) Statement -1 is false, Statement -2 is true.
1) Statement -1(A): The graphical representation of the frequency distribution
Marks: 0-20 20-40 40-60 60-100
No. of Student: 10 15 20. 25
is as given figure
statement-2 (R): In a histogram, the area of the rectangles are proportional to the frequencies. c
2) Statement -1(A): A bar graph is a pictorial representation of the numerical data by a number of rectangles of uniform width erected horizontally or vertically with equal spacing between them.
Statement-2 (R): In order to draw the histogram when mid-points of class intervals are given, it is assumed that the frequency corresponding to the variate value a (say) is spread over the interval a - h/2 to a + h/2 , where h is the jump from one value to other. b
3) Statement -1(A): In a histogram, the areas of each rectangle is proportional to the frequencies of its classes.
Statement-2(R): in a histogram the lengths or height of rectangles are proportional to the frequencies .
4) Statement -1(A): in a histogram, the area of each rectangle is proportional to the class size of the corresponding interval.
Statement-2 (R): To draw the histogram of a continuous frequency distribution with unequal class intervals, the frequencies of classes are adjusted by using the formula:
Adjusted frequency of a class= minimum class size/ class size x frequency of the class.
5) Statement -1(A): To draw the histogram of a continuous frequency distribution when class marks of class intervals are given, it is asumed that the frequency corresponding to the class mark a is spread over the interval a - h/2 to a + h/2, where h is the jump from one value to the other.
Statement-2 (R): The class marks of a continuous frequency distribution are:
1.04, 1.14, 1.24, 1.34, 1.44, 1.54, 1.64, then the last interval is 1.55-1.73.
Day- 7(19/6/24)
1) (a - b)³+ (b - c)³+ (c - a)³ is equal to
a) 2a³+ 2b³+ 2c³
b) (a - b) (b - c)(c - a)
c) 0
d) 3(a - b)(b - c)(c - a)
2) If x + y=12 and xy = 27, then x³+ y³=
a) 765 b) 756 c) 657 d) 675
3) If x+ y= -4 then x³+ y²- 12xy +64=
a) -64 b) 128 c) 0 d) none
4) If x = 2y+6, then x³- 8y³- 36xy=
a) 216 b) -216 c) 36 d) -36
5) (a+ b+ c){(c - b)²+ (b - c)²+ (c - a)²}=
a) a³+ b³+ c³- 3abc b) a³+ b³+ c³ c) 2(a³+ b³+ c³- 3abc) d) 3abc
6) If a³+ b³= 5 and a+ b=1, then ab=
a) -4/3 b) 4/3 c) -3/4 d) 3/4
7) If a³+ (b - a)³ - b³ = k(a - b), then k=
a) ab b) 3ab c) -3ab d) 3
8) If a+ b+ c= 0, then a²/bc + b²/ca + c²/ab=
a) 1 b) 0 c) -1 d) 3
9) The factor of x³ - x²y - xy²+ y³, are
a) (x+y)(x²- xy+ y²)
b) (x+y)(x²+ xy+ y²)
c) (x+y)²(x- y)
d) (x-y)²(x + y)
10) The factor of x³ - 1 +y³ + 3xy, are
a) (x-1+y)(x²+1+ y²+ x + y - xy)
b) (x+1+y)(x²+1+ y²+ 1- x - y - xy)
c) (x-1+y)(x²-1- y²+ x + y - xy)
d) 3(x-1+y)(x²-1+ y²)
11) The factor of 8a³+ b³- 6ab +1 are
a) (2a+ b-1)(4a²+ b²+1- 3ab- 2a)
b) (2a- b+1)(4a²+ b²+1- 4ab- 2a+ b)
c) (2a+ b+1)(4a²+ b²+1- 2ab- b -2a)
d) (2a+ b-1)(4a²+1- 2ab- b- 4a)
