30/9/24
1) The rth term of an AP is n and it's nth term is r; show that its mth term is r+ n- m.
2) If the 1st term of an AP is 34 and 6th term is 48, then find 2nd, 3rd, 4th and 5th term of the AP.
3) Find the middle term (or terms) and the sum of the following arithmetic series:
3+7+11+15+....+95.
4) The fifth term of an AP is 30 and its twelfth term is 65, find the sum of its 20 terms.
5) The sum of n terms of an AP is 3n²+ 5n. Find the number of the term which is equal to 152. 25
6) How many terms of the series {22+ 18+ 14+ 10 +....} must be added to get the sum 64 ?
7) Insert 7 arithmetic mean between 1 and 41.
8) Find the sum of all natural number between 500 and 1000 divisible by 13.
25/8/24
1) Show:
a) (1+ secx- tanx)/(1+ secx + tanx) = (1- sinx)/cosx
b) (sinx - cosx +1)/(sinx + cosx -1)= 1/(secx - tanx)
c) 2(sin⁶x + cos⁶x) - 3(sin⁴x + cos⁴x)+1= 0
d) (sinx - siny)/(cosx + cosy) + (cosx - cosy)/(sinx + siny)= 0
f) cos⁴x - cos²x = sin⁴x - sin²x
18/8/24
TEST PAPER -1
Time allowed=5/2 hours max. marks :80
General instructions
Attempt all questions from section A and any 4 questions from section B.
All working including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer.
Omission of essential working will result in loss of marks.
The intended marks for questions or parts of questions are given in bracket [ ]
Mathematical tables and graph paper are provided
-----------------------------------------
Section A (40 Marks)
(Attempt all questions from this Section)
______________::::::________________
Question 1: Choose the correct answer to the questions from the given options: [15]
(Do not copy the questions , write the correct answers only)
i) If A= 2 0 B= x & C= 2
0 4 y -8, with the relation AB= C then the value of x and y respectively are
a) 1,-2 b) -2, 1 c) 1,2 d) - 2, -1 e) none
ii) If x -2 is a factor x³- Kx - 12, then the value of k is:
a) 3 b) 2 c) -2 d) -3
iii) In the given,
RT is a tangent touching the at S. If angle PST= 30° and angle SPQ= 60° Then angle PSQ is :
a) 40° b) 30° c) 60° d) 90°
iv) A letter is chosen random from all the letters of the English alphabets, The probability that the letter chosen is a vowel, is
a) 4/26 b) 5/26 c) 21/26 d) 5/24
v) If 3 is a root of the quadric equation x²- px +3= 0, then p is equal to:
a) 4 b) 3 c) 5 d) 2
vi) In the given figure
angle BAP= angle DCP= 70°, PC= 6cm and CA= 4cm, then PD: DB
a) 5:3 b) 3:5 c) 3:2 d) 2:3
vii) The printed price of an article is Rs3080. If the rate of GST is 10%, then the GST charged is:
a) Rs154 b) Ra308 c) Rs30.80 d) Rs15.40
viii) (1+ sinA)(1- sinA) is equal to:
a) cosec²A b) sin²A c) sec²A d) cos²A
ix) The coordinates of the vertices of ∆ ABC are respectively (-4,-2), (6,2) and (4,6). The centroid G of ∆ ABC is:
a) (2,2) b) (2,3) c) (3,3) d) (0,-1)
x) The n-th term of an arithmetic progression is 3n+ 5. The 10th term is:
a) 15 b) 25 c) 35 d) 45
xi) The mean proportional between 4 and 9 is:
a) 4 b) 6 c) 9 d) 36
xii) Which of the following cannot be determined graphically for a grouped frequency distribution ?
