Chapters
Chapter 3: Algebra
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.1 [Pages 92 - 93]
Solve the following system of linear equations in three variables
x + y + z = 5; 2x – y + z = 9; x – 2y + 3z = 16
Solve the following system of linear equations in three variables
`1/x - 2/y + 4 = 0; 1/y - 1/z + 1 = 0; 2/z + 3/x = 14`
Solve the following system of linear equations in three variables
x + 20 = `(3y)/2 + 10` = 2z + 5 = 110 – (y + z)
Discuss the nature of solutions of the following system of equations
x + 2y – z = 6; – 3x – 2y + 5z = – 12; x – 2z = 3
Discuss the nature of solutions of the following system of equations
2y + z = 3(– x + 1); – x + 3y – z = – 4; 3x + 2y + z = `-1/2`
Discuss the nature of solutions of the following system of equations
`(y + z)/4 = (z + x)/3 = (x + y)/2`; x + y + z = 27
Vani, her father and her grandfather have an average age of 53. One-half of her grandfather’s age plus one-third of her father’s age plus one-fourth of Vani’s age is 65. Four years ago if Vani’s grandfather was four times as old as Vani then how old are they all now?
The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the former number. If the hundreds digit plus twice the tens digit is equal to the units digit, then find the original three-digit number?
There are 12 pieces of five, ten and twenty rupee currencies whose total value is ₹ 105. When first 2 sorts are interchanged in their numbers its value will be increased by ₹ 20. Find the number of currencies in each sort
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.2 [Pages 96 - 97]
Find the G.C.D. of the given polynomials
x^{4} + 3x^{3} – x – 3, x^{3} + x^{2} – 5x + 3
Find the G.C.D. of the given polynomials
x^{4} – 1, x^{3} – 11x^{2} + x – 11
Find the G.C.D. of the given polynomials
3x^{4} + 6x^{3} – 12x^{2} – 24x, 4x^{4} + 14x^{3} + 8x^{2} – 8x
Find the G.C.D. of the given polynomials
3x^{3} + 3x^{2} + 3x + 3, 6x^{3} + 12x^{2} + 6x + 12
Find the L.C.M. of the given expressions
4x^{2}y, 8x^{3}y^{2}
Find the L.C.M. of the given expressions
– 9a^{3}b^{2}, 12a^{2}b^{2}c
Find the L.C.M. of the given expressions
16m, – 12m^{2}n^{2}, 8n^{2}
Find the L.C.M. of the given expressions
p^{2} – 3p + 2, p^{2} – 4
Find the L.C.M. of the given expressions
2x^{2} – 5x – 3, 4x^{2} – 36
Find the L.C.M. of the given expressions
(2x^{2} – 3xy)^{2}, (4x – 6y)^{3}, (8x^{3} – 27y^{3})
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.3 [Pages 97 - 98]
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
21x^{2}y, 35xy^{2}
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
(x^{3} – 1) (x + 1), (x^{3} + 1)
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
(x^{2}y + xy^{2}), (x^{2} + xy)
Find the LCM pair of the following polynomials
a^{2} + 4a – 12, a^{2} – 5a + 6 whose GCD is a – 2
Find the LCM pair of the following polynomials
x^{4} – 27a^{3}x, (x – 3a)^{2} whose GCD is (x – 3a)
Find the GCD pair of the following polynomials
12(x^{4} – x^{3}), 8(x^{4} – 3x^{3} + 2x^{2}) whose LCM is 24x^{3} (x – 1)(x – 2)
Find the GCD pair of the following polynomials
(x^{3} + y^{3}), (x^{4} + x^{2}y^{2} + y^{4}) whose LCM is (x^{3} + y^{3}) (x^{2} + xy + y^{2})
Given the LCM and GCD of the two polynomials p(x) and q(x) find the unknown polynomial in the following table
LCM | GCD | p(x) | q(x) |
a^{3} – 10a^{2} + 11a + 70 | a – 7 | a^{2} – 12a + 35 |
Given the LCM and GCD of the two polynomials p(x) and q(x) find the unknown polynomial in the following table
LCM | GCD | p(x) | q(x) |
(x^{4} – y^{4})(x^{4} + x^{2}y^{2} + y^{2}) | (x^{2} – y^{2}) | (x^{4} – y^{4})(x^{2} + y^{2} – xy) |
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.4 [Page 99]
Reduce the following rational expression to its lowest form
`(x^2 - 1)/(x^2 + x)`
Reduce the following rational expression to its lowest form