12) (x + y)³ -(x - y)³ can be Factorized as
a) 2y(3x²+ y²) b) 2x(3x²+ y²) c) 2y(3y²+ x²) d) 2x(x²+ 3y²)
13) The expression (a - b)³ + (b - c)³+ (c - a)³ can be Factorized as
a) (a- b)(b - c)(c - a)
b) 3(a- b)(b - c)(c - a)
c) -3(a- b)(b - c)(c - a)
d) (a+ b+c)(a²+b² + c²- ab - bc - ca)
14) The value of {(2.3)³ - 0.027}/{(2.3)²+ 0.69+ 0.09}, is
a) 2 b) 3 c) 2.327 d) 2.273
15) The value of {(0.013)³ +(0.007)³}/{(0.013)² - 0.013 x 0.007+ (0.007)²} is
a) 0.006 b) 0.02 c) 0.0091 d) 0.00185
16) The factors of a² - 1 - 2x - x², are
a) (a - x +1)(a - x -1)
b) (a + x +1)(a - x +1)
c) (a + x +1)(a - x -1) d) none
17) The factors of x⁴+ x²+ 25, are
a) (x²+ 3x +5)(x²- 3x +5)
b) (x²+ 3x +5)(x²+ 3x -5)
c) (x²+ x +5)(x²- x +5) d) none
18) The factors of x²+ 4y²+ 4y - 4xy - 2x - 8, are
a) (x - 2y -4)(x - 2y +2)
b) (x - 2y +2)(x - 4y -4)
c) (x + 2y -4)(x + 2y +2) d) none
19) The factors of x³- 7x + 6, are
a) x(x -6)(x -1)
b) (x² -6)(x -1)
c) (x +1)(x +2)(x -3)
d) (x +3)(x -2)(x -1)
20) The expression x⁴+ 4 can be Factorized as
a) (x²+ 2x +2)(x²- 2x +2)
b) (x²+ 2x +2)(x²+ 2x -2)
c) (x²- 2x -2)(x²- 2x +2)
d) (x²+2)(x²- 2)
21) If 3x = a+ b + c, then the value of (x - a)³+ (x - b)³+(x - c)³ -3(x - a)(x - b)(x - c), is
a) a+ b + c b) (a - b)(b - c)(c - a) c) 0 d) none
22) If (x + y)³ - (x - y)³ - 6y(x²- y²)= ky³, then k=
a) 1 b) 2 c) 4 d) 8
23) If x³- 3x²+ 3x +7= (x +1)(ax²+ bx + c), then a+ b + c=
a) 4 b) 12 c) -10 d) 3
24) If x/y + y/x = -1 (x,y ≠ 0), then the value of x³- y³ is
a) 1 b) -1 c) 0 d) 1/2
25) Which of the following is a factor of (x + y)³ - (x + y³)?
a) x²+ y²+ 2xy
b) x²+ y²- xy
c) xy² d) 3xy
Assertion- Reason based
Each of the following examples contains STATEMENT-1(Assertion ) and STATEMENT-2( (Reason) and has following four choices (a), (b), (c) and (d ), only one of which is the correct choice.
a) Statement-1 and Statement -2 are True; statement-2 is a correct explanation for statement-1
b) Statement-1 and statement-2 are True ; Statement -2 is not a correct explanation for Statement-1.
c) Statement -1 is True , Statement -2 is False .
d) Statement -1 is False , Statement -2 is True .
1) Statement -1 (A): The value 1000³ - 900³ - 100³ is 270000000
Statement -2 (R): If a+ b + c= 0, then a³+ b³+ c³= 3abc. a
2) Statement -1 (A): The value of (0.093³+ 0.007³)/(0093² - 0.093 x 0.007 + 0.007²) is 0.1.
Statement -2(R): a³+ b³= (a+ b)(a²- ab + b²). a
3) Statement -1(A): a³(b - c)³+ b³(c - a)³+ c³(a - b)³= 3(a - b)(b - c)(c - a)
Statement -2(R): if a+ b + c = 0, then a³+ b³+ c³= 3abc. d
4) Statement -1(A): (a+ b + c){(a - b)²+ (b - c)²+ (c - a)²}= 2(a³+ b³+ c³ - 3abc)
Statement -2(R) If a+ b + c = 0 then (a+ b)³+ (b + c)³+ (c + a)³= - 3abc. b
5) Statement -1(A): The product of (x²+ 4y²+ z²+ 2xy + xyz - 2yz) and (-z + x - 2y) is x³- 8y³- z³ - 6xyz
Statement -2(R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c² - ab - bc - ca). a
Statement -1(A): a²+ b²+ c²- ab - bc - ca = 0 if and only if a= b= c.