a) median b) mode c) quartiles d) mean
xiii) Volume of a cylinder of height 3 cm is 48 π cm³, Radius of the cylinder is:
a) 48cm b) 16 cm c) 4cm d) 24cm
xiv) Naveen deposits Rs800 every month in a recurring deposit account for 6 months. If he receives Rs4884 at the time of maturity, then the interest he earns is:
a) Rs84 b) Rs42 c) Rs24 d) Rs284
xv) The solution set for the equation 2x + 4 ≤ 14, x ∈ W is:
a) {1,2,3,4,5} b) {0,1, 2,3,4,5} c) {1, 2, 3, 4} d) {0, 1, 2, 3, 4}
Question 2:
i) Find the value of 'a' if x - a is a factor of the polynomial 3x³+ x²- ax - 81. [4]
ii) Salman deposits Rs100 every month in a recurring deposit account for 2 years. If he receives Rs2600 on maturity, find:
a) the total intrest Salman earns.
b) the rate of interest. [4]
iii) In the given figure,
O is the centre of the circle. CE is tangent to the circle at A. If angle ABD= 26°, then find:
a) angle BDA
b) angle BAD
c) Angle CAD
d) Angle ODB. [4]
Question 3
i) Solve the following quadratic equation : x²+ 4x - 8= 0. Give your answer correct to one decimal place. ( use mathematical tables if necessary). [4]
ii) Prove the following identity: (sin²x -1)(tan²x +1)+ 1= 0. [4]
iii) Use graph sheet to answer this question. Take 2cm = 1 unit along both the axes.
a) plot A, B, C, where A(0,4), B(1,1) and C(4,0)
b) Reflect A and B on the x-axis and name them as E and D respectively.
c) Reflect B through the origin and name it F. Write down the coordinates of F.
d) Reflect B and C on the y-axis and name them as H and G respectively.
e) join points A, B, C, D, E, F, G, H and A in order and name the closed figure formed. [5]
Section - B (40 Marks)
(Attempt any four questions from this section)
_______________________________________
Question 4
i) If A= 1 3 B= 1 2 C= 4 1 & D= 1 0
2 4 2 4 1 5 0 1
Find A(B+ C)- 14I. [3]
ii) ABC is a triangle whose vertices are A(1,-1), B(0,4) and C(-6,4). D is the midpoint of BC. Find the:
a) coordinates of D
b) the equation of the median AD. [3]
iii) In the given figure, O is the centre of the circle. PQ is a tangent to the circle at T. chord AB produced meets the tangent at P. 
AB= 9cm, BP=16cm, angle PTB= 50°, angle OBA= 45°
Find :
a) length of PT
b) angle BAT
c) angle BOT
d) angle ABT. [4]
Question 5:
i) Mrs Arora bought the following articles from a departmental store:
S. No Items Price rate of GST discount
1. hair oil Rs1200 18% Rs100
2. cashew nuts Rs600 12% --
Find the:
a) total GST paid.
b) total bill amount including GST. [3]
ii) Solve the following inequation. Write down the solution set and represent it on the real number.
-5(x -9)≥ 17 -9x > x+2, x ∈ R. [3]
iii) In the given figure,
AC || DE || BF.
If AC =24cm, EG= 8cm, GB= 16cm, BF= 30cm.
a) prove ∆ GED ~ ∆ GBF
b) Find DE
c) DB: AB. [4]
Question 6:
i) The following distribution gives the daily wages of 60 workers of a factory.
Daily income in Rs frequency
200-300 6
300-400 10
400-500 14
500-600 16
600-700 10
700-800 4
Use graph paper to answer this question.
Take 2 cm= Rs100 along one axis and 2cm =2workers along the other axis.
Draw a histogram and hence find the mode of the given distribution. [3]
ii) The 5th and 9th term of an Arithmetic progression are 4 and -12 respectively. Find :
a) the first term
b) common difference
c) sum of 16 terms of an AP . [3]
iii) A and B are the two points on the x-axis and y-axis respectively.
a) Write down the coordinates of A and B.
b) P is a point on AB such that AP: PB = 3:1. Using section formula find the coordinanates of point P.
c) Find the equation of a line passing through P and perpendicular to AB. [4]
Question 7:
i) A bag contains 25 cards numbered through 1 to 25. A card is drawn at random. What is the probability that the number on the card drawn is:
a) a multiple of 5.
b) a perfect square
c) A prime number ? [3]
ii) A man covers a distance of 100km, travelling with a uniform speed of x kmph. Had the speed bean 5 kmph more it would taken 1 hour less. Find x, the original speed. [3]
iii) A solid is in the shape of hemisphere of radius 7cm, surmounted by a cone of height 4 cm. The solid is immersed completly in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14 cm, find the rise in the water. [4]
Question 8:
i) The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution by using the shortcut method.