`(x^2 - 11x + 18)/(x^2 - 4x + 4)`
Reduce the following rational expression to its lowest form
`(9x^2 + 81x)/(x^3 + 8x^2 - 9x)`
Reduce the following rational expression to its lowest form
`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p")`
Find the excluded values, of the following expression
`y/(y^2 - 25)`
Find the excluded values, of the following expression
`"t"/("t"^2 - 5"t" + 6)`
Find the excluded values, of the following expression
`(x^2 + 6x + 8)/(x^2 + x - 2)`
Find the excluded values, of the following expression
`(x^3 - 27)/(x^3 + x^2 - 6x)`
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.5 [Page 101]
Simplify `(4x^2y)/(2z^2) xx (6xz^3)/(20y^4)`
Simplify `("p"^2 - 10"p" + 21)/("p" - 7) xx ("p"^2 + "p" - 12)/("p" - 3)^2`
Simplify `(5"t"^3)/(4"t" - 8) xx (6"t" - 12)/(10"t")`
Simplify `(x + 4)/(3x + 4y) xx (9x^2 - 16y^2)/(2x^2 + 3x - 20)`
Simplify `(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`
Simplify `(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
Simplify `("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
Simplify `(x + 2)/(4"y") ÷ (x^2 - x - 6)/(12y^2)`
Simplify `(12"t"^2 - 22"t" + 8)/(3"t") ÷ (3"t"^2 + 2"t" - 8)/(2"t"^2 + 4"t")`
If x = `("a"^2 + 3"a" - 4)/(3"a"^2 - 3)` and y = `("a"^2 + 2"a" - 8)/(2"a"^2 - 2"a" - 4)` find the value of x^{2}y^{–2 }
If a polynomial p(x) = x^{2} – 5x – 14 is divided by another polynomial q(x) we get `(x - 7)/(x + 2)`, find q(x)
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.6 [Page 103]
Simplify `(x(x + 1))/(x - 2) + (x(1 - x))/(x - 2)`
Simplify `(x + 2)/(x + 3) + (x - 1)/(x - 2)`
Simplify `(x^3)/(x - y) + (y^3)/(y - x)`
Simplify `((2x + 1)(x - 2))/(x - 4) - ((2x^2 - 5x + 2))/(x - 4)`
Simplify `(4x)/(x^2 - 1) - (x + 1)/(x - 1)`
Subtract `1/(x^2 + 2)` from `(2x^3 + x^2 + 3)/(x^2 + 2)^2`
Identify rational expression should be subtracted from `(x^2 + 6x + 8)/(x^3 + 8)` to get `3/(x^2 - 2x + 4)`
If A = `(2x + 1)/(2x - 1)`, B = `(2x - 1)/(2x + 1)` find `1/("A" - "B") - (2"B")/("A"^2 - "B"^2)`
If A = `x/(x + 1)` B = `1/(x + 1)` prove that `(("A" + "B")^2 + ("A" - "B")^2)/("A" + "B") = (2(x^2 + 1))/(x(x + 1)^2`
Pari needs 4 hours to complete the work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?
Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.7 [Page 105]
Find the square root of the following rational expression
`(400x^4y^12z^16)/(100x^8y^4z^4)`
Find the square root of the following rational expression
`(7x^2 + 2sqrt(14)x + 2)/(x^2 - 1/2 x + 1/16)`
Find the square root of the following rational expression
`(121("a" + "b")^8 (x + y)^8 ("b" - "c")^8)/(81("b" - "c")^4 ("a" - "b")^12 ("b" - "c")^4)`
Find the square root of the following
4x^{2} + 20x + 25
Find the square root of the following
9x^{2} – 24xy + 30xz – 40yz + 25z^{2} + 16y^{2 }
Find the square root of the following
`1 + 1/(x^6) + 2/(x^3)`
Find the square root of the following
(4x^{2} – 9x + 2)(7x^{2} – 13x – 2)(28x^{2} – 3x – 1)
Find the square root of the following
`(2x^2 + 17/6 x + 1) (3/2 x^2 + 4x + 2) (4/3 x^2 + 11/3 x + 2)`
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.8 [Page 106]
Find the square root of the following polynomials by division method
x^{4} – 12x^{3} + 42x^{2} – 36x + 9
Find the square root of the following polynomials by division method
37x^{2} – 28x^{3} + 4x^{4} + 42x + 9
Find the square root of the following polynomials by division method
16x^{4} + 8x^{2} + 1
Find the square root of the following polynomials by division method
121x^{4} – 198x^{3} – 183x^{2} + 216x + 144
Find the values of a and b if the following polynomial is a perfect square
4x^{4} – 12x^{3} + 37x^{2} + bx + a
Find the values of a and b if the following polynomial is a perfect square
ax^{4} + bx^{3} + 361x^{2} + 220x + 100
Find the values of m and n if the following polynomial is a perfect square