Statement -2(R): a³+ b³+ c³ - 3abc = (a+ b + c)(a²+ b²+ c²- ab - bc - ca). b
6) statement-1(A): (a - b)³+ (b - c)³+ (c - a)³= 3(a - b)(b - c)(c - a)
Statement -2:(R): if a+ b + c = 0, then a³+ b³+ c³= 3abc. a
7) Statement-1(A): if 3x= a+ b + c, then (x - a)³+ (x - b)³+ (x - c)³= 3(x - a)(x - b)(x - c)
Statement -2(R): if a+ b + c= 0, then a³+ b³+ c³= 3abc. a
8) Statement -1(A): if a+ b + c = 5 and ab + bc+ ca= 10, then a³+ b³+ c³ - 3abc = 25
Statement-2(R): a³+ b³+ c³ - 3abc = (a+ b + c){(a+ b + c)² -3(ab + bc+ ca)}. d
9) Statement -1(A): If a,b,c are all non-zero such that a+ b + c = 0, then a²/bc + b²/ca + c²/ab = 3
Statement-2 (R): If a+ b + c = 9 and a²+ b² + c²= 35, then ab + bc+ ca= 23. b
10) Statement -1(A): The value of (0.027³+ 0.023³)/(0.027²- 0.027 x 0.023 + 0.023²) is 0.05
Statement-2 (R): a³- b³= (a- b)(a²- ab + b²). c
Day- 6 ( 14/6/24)
1) The square root of a²+ 1/a²+ 2 is
a) a+ 1/a b) a- 1/a c) a²+ 1/a² d) a²- 1/a²
2) The square root of a+ 1/a - 2 is
a) a -1/a b) √a+ 1/√a c) ±(√a- 1/√a) d) a+ 1/a
3) The value of (a+ b)²/{(b -c)(c - a)} + (b + c)²/{(a - b)(c - a) + (c + a)²/{(a - b)(b - c)} is
a) -1 b) 0 c) 1 d) 2
4) The square root of the expression (1/abc) (a²+ b²+ c²) +2(1/a + 1/b+ 1/c) is
a) (a+ b+ c)/abc b) √a + √b + √c c) √(bc/a) + √(ca/b) + √(ab/c) d) √(a/bc)+ √(b/ca) + √c/ab)
5) The square root of x²/9 + 9/4x² - x/3 - 3/2x + 5/4 is
a) 2x/3 + 3/2x - 1/2 b) x/3 + 3/2x +1 c) 3/x + 2/3x - 1/2 d) x/3 + 3/2x - 1/2
6) The square root of the expression is (xy + xz - yz)² - 4xyz(x - y) is
a) xy + yz - 2xyz b) x + y - 2xyz c) xy + z - y d) xy + yz - xz
7) The square root of a²/4 + 1/a² - 1/a + a/2 - 3/4 is
a) a/2 - 1/a + 1/2 b) a/2 + 2/a - 1 c) a/2 + 1/a - 1/2 d) a/2 - 2/a - 1/2
8) The expression (4a + 5b+ 5c)² - (5a + 4b+ 4c)² + 9a² is a perfect square of the expression
a) √3(b + c) b) 3(a+ b + c) c) 3(b+ c) d) 3(-b + c - a)
9) The expression (3a + 2b+ 3c)² - (2a + 3b+ 2c)² + 5b² is a perfect square of the expression √(a + b+ c) b) √((a + b) c) √5(a +c) d) √5(a - b+ c)
10) If a/b + b/a =2, then (a/b)¹⁰ - (b/a)¹⁰ is equal to
a) (2¹⁰-1)/2¹⁰ b) 2 c) 0 d) (2²⁰+1)/2¹⁰
11) If ab c = 6 and a + b + 6 = 6, then 1/ac + 1/ab + 1/bc =
a) 2 b) 1 c) 3 d) 0
12) √{(a + b+ c)²+ (a + b- c)²+ 2(c² -b²- a²- 2ab) is equal to