Marks number of students
00-10 3
10-20 8
20-30 14
30-40 9
40-50 4
50-60 2 [3]
ii) What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion ? [3]
iii) Using ruler and compass, construct a triangle ABC in which AB= 6cm, angle BAC= 120° and AC= 5cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle. [4]
Question 9:
i) Using componendo and dividendo solve for x:
{√(2x+2) + √(2x -1)}/{√(2x +2) - √(2x -1)}= 3. [3]
ii) Which term of the arithmetic progression(AP) 15, 30, 45, 60....is 300 ? Hence find the sum of all the terms of the arithmetic progression. [3]
iii) From the top of the tower 100m high a man observes the angles of depression of two ships A and B , on opposite sides of the tower as 45° and 30° respectively. if the foot of the tower and the ships are in the same horizontal line find the distance between the two ships A and B to the nearest metre. [4]
Question 10:
i) Factorise completely using factor theorem:
2x³- x²- 13x -6. [4]
ii) Use graph paper to answer this question.
During a medical checkup of 60 students in a school, weights were are recorded as follows: [6]
Weight (in kg) no of students
28-32 2
30-32 4
32-34 10
34-36 13
36-38 15
38-40 9
40-42 5
42-44 2
taking 2 cm 2 kg along one axis and 2cm= 10 students along the other axis, draw an ogive. Use your graph to find the
a) median
b) upper quartile
c) number Students whose weight is above 37 kg. [6]
Day- 11(14/8/24)
1) On What sum of money, the difference between 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.
5) Sita deposit Rs400 per month in a bank in recurring deposit. On maturity she gets Rs97854.40. Find the period of which she had deposited .
6) Which is the better investment 8% Rs100 shares at Rs 20 premium or 6% Rs100 shares at 20 discount?
7) A company declares a semi-annual dividend of 5%. Sanjay owns 25 shares of par value Rs12.50 each . How much annual dividend must he receive ?
8) A company having a capital stock of Rs 450000 declares a dividend of 4% semi-annually.
a) What is the annual income a stock holder owning 135 share at par of Rs 10 ?
b) What is the total amount of dividend paid annually by the company ?
9) Vinoy owns 150 Rs 25 shares of a company which declares a dividend of 12%. What is Vinay's dividend income? If he sells the shares at Rs40 and invests the proceeds in 7% stock (par value Rs100) at Rs80, what is the change in his dividend income ?
10) Mr Gupta purchased 360 Rs50 shares at Rs20 premium. The company declares an annual dividend 12%.
a) Find his dividend income from the shares.
b) Find his total investment in the shares.
11) A man invests Rs1426 in 5% stock at Rs115. He sells this stock at Rs125 and invests the proceeds in 3% stock at 93. Find the change in his income.
12) Solve : (11- 2x)/(9- 3x) ≥ 5/8, x ∈ R, x < 3.
13) Solve: 8/3 ≤ x + 1/3 < 10/3, x ∈ R. Hence represent the solution on a number lines.
14) A= {x: -1< x ≤ 5, x ∈ R}
B={x : -4 ≤ x < 3, x ∈ R}
Represent a) A ∩ B b) A' ∩ B on different number lines, where universal set is R.
15) Solve the equation 3x²- x - 7= 0 and give your answer correct to 2decimal places.
16) Find the roots of x²- 6x +2= 0, using formula method.
17) Find the roots of √3 x²- 9x + 6 √3= 0, using formula method.
18) Solve for x, (4x²-1) - 3(2x +1) + x(2x +1)= 0.