`1/(x^4) - 6/(x^3) + 13/(x^2) + "m"/x + "n"`
Find the values of m and n if the following polynomial is a perfect square
x^{4} – 8x^{3} + mx^{2} + nx + 16
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.9 [Page 109]
Determine the quadratic equation, whose sum and product of roots are – 9, 20
Determine the quadratic equation, whose sum and product of roots are `5/3, 4`
Determine the quadratic equation, whose sum and product of roots are `(-3)/2`, – 1
Determine the quadratic equation, whose sum and product of roots are – (2 – a)^{2}, (a + 5)^{2}
Find the sum and product of the roots for the following quadratic equation
x^{2} + 3x – 28 = 0
Find the sum and product of the roots for the following quadratic equation
x^{2} + 3x = 0
Find the sum and product of the roots for the following quadratic equation
`3 + 1/"a" = 10/"a"^2`
Find the sum and product of the roots for the following quadratic equation
3y^{2} – y – 4 = 0
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.10 [Page 111]
Solve the following quadratic equation by factorization method
4x^{2} – 7x – 2 = 0
Solve the following quadratic equation by factorization method
3(p^{2} – 6) = p(p + 5)
Solve the following quadratic equation by factorization method
`sqrt("a"("a" - 7)) = 3sqrt(2)`
Solve the following quadratic equation by factorization method
`sqrt(2)x^2 + 7x + 5sqrt(2)` = 0
Solve the following quadratic equation by factorization method
`2x^2 - x + 1/8` = 0
The number of volleyball games that must be scheduled in a league with n teams is given by G(n) = `("n"^2 - "n")/2` where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.11 [Page 114]
Solve the following quadratic equation by completing the square method
9x^{2} – 12x + 4 = 0
Solve the following quadratic equation by completing the square method
`(5x + 7)/(x - 1)` = 3x + 2
Solve the following quadratic equation by formula method
2x^{2} – 5x + 2 = 0
Solve the following quadratic equation by formula method
`sqrt(2)"f"^2 - 6"f" + 3sqrt(2)` = 0
Solve the following quadratic equation by formula method
3y^{2} – 20y – 23 = 0
Solve the following quadratic equation by formula method
36y^{2} – 12ay + (a^{2} – b^{2}) = 0
A ball rolls down a slope and travels a distance d = t^{2} – 0.75t feet in t seconds. Find the time when the distance travelled by the ball is 11.25 feet
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.12 [Pages 116 - 117]
If the difference between a number and its reciprocal is `24/5`, find the number
A garden measuring 12m by 16m is to have a pedestrian pathway that is ‘ω’ meters wide installed all the way around so that it increases the total area to 285 m^{2}. What is the width of the pathway?
A bus covers a distance of 90 km at a uniform speed. Had the speed been `(15"km")/"hour"` more it would have taken 30 minutes less for the journey. Find the original speed of the bus
A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages.
A pole has to be erected at a point on the boundary of a circular ground of diameter 20 m in such a way that the difference of its distances from two diametrically opposite fixed gates P and Q on the boundary is 4 m. Is it possible to do so? If answer is yes at what distance from the two gates should the pole be erected?
From a group of 2x^{2} black bees, square root of half of the group went to a tree. Again eight-ninth of the bees went to the same tree. The remaining two got caught up in a fragrant lotus. How many bees were there in total?
Music is been played in two opposite galleries with certain group of people. In the first gallery a group of 4 singers were singing and in the second gallery 9 singers were singing. The two galleries are separated by the distance of 70 m. Where should a person stand for hearing the same intensity of the singers voice?