a) 2c b) 2a c) 2b d) a + b+ c
13) If a/b + b/a = -1, then a³- b³=
a) 1 b) -1 c) 1/2 d) 0
14) If a+ b=8 and ab= 12, then a³+ b³=
a) 244 b) 224 c) 144 d) 284
15) If (a + 1/a +2)²=4, then a²+ 1/a²=
a) 12 b) 13 c) 14 d) -14
16) If x+ 1/x =7, then x³- 1/x³=
a) 9√5 b) 144√5 c) 135√5 d) √5
17) {(a - b)³ - (a + b)³}/2 + a(a²+ 3b²)=
a) a³- b³ b) (a + b)³ c) a³+ b³ d) (a - b)³
18) If x+ 1/x =5, then x²+ 1/x²=
a) 25 b) 10 c) 23 d) 27
19) If x+ 1/x =2, then x³ + 1/x³=
a) 64 b) 14 c) 8 d) 2
20) If x+ 1/x =4, then x⁴ + 1/x⁴=
a) 196 b) 194 c) 192 d) 190
21) If x+ 1/x =3, then x⁶ 1/x⁶=
a) 927 b) 414 c) 364 d) 322
22) If x² + 1/x² =102, then x- 1/x=
a) 8 b) 10 c) 12 d) 13
23) If x³+ 1/x³ =110, then x + 1/x =
a) 5 b) 10 c) 15 d) none
24) If x³- 1/x³ =14, then x- 1/x=
a) 5 b) 4 c) 3 d) 2
25) If a+ b+ c= 9 and ab+ bc+ ca= 23, then a²+ b²+ c²=
a) 35 b) 58 c) 127 d) none
26) (a - b)³+ (b - c)³+ (c - a)³=
a) (a+ b+ c)(a²+ b²+ c²- ab - bc - ca)
b) (a - b)(b - c)(c - a)
c) 3(a - b)(b - c)(c - a) d) none
27) a+ b= 3 and ab = 2, then a³+ b³=
a) 6 b) 4 c) 9 d) 12
28) If a- b =-8 auab = -12, then a³- b³=
a) -244 b) -240 c) -224 d) -260
29) if the volume of a cuboid is 3x²- 27, then its possible dimensions are
a) 3, x, -27x b) 3, x -3, x+3 c) 3, x², 27x d) 3,3,3
30) 75 x 75 +2 x 75 x 25+25 x 25 is equal to
a) 10000 b) 6250 c) 7500 d) 3750
31) (x - y)(x+ y)(x²+ y²)(x⁴+ y⁴) is equal to
a) x¹⁶- y¹⁶ b) x⁸- y⁸ c) x⁸+ y⁸ d) x¹⁶+ y¹⁶
32) If x⁴+ 1/x⁴ =623, then x + 1/x=
a) 27 b) 25 c) 3√3 d) -3√3
33) If x- 1/x = 15/4, then x + 1/x =
a) 4 b) 17/4 c) 13/4 d) 1/4
34) If 3x+ 2/x = 7, then 9x² - 4/x² =
a) 25 b) 35 c) 49 d) 30
35) If a²+ b²+ c²- ab - bc - ca = 0, then
a) a+ b = c b) b + c = a c) c + a= b d) a= b= c
36) If a+ b + c = 0, then a²/bc + b²/ca + c²/ab is
a) 0 b) 1 c) -1 d) 3
37) If a¹⁾³ + b¹⁾³ + c¹⁾³= 0, then
a) a+ b+ c= 0 b) (a+ b + c)³= 27abc c) a+ b + c = 3abc d) a³+ b³+ c³= 0
38) If a+ b + c = 9, then ab+ bc + ca =23, then a³+ b³+ c³- 3abc=
a) 108 b) 207 c) 669 d) 729
39) {(a² - b²)³+ (b²- c²)³+ (c²- a²)³}/{(a - b)+ (b - c)+(c - a)}=
a) 3(a + b) (b +c)(c +a) b) 3(a - b)(b - c)(c - a)} c) (a - b) (b - c)(c - a) d) (a + b) (b +c)(c+ a)
40) The product (a + b)(a - b)(a²- ab+ b²)(a²+ ab+ b²) =
a) a⁶+ b⁶ b) a⁶- b⁶ c) a³- b³ d) a³+ b³