19) Solve for x, using formula method, x² - 1/x² = (29/10) (x - 1/x).
20) Solve the following quadratic equation: √(x +15) = x + 3, x ∈ N.
21) Solve: √(x(x -3))= √10, State sum of the roots.
22) Solve : √(6x -5) - √(3x -2)= 2 using formula method.
23) A two-digit number is 4 times the sum and two times the product of its digits . Find the number.
24) A says to B, ' I am twice as old as you were when I was old as you are'. If the product of their ages is 588. Find their present ages.
25) A number consists of two digits such that the square of the digit in the ten's place exceeds the digits in the unit place by 11. If the number is 5 times the sum of the digits, find the number.
26) 10 years ago, the sum of the ages of two sons was half of their father's age. The ratio of the present ages of the two sons is 4:3 and the sum of the present ages of all the three is 117 years. Find the present ages of the father and each of the two sons.
27) A party of students arranged an excursion costing Rs540, whose amount was to be shared equally by all of them. But later, it was found that three of the students, could not pay, though they had joined the excursion . As a result , the rest of the students had each to pay Rs2 more. Find the total number of students in the party.
28) In a certain examination, the those number of candidates passed was 4 times the number of those who failed. If the number of candidates that appeared had been 35 less, and the number been twice the number failing. Find the total number of candidates that appeared at the examination
Day-10(11/8/24)
PROBABILITY - TEST
1) A coin is tossed 500 times. We obtain a head 260 times. On tossing the coin at random, find the probability of getting
i)A head
a) 12/25 b) 13/25 c) 14/25 d) 16/25
ii) A tail
a) 12/25 b) 13/25 c) 14/25 d) 16/2
2) A die is rolled 50 times and the number 6 is obtained 8 times. Now, if the die is rolled at random, find the probability of getting the number 6.
a) a) 4/25 b) 13/25 c) 14/25 d) 16/25
3) There are 10 cards in a bag bearing numbers from 1 to 10. A card is drawn from the bag 60 times. Each time, the number obtained is noted and the card drawn is replaced. It was found that the card number bearing number 7 was drawn 4 times. Now, if a card is drawn at random, find the probability of getting the card bearing 7.
a) 1/15 b) 2/15 c) 4/15 d) 7/15
4) A die is rolled 100 times and the outcomes are noted and tabulated as shown :
Outcomes: 1 2 3 4 5 6
Frequency: 9 15 19 21 24 12
When a die is rolled at random, find the probability of getting the number
i) 2
a) 3/20 b) 21/100 c) 3/25 d) 6/25
ii) 4
a) 3/20 b) 21/100 c) 3/25 d) 6/25
iii) 6
a) 3/20 b) 21/100 c) 3/25 d) 6/25
ASSASSIN REASONS QUESTIONS:
DIRECTIONS: In the following questions , a statement of Assertion(A) is followed by a statement of Reason(R). Choose the correct option:
1) Assertion (A): A coin is tossed 16 times and the outcomes are recorded as below:
H T T H T H H H T T H T H T T H
The probability of occurrence of a both is 50% .
Reason : When a coin is tossed, there are two possible outcomes-- Head and Tail.
a) both Assertion (A) and Reason(R) are true and Reason(R) is the correct explanation of Assertion (A).
b) both Assertion (A) and Reason(R) are true and Reason(R) is not the correct explanation of Assertion (A).
c) Assertion (A) is true but Reason(R) is false.
d) Assertion (A) is false but Reason (R) is true.
2) Assertion (A): When a spinner with 3 colour Red(R), Green (G) and Black (B) as shown is rotated , red and green colours have equal probability to show up with arrow. 
Reason (R): The probability of occurrence of an event E is given by
P(E)= total number of trials/number of trials in which occurs
a) both Assertion (A) and Reason(R) are true and Reason(R) is not the correct explanation of Assertion (A).
b) both Assertion (A) and Reason(R) are true and Reason (R) is not correct explanation of Assertion (A).
c) Assertion (A) is true but Reason (R) is false
d) Assertion (A) is false but Reason (R) is true
Day- 9 (8/7/24)
1) From a pack of cards of 52 cards two are drawn at random. Find the chance that one is a knave and the other a queen.
