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ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Chapter Test

Question 1.
Solve the inequation : 5x – 2 ≤ 3(3 – x) where x ∈ { – 2, – 1, 0, 1, 2, 3, 4}. Also represent its solution on the number line.
Solution:

Question 2.
Solve the inequations :
6x – 5 < 3x + 4, x ∈ I.
Solution:

Question 3.
Find the solution set of the inequation
x + 5 < 2 x + 3 ; x ∈ R
Graph the solution set on the number line.
Solution:

Question 4.
If x ∈ R (real numbers) and -1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.
Solution:

Question 5.
Solve the inequation :
\(\frac { 5x+1 }{ 7 } -4\left( \frac { x }{ 7 } +\frac { 2 }{ 5 } \right) \le 1\frac { 3 }{ 5 } +\frac { 3x-1 }{ 7 } ,x\in R\)
Solution:

Question 6.
Find the range of values of a, which satisfy 7 ≤ -4x + 2 < 12, x ∈ R. Graph these values of an on the real number line.
Solution:

Question 7.
If x ∈ R, solve \(2x-3\ge x+\frac { 1-x }{ 3 } >\frac { 2 }{ 5 } x\)
Solution:

Question 8.
Find positive integers which are such that if 6 is subtracted from five times the integer then the resulting number cannot be greater than four times the integer.
Solution:

Question 9.
Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is at least 3.
Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations MCQS

Choose the correct answer from the given four options (1 to 5):

Question 1.
If x ∈ { – 3, – 1, 0, 1, 3, 5}, then the solution set of the inequation 3x – 2 ≤ 8 is
(a) { -3, -1, 1, 3}
(b) { -3, -1, 0, 1, 3}
(c) { -3, -2, -1, 0, 1, 2, 3}
(d) { -3, -2, -1, 0, 1, 2}
Solution:

Question 2.
If x ∈ W, then the solution set of the inequation 3x + 11 ≥ x + 8 is
(a) { -2, -1, 0, 1, 2, …}
(b) { -1, 0, 1, 2, …}
(c) {0, 1, 2, 3, …}
(d) {x : x ∈ R, x ≥ \(– \frac { 3 }{ 2 } \)}
Solution:

Question 3.
If x ∈ W, then the solution set of the inequation 5 – 4x ≤ 2 – 3x is
(a) {…, -2, -1, 0, 1, 2, 3}
(b) {1, 2, 3}
(c) {0, 1, 2, 3}
(d) {x : x ∈ R, x ≤ 3}
Solution:

Question 4.
If x ∈ I, then the solution set of the inequation 1 < 3x + 5 ≤ 11 is
(a) { -1, 0, 1, 2}
(b) { -2, -1, 0, 1}
(c) { -1, 0, 1}
(d) {x : x ∈ R, \(– \frac { 4 }{ 3 } \) < x ≤ 2}
Solution:

Question 5.
If x ∈ R, the solution set of 6 ≤ – 3 (2x – 4) < 12 is
(a) {x : x ∈ R, 0 < x ≤ 1}
(b) {x : x ∈ R, 0 ≤ x < 1}
(c) {0, 1}
(d) none of these
Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4

Question 1.
Solve the inequation 3x – 11 < 3 where x ∈ {1, 2, 3,……, 10}. Also, represent its solution on a number line
Solution:

Question 2.
Solve 2(x – 3) < 1, x ∈ {1, 2, 3, …. 10}
Solution:

Question 3.
\(E=mc^2\)
Solve 5 – 4x > 2 – 3x, x ∈ W. Also represent its solution on the number line.
Solution:

Question 4.
List the solution set of 30 – 4 (2x – 1) < 30, given that x is a positive integer.
Solution:

Question 5.
Solve : 2 (x – 2) < 3x – 2, x ∈ { – 3, – 2, – 1, 0, 1, 2, 3} .
Solution:

Question 6.
If x is a negative integer, find the solution set of \(\\ \frac { 2 }{ 3 } \)+\(\\ \frac { 1 }{ 3 } \) (x + 1) > 0.
Solution:

Question 7.
Solve: \(\frac { 2x-3 }{ 4 } \ge \frac { 1 }{ 2 }\), x ∈ {0, 1, 2,…,8}
Solution:

Question 8.
Solve x – 3 (2 + x) > 2 (3x – 1), x ∈ { – 3, – 2, – 1, 0, 1, 2, 3}. Also represent its solution on the number line.
Solution:

Question 9.
Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9} solve x – 3 < 2x – 1.
Solution:

Question 10.
Given A = {x : x ∈ I, – 4 ≤ x ≤ 4}, solve 2x – 3 < 3 where x has the domain A Graph the solution set on the number line.
Solution:

Question 11.
List the solution set of the inequation
\(\\ \frac { 1 }{ 2 } \) + 8x > 5x \(– \frac { 3 }{ 2 } \), x ∈ Z
Solution:

Question 12.
List the solution set of \(\\ \frac { 11-2x }{ 5 } \) ≥ \(\\ \frac { 9-3x }{ 8 } \) + \(\\ \frac { 3 }{ 4 } \), x ∈ N
Solution:

Question 13.
Find the values of x, which satisfy the inequation : \(-2\le \frac { 1 }{ 2 } -\frac { 2x }{ 3 } \le 1\frac { 5 }{ 6 } \), x ∈ N. Graph the solution set on the number line. (2001)
Solution:

Question 14.
If x ∈ W, find the solution set of
\(\frac { 3 }{ 5 } x-\frac { 2x-1 }{ 3 } >1\)
Also graph the solution set on the number line, if possible.
Solution:

Question 15.
Solve:
(i)\(\frac { x }{ 2 } +5\le \frac { x }{ 3 } +6\) where x is a positive odd integer.
(ii)\(\frac { 2x+3 }{ 3 } \ge \frac { 3x-1 }{ 4 } \) where x is positive even integer.
Solution:

Question 16.
Given that x ∈ I, solve the inequation and graph the solution on the number line:
\(3\ge \frac { x-4 }{ 2 } +\frac { x }{ 3 } \ge 2 \) (2004)
Solution:

Question 17.
Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9}, find the values of x for which -3 < 2x – 1 < x + 4.
Solution:

Question 18.
Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N
Solution:

Question 19.
If x ∈ Z, solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.
Solution:

Question 20.
Solve the inequation = 12 + \(1 \frac { 5 }{ 6 } x\) ≤ 5 + 3x, x ∈ R. Represent the solution on a number line. (1999)
Solution:

Question 21.
Solve: \(\\ \frac { 4x-10 }{ 3 } \)≤\(\\ \frac { 5x-7 }{ 2 } \) x ∈ R and represent the solution set on the number line.
Solution:

Question 22.
Solve \(\frac { 3x }{ 5 } -\frac { 2x-1 }{ 3 } \) > 1, x ∈ R and represent the solution set on the number line.
Solution:

Question 23.
Solve the inequation – 3 ≤ 3 – 2x < 9, x ∈ R. Represent your solution on a number line. (2000)
Solution:

Question 24.
Solve 2 ≤ 2x – 3 ≤ 5, x ∈ R and mark it on a number line. (2003)
Solution:

Question 25.
Given that x ∈ R, solve the following inequation and graph the solution on the number line: -1 ≤ 3 + 4x < 23. (2006)
Solution:

Question 26.
Solve tlie following inequation and graph the solution on the number line. (2007)
\(-2\frac { 2 }{ 3 } \le x+\frac { 1 }{ 3 } <3+\frac { 1 }{ 3 } \) , x ∈ R
Solution:

Question 27.
Solve the following inequation and represent the solution set on the number line:
\(-3<-\frac { 1 }{ 2 } -\frac { 2x }{ 3 } \le \frac { 5 }{ 6 } ,x\in R\)
Solution:

Question 28.
Solve \(\frac { 2x+1 }{ 2 } +2(3-x)\ge 7,x\in R\). Also graph the solution set on the number line
Solution:

Question 29.
Solving the following inequation, write the solution set and represent it on the number line. – 3(x – 7) ≥ 15 – 7x > \(\\ \frac { x+1 }{ 3 } \), n ∈ R
Solution:

Question 30.
Solve the inequation :
\(-2\frac { 1 }{ 2 } +2x\le \frac { 4x }{ 3 } \le \frac { 4 }{ 3 } +2x,\quad x\in W\). Graph the solution set on the number line.
Solution:

Question 31.
Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line. (2011)
Solution:

Question 32.
If x ∈ I, A is the solution set of 2 (x – 1) < 3 x – 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩ B.
Solution:

Question 33.
If P is the solution set of -3x + 4 < 2x – 3, x ∈ N and Q is the solution set of 4x – 5 < 12, x ∈ W, find
(i) P ∩ Q
(ii) Q – P.
Solution:

Question 34.
A = {x : 11x – 5 > 7x + 3, x ∈ R} and B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}
Find the range of set A ∩ B and represent it on a number line
Solution:

Question 35.
Given: P {x : 5 < 2x – 1 ≤ 11, x ∈ R)
Q {x : – 1 ≤ 3 + 4x < 23, x ∈ I) where
R = (real numbers), I = (integers)
Represent P and Q on number line. Write down the elements of P ∩ Q. (1996)
Solution:

Question 36.
If x ∈ I, find the smallest value of x which satisfies the inequation \(2x+\frac { 5 }{ 2 } >\frac { 5x }{ 3 } +2\)
Solution:

Question 37.
Given 20 – 5 x < 5 (x + 8), find the smallest value of x, when
(i) x ∈ I
(ii) x ∈ W
(iii) x ∈ N.
Solution:

Question 38.
Solve the following inequation and represent the solution set on the number line:
\(4x-19<\frac { 3x }{ 5 } -2\le -\frac { 2 }{ 5 } +x,x\in R\)
Solution:

Question 39.
Solve the given inequation and graph the solution on the number line:
2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.
Solution:

Question 40.
Solve the inequation and represent the solution set on the number line.
\(-3+x\le \frac { 8x }{ 3 } +2\le \frac { 14 }{ 3 } +2x,Where\quad x\in I\)
Solution:

Question 41.
Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.
Solution:

Question 42.
One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.
Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 3 Shares and Dividends Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 3 Shares and Dividends Chapter Test

Question 1.
If a man received ₹1080 as dividend from 9% ₹20 shares, find the number of shares purchased by him.
Solution:

Question 2.
Find the percentage interest on capital invested in 18% shares when a Rs 10 share costs Rs 12.
Solution:

Question 3.
Rohit Kulkarni invests Rs 10000 in 10% Rs 100 shares of a company. If his annual dividend is Rs 800, find :
(i) The market value of each share.
(ii) The rate per cent which he earns on his investment.
Solution:

Question 4.
At what price should a 9% Rs 100 share be quoted when the money is worth 6%?
Solution:

Question 5.
By selling at Rs 92, some 2.5% Rs 100 shares and investing the proceeds in 5% Rs 100 shares at Rs 115, a person increased his annual income by Rs 90. Find:
(i) the number of shares sold.
(ii) the number of shares purchased.
(iii) the new income.
(iv) the rate per cent which he earns on his investment.
Solution:

Question 6.
A man has some shares of Rs. 100 par value paying a 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% Rs. 50 shares at a premium of Rs. 10. This transaction decreases his income from dividends by Rs. 120. Calculate:
(i) the number of shares before the transaction.
(ii) the number of shares he sold.
(iii) his initial annual income from shares.
Solution:

Question 7.
Divide Rs. 101520 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 50 shares at 8% premium, the annual incomes are equal.
Solution:

Question 8.
A man buys Rs. 40 shares of a company which pays a 10% dividend. He buys the shares at such a price that his profit is 16% on his investment. At what price did he buy each share?
Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 3 Shares and Dividends MCQS

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 3 Shares and Dividends MCQS

Question 1.
If Jagbeer invest ₹10320 on ₹100 shares at a discount of ₹ 14, then the number of shares he buys is
(a) 110
(b) 120
(c) 130
(d) 150
Solution:

Question 2.
If Nisha invests ₹19200 on ₹50 shares at a premium of 20%, then the number of shares she buys is
(a) 640
(b) 384
(c) 320
(d) 160
Solution:

Question 3.
₹ 40 shares of a company are selling at a 25% premium. If Mr Jacob wants to buy 280 shares of the company, then the investment required by him is
(a) ₹ 11200
(b) ₹ 14000
(c) ₹ 16800
(d) ₹ 8400
Solution:

Question 4.
Arun possesses 600 shares of ₹25 of a company. If the company announces a dividend of 8%, then Arun’s annual income is
(a) ₹ 48
(b) ₹ 480
(c) ₹ 600
(d) ₹ 1200
Solution:

Question 5.
A man invests ₹24000 on ₹60 shares at a discount of 20%. if the dividend declared by the company is 10%, then his annual income is
(a) ₹ 3000
(b) ₹ 2880
(c) ₹ 1500
(d) ₹ 1440
Solution:

Question 6.
Salman has some shares of ₹ 50 of a company paying a 15% dividend. If his annual income is ₹ 3000, then the number of shares he possesses is
(a) 80
(b) 400
(c) 600
(d) 800
Solution:

Question 7.
₹ 25 shares of a company are selling at ₹ 20. If the company is paying a dividend of 12%, then the rate of return is
(a) 10%
(b) 12%
(c) 15%
(d) 18%
Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 3 Shares and Dividends Ex 3

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 3 Shares and Dividends Ex 3

Question 1.
Find the dividend received on 60 shares of Rs, 20 each if 9% dividend is declared.
Solution:

Question 2.
A company declares 8 per cent dividend to the shareholders. If a man receives Rs. 2840 as his dividend, find the nominal value of his shares.
Solution:

Question 3.
A man buys 200 ten-rupee shares at Rs 12.50 each and receives a dividend of 8%. Find the amount invested by him and the dividend received by him in cash.
Solution:

Question 4.
Find the market price of 5% share when a person gets a dividend of Rs 65 by investing Rs. 1430.
Solution:

Question 5.
Salman buys 50 shares of face value Rs 100 available at Rs 132.
(i) What is his investment?
(ii) If the dividend is 7.5% p.a., what will be his annual income?
(iii) If he wants to increase his annual income by Rs 150, how many extra shares should he
Solution:

Question 6.
A lady holds 1800, Rs. 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return does she get on her investment? Give your answer to the nearest integer.
Solution:

Question 7.
What sum should a person invest in Rs 25 shares, selling at Rs 36, to obtain an income of Rs 720, if the dividend declared is 12%? Also, find the percentage return on his income.
(i) The number of shares bought by him.
(ii) The percentage return on his income.
Solution:

Question 8.
Ashok invests Rs 26400 on 12% Rs 25 shares of a company. If he receives a dividend of Rs 2475, find:
(i) the number of shares he bought.
(ii) the market value of each share. (2016)
Solution:

Question 9.
Amit Kumar invests Rs 36,000 in buying Rs 100 shares at Rs 20 premium. The dividend is 15% per annum. Find :
(i) The number of shares he buys
(ii) His yearly dividend
(iii) The percentage return on his investment.
Give your answer correct to the nearest whole number.
Solution:

Question 10.
Mr Tiwari invested Rs 29,040 in 15% Rs 100 shares at a premium of 20%. Calculate:
(i) The number of shares bought by Mr Tiwari.
(ii) Mr Tiwari’s income from the investment.
(iii) The percentage return on his investment.
Solution:

Question 11.
A man buys shares at the par value of Rs 10 yielding 8% dividend at the end of a year. Find the number of shares bought if he receives a dividend of Rs 300.
Solution:

Question 12.
A man invests Rs 8800 on buying shares of the face value of rupees hundred each at a premium of 10%. If he earns Rs 1200 at the end of the year as a dividend, find:
(i) the number of shares he has in the company.
(ii) the dividend percentage per share.
Solution:

Question 13.
A man invested Rs. 45000 in 15% Rs. 100 shares quoted at Rs. 125. When the market value of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8400. Calculate :
(i) the number of shares he still holds. (2004)
(ii) the dividend due to him on these shares.
Solution:

Question 14.
A company pays a dividend of 15% on its ten-rupee shares from which it deducts tax at the rate of 22%. Find the annual income of a man, who owns one thousand shares of this company.
Solution:

Question 15.
Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate.
(i) the dividend that Ajay will get.
(ii) the rate of interest, on his investment, if Ajay has paid Rs. 30 for each share. (2007)
Solution:

Question 16.
A company with 10000 shares of the nominal value of Rs. 100 declares an annual dividend of 8% to the shareholders.
(i) Calculate the total amount of dividend paid by the company.
(ii) Ramesh bought 90 shares of the company at Rs. 150 per share.
Calculate the dividend he received and the percentage return on his investment. (1994)
Solution:

Question 17.
A company with 4000 shares of the nominal value of Rs. 110 declares an annual dividend of 15%. Calculate :
(i) the total amount of dividend paid by the company,
(ii) the annual income of Shah Rukh who holds 88 shares in the company,
(iii) if he received only 10% on his investment, find the price Shah Rukh paid for each share. (2008)
Solution:

Question 18.
By investing in Rs. 7500 in a company paying 10 per cent dividend, an income of Rs. 500 is received. What price is paid for each Rs 100 share
Solution:

Question 19.
A man invests Rs. 8000 in a company paying 8% dividend when a share of the face value of Rs. 100 is selling at Rs. 60 premium,
(i) What is his annual income,
(ii) What per cent does he get on his money?
Solution:

Question 20.
A man buys 400 ten-rupee shares at a premium of Rs. 2.50 on each share. If the rate of dividend is 8%, Find,
(i) his investment
(ii) dividend received
(iii) yield.
Solution:

Question 21.
A man invests Rs. 10400 in 6% shares at Rs. 104 and Rs. 11440 in 10.4% shares at Rs. 143. How much income would he get in all?
Solution:

Question 22.
Two companies have shares of 7% at Rs. 116 and 9% at Rs. 145 respectively. In which of the shares would the investment be more profitable?
Solution:

Question 23.
Which is a better investment: 6% Rs. 100 shares at Rs. 120 or 8% Rs. 10 shares at Rs. 15
Solution:

Question 24.
A man invests Rs -10080 in 6% hundred- rupee shares at Rs. 112. Find his annual income. When the shares fall to Rs. 96 he sells out the shares and invests the proceeds in 10% ten-rupee shares at Rs. 8. Find the change in his annual income.
Solution:

Question 25.
A man bought 360 ten-rupee shares paying 12% per annum. He sold them when the price rose to Rs. 21 and invested the proceeds in five-rupee shares paying \(4 \frac { 1 }{ 2 }\) % per annum at Rs. 3.5 per share. Find the annual change in his income.
Solution:

Question 26.
A person invests Rs. 4368 and buys certain hundred-rupee shares at 91. He sells out shares worth Rs. 2400 when they have t risen to 95 and the remainder when they have fallen to 85. Find the gain or loss on the total transaction,
Solution:

Question 27.
By purchasing Rs. 50 gas shares for Rs. 80 each, a man gets a 4% profit on his investment. What rate per cent is company paying? What is his dividend if he buys 200 shares?
Solution:

Question 28.
Rs. 100 shares of a company are sold at a discount of Rs. 20. If the return on the investment is 15%. Find the rate of dividend declared
Solution:

Question 29.
A company declared a dividend of 14%. Find the tire market value of Rs. 50 shares if the return on the investment was 10%.
Solution:

Question 30.
At what price should a 6.25% Rs. 100 shares are quoted when the money is worth 5%?
Solution:

Question 31.
At what price should a 6.25% Rs. 50 share be quoted when the money is worth 10%?
Solution:

Question 32.
A company with 10000 shares of Rs. 100 each, declares an annual dividend of 5%.
(i) What is the total amount of dividend paid by the company?
(ii) What would be the annual income of a man, who has 72 shares, in the company?
(iii) If he received only 4% on his investment, find the price he paid for each share. (1998)
Solution:

Question 33.
A man sold some Rs. 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs. 100 shares paying a 16% dividend quoted at Rs. 80 and thus increased his income by Rs. 2000. Find the number of shares sold by him.
Solution:

Question 34.
By selling at Rs. 77, some \(2 \frac { 1 }{ 4 } \) % shares of face value Rs. 100, and investing the proceeds in 6% shares of face value Rs. 100, selling at 110, a person increased his income by Rs, 117 per annum. How many shares did he sell?
Solution:

Question 35.
A man invests Rs. 6750, partly in shares of 6% at Rs. 140 and partly in shares of 5% at Rs. 125. If his total income is Rs. 280, how much has he invested in each?
Solution:

Question 36.
Divide Rs. 20304 into two parts such that if one part is invested in 9% Rs. 50 shares at 8% premium and the other part are invested in 8% Rs. 25 shares at 8% discount, then the annual incomes from both the investment are equal
Solution:

ML Aggarwal Class 10 Solutions for ICSE Maths