41) The product (x²-1)(x⁴+ x²+1) is equal to
a) x⁸-1 b) x⁸+1 c) x⁶-1 d) x⁶+1
42) If a/b + b/a = 1, then a³+ b³=
a) 1 b) -1 c) 1/2 d) 0
43) If 49a²- b = (7a + 1/2)(7a - 1/2), then the value of b is
a) 0 b) 1/4 c) 1/√2 d) 1/2
44) One of the factors of (5x +1)² -(5x -1)² is
a) 5 + x b) 5- x c) 5x -1 d) 20x
45) If 9x² - b =(3x + 1/2)(3x - 1/2), then the value of b is
a) 0 b) 1/√2 c) 1/4 d) 1/2
46) The Coefficient of x in (x +3)³ is
a) 1 b) 9 c) 18 d) 27
47) The value of 249²- 248² is
a) 1 b) 477 c) 487 d) 497
48) Which of the following is a factor of (x + y)³-(x³+ y³)?
a) x²+ 2xy + y² b) x² - xy + y² c) xy² d) 3xy
49) If x/y + y/x = -1 (x,y ≠ 0), the value of x³- y³ is
a) 1 b) -1 c) 0 d) 1/2
50) If x + y=2 and xy = 1, then x⁴+ y⁴=
a) 6 b) 4 c) 8 d) 2
51) If x² + y²+ xy =1 and x + y = 2, then xy=
a) -3 b) 3 c) -3/2 d) 0
52) If a, b, c are natural numbers such that a²+ b²+ c²= 29 and ab + bc + ca = 26, and a+ b + c=
a) 9 b) 6 c) 7 d) 10
53) If 2x + y/3= 12 and xy = 30, then 8x³+ y³/27=
a) 1008 b) 168 c) 106 d) none
ASSERTION- REASON
Each of the following examples contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
a) Statement-1 and statement-2 are true; Statement-2 is a correct explanation for statement-1 .
b) Statement -1 and Statement-2 are true; Statement -2 is not a correct explanation for statement-1.
c) Statement -1 is true, statement -2 is false.
d) Statement -1 is False, Statement -2 is true.
1) Statement -1(A): √{(a+ b + c)+ (a - b + c)+2(b²- a²- c²- 2ac)}= 2b
Statement-2 (R): (x + y+ z)²= x²+ y²+ z²+ 2(xy + yz + zx). a
2) Statement -1(A): a³+ b³+ 3ab -1= (a+ b -1)(a²+ b²+ a+ b - ab +1)
Statement-2 (R): a³+ b³+ c³- 3abc= (a+ b + c)(a²+ b²+ c²+ ab + bc + ca). c
3) Statement -1(A): (a - b)³+(b - c)³+(c - a)³= 3(a - b)(b - c)(c - a)
Statement-2 (R): If a+ b + c = 0, then a³+ b³+ c³= 3abc. a
4) Statement -1(A): a²+ b²+ c²- ab - bc - ca = 0 if and only if a= b = c.
Statement-2 (R): (a+ b + c)²= a²+ b²+ c²+ 2ab + 2bc + 2ca. b
5) Statement -1(A): a+ b + c = 6 and 1/a + 1/b + 1/c = 3/2, then a/b + a/c + b/a + b/c + c/a + c/b = 6
Statement-2 (R): (a + b + c)²= a²+ b²+ c²+ 2(ab + bc + ca). b
6) Statement -1(A): if a+ b + c = 0, then a³+ b³+ c³= 3abc
Statement-2 (R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c²-ab - bc - ca).