2) Show that the chances of throwing six with 4,3 or 2 dice respectively are as 1:6:18
3) What is the chance of throwing a number greater than 4 with an ordinary die whose faces are numbered from 1 to 6 ?
4) Find the chance of throwing 9 atleast in a single throw with two dice.
5) From 20 tickets marked with the first 20 numerals, one is drawn at random, find the chance that it is a multiple of 3 or of 7 ?
Day- 8(24/6/24)
1) If x²= 3x, then
a) x= 0 b) x=0 or x=3 c) x=3 d) x=0 and x= 3
2) If 3x²+ 8= 10x, then
a) x= 2 or 4/3 b) x=2 or x=3 c) x=3 or 4/3 d) x=1 and x= 1/3
3) The quadratic equation whose solution set is {-2, 3} is
a) x²- 3x -6=0 b) x²- x + 6=0 c) x² +x -6=0 d) x²- x -6=0
4) One of the roots of 2x²- 7x +6=0, is
a) -2 b)2 c)!-3/2 d) 4
5) The discriminant of the quadratic equation 2x²- x +3 =0 is:
a) 24 b) 25 c) -23 d) -20
6) On solving x² +4x - 21=0, we get
a) x= -3, or -7 b) x=7 or -3 c) x =7 or 3 d) x =-7 or 3
7) The roots of the quadratic equation 2x² + x x - 1 =0 are
a) 1/2 or -1 b) -1/2 or 1 c) -1/2 or -1 d) 1/2 or 1
8) The discriminant of x²- 4x - 7 =0 is:
a) 44 b) √44 c) 12 d) -12
9) The quadratic equation whose roots are -1, -5 is:
a) x² +6x +5 =0 b) x²- 6x +5 =0 c) x²+ 6x - 5=0 d) x²- 6x - 5=0
10) For the equation 3x²- 4x - 2 =0, the roots are:
a) real and equal b) real and unequal c) imaginary d) both (a) and (b)
11) For the quadratic equation 2x²- 4x + 1 =0, the discriminant is:
a) 0 b) +ve c) -ve d) none
12) For the quadratic equation 2x²- 3x + 1 =0, the discriminant is:
a) 1 b) -1 c) 0 d) 9
13) For the quadratic equation 9x²+ 6x +1 =0, the discriminant is :
a) +ve b) -ve c) 0 d) imaginary
14) For the quadratic equation 2x² + ax - a²=0, the sum of the roots is:
a) a/2 b) -a/2 c) 2a d) -a
15) Given a quadratic equation mx²+ 8x -2 =0, m≠ 0. For this quadratic equation the value of discriminant is:
a) 64- 8m b) √(64+ 8m) c) 64+ 8m d) √(8m - 64)
16) For the quadratic equation 3x²+ 7x + 8 =0, the roots are:
a) real and distinct b) real and equal c) imaginary d) both (a) and (b)
17) The roots of the quadratic equation 2x²- kx + k =0 are equal . If k ∈N, then k is
a) 0 b) 8 c) 6 d) -6
18) Given the quadratic equation x² + 2√2x +1 =0. The roots of the quadratic equation are:
a) (-√2±1)/2 b) (√2±1)/2 c) (√2±1) d) (-√2±1)
19) The quadric equations (m +1)x² + 2(m +3)x +(m +8) =0. has equal roots. The value of m is :
a) 1/3 b) 1/4 c) 3 d) -3
20) The quadratic equation x² + m(2x + m -1)+ 2 =0 has equal roots . The value of m is
a) 1 b) 2 c) -2 d) 0
5/5/24 day- 7
1) Find the remainder when divided by 2x³- 3x²+ 7x - 8 is divided by x - 2. (2)
2) Solve: 21x²- 8x - 4 = 0. (2)
3) Find the coordinates of the image of (5,-4) after reflection in
a) x= 0
b) y= 2. (2)
4) List the solution set of the following inequation and graph the solution set:
1/2 + 8x > 5x - 3/2 p, x belongs to Z. (3)
5) Calculate the ratio in which the line joining A(6,5) and B(4,-3) is divided by the line y= 2. (2)
6) Given A= 1 1
8 3 evaluate A²- 3A. (3)
7) Show that: √{(1- cosx)/(1+ cosx)= sinx/(1+ cosx). (3)
8) Calculate the amount receivable on maturity of a recurring deposit of Rs800 every month for 5 years at 11% per annum. (3)
9) A and B are points on positive side of the x-axis and y axis respectively. The point P(4,3) divides the join of AB in the ratio 3:1. Find the equation the line AB. (2)
Day- 6
1) When 7x²- 3x +8 is divided by x -4, find the remainder (using remainder theorem (2)
2) If x∈ Z, find the solution set for the inequation 5 < 2x -3 ≤ 14 and graph the solution on a number line. (3)
3) Find p and q if g(x)= x +2 is a factor of f(x)= x³- 0x + x + q and f(2)= 4. (3)
4) Find the equation of a line that passes through (1,3) and slope is 3. (3)
5) The midpoint of the line joining A(2,p) and B(q,4) is (3,5). Find the numerical values of p and q. (3)
Day - 5
Find the value of x, which satisfies the inquation -2≤ 1/2 - 2x/3 ≤ 11/6, x ∈N.
Graph the solution set on the number line.
2) Solve the following inequation, write the solution set and represent it on the number line.
-3(x -7)≥ 15 - 7x > (x +1)/3, x ∈R
3) Solve the following inequation, write down the solution set and represent it on the real number line:
-2+ 10x ≤ 13x +10 < 24+ 10x, x ∈ Z
4) Solve the following inequation and write down the solution set:
11x - 4 < 15x +4 ≤ 13x + 14, x ∈ W
Represent the solution on a real number line.
5) Solve the given inequation and graph the solution set on the number line:
2y - 3 < y +1 ≤ 4y +7, y ∈ R
6) Solve the following inequation and represent the solution set on the number line:
2x -5 ≤ 5x +4 < 11, x ∈I
7) Solve the following inequation and write the solution set:
13x -5 < 15x +4 < 7x +12, x∈R
Day -4
1) If 2x - 7 < 4, where x is a natural number less than 8, than the solution set is:
a) {0,1,2,3,4} b) {1,2,3,4,5} c) {1,2,3,4,5,6} d) {0,1, 2,3,4,5,6}
2) If - x ≥ -3 then:
a) x≤ -3 b) x ≥ 3 c) x = 3 d) x ≤ 3
3) if 2 + 4 x< 2 x - 5 ≤ 3x ∈Z, then the solution set is :
a) {5,4} b) {- 5,-4} c) {- 5, -4, -3} d) {- 4,-3,-2,-1}
4) if 2≤2x - 3 ≤ 5, x∈ R, then the solution set is:
a) {2.5≤ x ≤ 4, x∈ R} b) {2≤ x ≤ 5, x∈ R} c) {3≤ x ≤ 5, x∈ R} d) {2< x < 4, x∈ R}
5) If a> b, then:
a) a - c ≤ b - c b) a - c≥ b - c c) a - c = b - c d) a - c > b - c
6) If x≥ 5 and- ax ≥ 5a, then :
a) a > 0 b) a < 0 c) both a and b d) neither a nor b
7) If x+1≥ 13 - 5x, x ∈{1,2,3,4.....10}, then the solution set is:
a) {1,2,3,4,5,6} b) {6,7,8,9,10} c) {7,8,9,10} d) {6,7,8.....}