7) Statement -1(A): (a+ b + c)² = a²+ b²+ c²-2(ab+ bc + ca)
Statement-2 (R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c²-ab - bc - ca).
8) Statement -1(A): a³ + 3ax/8 + cpx³/64 - 1/8 = (a + x/4 - 1/2)(a²+ x²/16 + 1/4 - ax/4 + x/8 + a/2)
Statement-2 (R): a³+ b³+ c³ + 3abc = (a + b + c)(a²+ b²+ c²+ ab + bc + ca).
9) Statement -1(A): If a+ b + c =0, ab + bc+ ca = 11, then a²+ b² + c²= 14
Statement-2 (R): (a+ b+ c)³ = a²+ b²+ c²+ 2(ab + bc + ca).
10) Statement -1(A): {(x²- y²)³+(y²- z²)³+(z³- x²)³}/{(x - y)³+(y - z)³+ (z - x)³}= (x + y)(y+ z)(z + x).
Statement-2 (R): If a + b + c= 0, then a³+ b³+ c³= 3abc.
11) Statement -1(A): (1/abc) (a²+ b² + c²)+ 2(1/a + 1/b+ 1/c) is √(a/bc) + √(b/ca) + √(c/ab).
Statement-2 (R): a³+ b³+ c³ - 3abc = (a + b + c)(a²+ b²+ c²-ab - bc - ca).
Day- 5 (11/5/24)
1) simplify
a) (a²+ 3b³)(a³- 2b²)
b)
(ab - 3ad/2)(2ab + 3cd)
c) (2/5 + x)(2/5 - x)(4/25 + x²)
2) Simplify with the help of formula
a) 88 x 112
b) 10.8 x 9.2
c) 10/3 x 14/3
3) Expand:
a) (8+ 3p)²
b) (4+ √5 y)²
c) (3a + 5b/3)²
d) (2/a - 3/b)²
e) (3x - 1/3x)²
4) If x+ 1/x = 4, find the value of
a) x - 1/x b) x²+ 1/x² c) x⁴+ 1/x⁴
5) If x²+ 1/x²= 102, find the value of
a) x - 1/x b) x + 1/x c) x²- 1/x² d) x⁴ - 1/x⁴
6) If a²+ b²= 13 and ab = 6, find the value of a+ b and a- b
7) If a²+ b²= 52 and ab = 24, find the value of a - b
8) Find the value of 36x²+ 49y²+ 84xy, when x= 3, y= 6.
Day -4 7/5/24
1) Factorize the following:
a) x²- 1 - 2a - a²
b) 2 - 50x²
c) 20x² - 45
d) a - b - a²+ b²
e) a²+ b - ab - a
f) x - 64x³
g) a(a + b - c) - bc
h) 1+ 2ab - a²- b²
i) a²+ b²+ 2ab - c²
j) ab(c²+ 1) + c(a²+ b²)
Day -3
1) The value of (0.538 x 0.538 - 0.462 x 0.462)/(1- 0.924)
2) The approximate value of of
(6.385x 6.385 - 5.385 x 5.385)/(6.385 x 6.385 + 2x 6.385 x 5.385 + 5.385 x 5.385)
3) The value of {856+ 167)²+ (856 - 167)²}/(856 x 856 + 167 x 167)
4) If a+ b + c= 0 then the value of (a + b - c)³+ (b + c - a)³+ (c + a - b)³
5) If (x + 1/x)= 3 then find the value of x²+ 1/x².
6) If x- 1/x = 1/2 then value of 4x²+ 4/x²
7) If 2x - 3/x then the value of 4x²- 9/x²
8) Factorize:
a) t⁴ - 16
b) x² - (y+1)²
c) x² + 1/x² - 3.
d) (x² - 2a - 1 - a²)
e) 2 - 50x²
Day- 2
1) Find the value of (a+ b)² - (a - b)².
2) If a²bc²= 5³ and ab²= 5⁶ then find the value of abc.
3) (a+ b)²= a²+ 2ab + b² is true for all
a) natural numbers only b) integers only c) real numbers d) cannot say
4) If x+ y= 17 and x²+ y²= 167 then find the value of xy.
5) If m- n = 16 and m²+ n²= 400 then find the value of mn.
6) (a²/5 - b²/3)(a²/5 + b²/3) = ?
7) If (5x + 1/2)(5x - 1/2)= 25x² - p then find the value of p.
8) The square of (4x - 5y) is...
9) Expand (11x - 9xy)².
10) If x- y= 1 and x²+ y²= 41 then find the value of x + y
11) What is (a+ b)(a - b)(a⁴+ b⁴) equal to?
Day- 1
1) If (3x -4)(5x +7)= 15x²- ax - 28 then find the value of a.
2) The product of (x²+ 3x +5) and (x²-1) is.
3) In the product (2- y)(5- 3y)(1- 7y), the co-efficient of y² is...
4) Given that (3x -1)(x + p)= 3x²+ qx -2, find the value of p+ q - pq.
5) The value of (a+ b)²+ (a - b)² is
6) If a²+ b²= 47 and ab = 19/2 then find the value of 2(a+ b)²+ (a - b)².
7) If ab= 6 and a+ b = 5 then find the value of a²+ b².
8) If x+ y =17 and x²+ y²= 167 then find the value of xy.
9) If a²+ b²= 74 and ab = 35 then find the value of a+ b.
10) If xy = b and 1/x² + 1/y²= a then find the value of (x + y)².
28/11/23
1) Find the difference between compound and simple intrest at 5% per annum for 4 years on Rs20000.
2) Solve: z + √z = 6/25.
3) (6x+2)/4 + (2x²-1)/(2x²+2) = (10x -1)/4x.
4) Factorize:
a) a⁴- 2a²b² + b⁴
b) x⁴- (y+ z)⁴
5) Evaluate:cos²60. Cos²45. Cos²30.
6) If tanx =a/b, find the value of (a sinx + b cosx)/(asinx - b cosx).
7) A diameter of a circle has the extreme points (7,9) and (-1,-3). Then find coordinates of the centre.
8) 4ˣ⁻¹ = 3. 2ˣ - 8. Find x.
9) If (5⁵ + 0.01)² - (5⁵ - 0.01)²= 5ˣ then x is
10) If log2= 0.3010, log3= 0.4771, log7= 0.8451, find the value of log294.
25/11/23
1) If 4ˣ = 8ʸ then find x/y - 1.
2) Evaluate: (2ᑫ. 6ᵖ⁺¹. 10ᵖ⁻ᑫ . 15ᵖ⁺ᑫ⁻²)/(4ᵖ. 3²ᵖ⁺ᑫ. 25ᵖ⁻¹).
3) If log2= x and log3= y, then find the value for log60.
4) Evaluate: 4 log(8/25) - 3 log(16/125) - log 5.
5) Solve: 3x²- 14x +16=0.
6) Solve: x²- (a+ b)x + ab=0.
7) In ∆ABC, AB=26cm, BC=28cm and the altitude AD=24cm. Calculate AC.
8) The area between two concentric circles is 3168cm². Find the radii of the two circles if
A) their sum is 42cm
B) their difference is 28cm
23/11/23
1) (3+ √5)/(3- √5)= a + b √5, find the value of a and b.
2) If x= 4 +√15. Then find the value of x² + 1/x²
3) Simplify (√11- √7)(√11+ √7)
4) Rationalise: 1/(7+ 3 √2)
5) Rationalise: 5/(3√3+ 2√2).
6) If (2/3)⁶(9/4)⁵=(3/2)ᵐ⁺² then find the value of m
7) simplify: x³ +3 √x³/√x
8) simplify: (√3+ 1)(1- √12)+ 9/(√3+ √12)
9) 12x² - 7x +1
10) 2x² + 7x +3.
11) 6x² + 5x -6.
12) 3x² - x - 4