8) If 7 - 5x ≥ 3x -1, then the solution set, when x ∈ W is:
a) {0,1} b) {0} c) {1} d) {0,1,2}
9) Given a >0, b >0, c >0 and d <0, then a < b implies :
a) a+ d> b + d b) a - d < b - d c) a - d > b - d d) a + d = b + d
10) Given 2x - 5≤ 5x +4 < 11. If x ∈ I, the solution set is:
a) {-2,-1,0,1} b) {-3,-2,-1,0,1} c) {-3,-2,-1,0} d) {-2,-1,0,1}
11) If 23> 3 + 4x ≥ -1, x ∈ R, then the greatest integer value of x is:
a) 5 b) 4 c) 3 d) 2
12) If 2x -3< x +1 ≤ 4x +7, x ∈ R, then the smallest integer value of x is:
a) -2 b) -1 c) 0 d) 1
13) If -9(x -7)≥ 45 - 21x > x +1, x ∈ R, then the solution set is:
a) {-3/2≤ x < 2, x ∈R}
b) {-3/2 < x < 2, x ∈R}
c) {-2/3 ≤ x ≤ 1, x ∈R}
d) {-1/3 ≤ x ≤ 2, x ∈R}
14) If 2x - 5 ≤ 5x + 4 < 11, x ∈ I, then the smallest whole number for x is:
a) 0 b) 1 c) -3 d) 2
15) If 5 - 3x < 11, x ∈ R, then the solution set is:
a) {x> -2, x∈R} b) {x≥ -2, x∈R} c) {x< 2, x∈R} d) {x< -2, x∈R}
16) Given 3x -1 ≤ x +5, x ∈N, then the solution set is:
a) {1,2,3} b) {1,2,3,4} c) {1,2} d) {0,1,2,3}
17) If 8 < 5(x +1) -2 ≤ 18, x ∈R, then the smallest integer value of x is:
a) 1 b) 0 c) -1 d) 2
18) Given a >0, b >0, c >0 and d <0. Then a > b implies:
a) ad >bd b) ad = bd c) ad < bd d) none
Day 3
Solve the following:
1) 35x²+ 13x -12=0.
2) mnx²+ (n²- m²)x - mn=0
3) x²- x - 42= 0.
Day- 2
1) Calculate, without actual division, the remainder when 5x³+8x²- 2x-9 is divided by x+2.
a) 6 b) 7 c) 8 d) 9 e) none
2) If f(x)= 24x³+ px²- 5x+ q has 8 factors 2x+1 and 3x-1, then find p and q. Also Factorise f(x) completely.
3) remainder if 2x³-3x²+7x-8 is divided by x-1
A) 2 B) -2 C) 3 D) -3
4) Find the number should be added with the number 2x²+3x+1 to make x-1 is the factor .
A) 6 B)-6 C) none D) none of these
5) If f(x)= 24x³ + px² - 5x +q has two factors 2x+1 and 3x-1, then find p and q.Also Factorise completely.
6) Factorise completely : x³ + x² - 4x -4.
7) find remainder when 3x³+ 5x²- 11x -4 is divided by 3x+1. (2)
e) When kx³+ 9x²+ 4x -10 is divided by (x+1), the remainder is 2. Find k.
8) Factorise completely: x³ - 3x² - 4x +12. (5)
Day- 1
a) 6 b) -6 c) -3 d) 0
2) If on dividing 4x²- 3kx +5 by x+2, the remainder is -3 then the value of k is
a) 4 b) -4 c) 3 d) -3
3) If on dividing 2x³+ 6x² - (2k -7)x+5 by x+ 3, the remainder is k -1 then the value of k is
a) 2 b) -2 c) -3 d) 3
4) The remainder when x⁵¹+ 51 is divided by x+1, is
a) 51 b) 50 c) -1 d) 0
5) The remainder when x²+ 2x +1 is divided by x +1 is
a) 4 b) 0 c) 1 d) -2
6) The remainder when f(x)= x³+ 4x²- 3x +1 is divided by x -2 is
a) 16 b) 12 c) 17 d) 19
4) If x+1 is a factor of 3x³+ kx²+ 7x +4, then the value of k is
a) -1 b) 0 c) 6 d) 10
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