(Hint: The ratio of the sound intensity is equal to the square of the ratio of their corresponding distances)
There is a square field whose side is 10 m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and gravelling the path at ₹ 3 and ₹ 4 per square metre respectively is ₹ 364. Find the width of the gravel path
The hypotenuse of a right angled triangle is 25 cm and its perimeter 56 cm. Find the length of the smallest side
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.13 [Page 119]
Determine the nature of the roots for the following quadratic equation
15x^{2} + 11x + 2 = 0
Determine the nature of the roots for the following quadratic equation
x^{2} – x – 1 = 0
Determine the nature of the roots for the following quadratic equation
`sqrt(2)"t"^2 - 3"t" + 3sqrt(2)` = 0
Determine the nature of the roots for the following quadratic equation
`9y^2 - 6sqrt(2)y + 2` = 0
Determine the nature of the roots for the following quadratic equation
9a^{2}b^{2}x^{2} – 24abcdx + 16c^{2}d^{2} = 0, a ≠ 0, b ≠ 0
Find the value of ‘k’ to identify the roots of the following equation is real and equal
(5k – 6)x^{2} + 2kx + 1 = 0
Find the value of ‘k’ to identify the roots of the following equation is real and equal
kx^{2} + (6k + 2)x + 16 = 0
If the roots of (a – b)x^{2} + (b – c)x + (c – a) = 0 are real and equal, then prove that b, a, c are in arithmetic progression
If a, b are real then show that the roots of the equation (a – b)x^{2} – 6(a + b)x – 9(a – b) = 0 are real and unequal
If the roots of the equation (c^{2} – ab)x^{2} – 2(a^{2} – bc)x + b^{2} – ac = 0 are real and equal prove that either a = 0 (or) a^{3} + b^{3} + c^{3} = 3abc
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.14 [Page 122]
Write the following expression in terms of α + β and αβ
`alpha/(3beta) + beta/(3alpha)`
Write the following expression in terms of α + β and αβ
`1/(alpha^2beta) + 1/(beta^2alpha)`
Write the following expression in terms of α + β and αβ
(3α – 1) (3β – 1)
Write the following expression in terms of α + β and αβ
`(alpha + 3)/beta + (beta + 3)/alpha`
The roots of the equation 2x^{2} – 7x + 5 = 0 are α and β. Without solving for the roots, find `1/alpha + 1/beta`
The roots of the equation 2x^{2} – 7x + 5 = 0 are α and β. Without solving for the roots, find `alpha/beta + beta/alpha`
The roots of the equation 2x^{2} – 7x + 5 = 0 are α and β. Without solving for the roots, find `(alpha + 2)/(beta + 2) + (beta + 2)/(alpha + 2)`
The roots of the equation x^{2} + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are α^{2} and β^{2}
The roots of the equation x^{2} + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are `2/alpha` and `2/beta`
The roots of the equation x^{2} + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are α^{2}β and β^{2}α
If α, β are the roots of 7x^{2} + ax + 2 = 0 and if β – α = `(-13)/7` Find the values of a
If one root of the equation 2y^{2} – ay + 64 = 0 is twice the other then find the values of a
If one root of the equation 3x^{2 }+ kx + 81 = 0 (having real roots) is the square of the other then find k
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.16 [Page 137]
Graph the following quadratic equation and state their nature of solution
x^{2} – 9x + 20 = 0
Graph the following quadratic equation and state their nature of solution
x^{2} – 4x + 4 = 0
Graph the following quadratic equation and state their nature of solution
x^{2} + x + 7 = 0
Graph the following quadratic equation and state their nature of solution
x^{2} – 9 = 0
Graph the following quadratic equation and state their nature of solution
x^{2} – 6x + 9 = 0
Graph the following quadratic equation and state their nature of solution
(2x – 3) (x + 2) = 0
Draw the graph of y = x^{2} – 4 and hence solve x^{2} – x – 12 = 0
Draw the graph of y = x^{2} + x and hence solve x^{2} + 1 = 0
Draw the graph of y = x^{2} + 3x + 2 and use it to solve x^{2} + 2x + 1 = 0
Draw the graph of y = x^{2} + 3x – 4 and hence use it to solve x^{2} + 3x – 4 = 0
Draw the graph of y = x^{2} – 5x – 6 and hence solve x^{2} – 5x – 14 = 0
Draw the graph of y = 2x^{2} – 3x – 5 and hence solve 2x^{2} – 4x – 6 = 0
Draw the graph of y = (x – 1) (x + 3) and hence solve x^{2} – x – 6 = 0
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.17 [Page 144]
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, write The number of elements
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, write The order of the matrix
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, Write the elements a_{22}, a_{23}, a_{24}, a_{34}, a_{43}, a_{44}
If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?
Construct a 3 × 3 matrix whose elements are given by a_{ij} = |i – 2j|
Construct a 3 × 3 matrix whose elements are given by a_{ij} = `("i" + "j")^3/3`
If A = `[(5, 4, 3),(1, -7, 9),(3, 8, 2)]` then find the transpose of A
If A = `[(sqrt(7), - 3),(- sqrt(5), 2),(sqrt(3), -5)]` then find the transpose of – A
If A = `[(5, 2, 2),(-sqrt(17), 0.7, 5/2),(8, 3, 1)]` then verify (A^{T})^{T} = A
Find the values of x, y and z from the following equation
`[(12, 3),(x, 3/2)] = [(y, z),(3, 5)]`
Find the values of x, y and z from the following equation
`[(x + y, 2),(5 + z, xy)] = [(6, 2),(5, 8)]`
Find the values of x, y and z from the following equation
`[(x + y + z),(x + z),(y + z)] = [(9),(5),(7)]`
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.18 [Pages 148 - 149]
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + B = B + A
If A = `[(1, 9),(3, 4),(8, -3)]`, B = `[(5, 7),(3, 3),(1, 0)]` then verify that A + (– A) = (– A) + A = 0
If A = `[(4, 3, 1),(2, 3, -8),(1, 0, -4)]`, B = `[(2, 3, 4),(1, 9, 2),(-7, 1, -1)]` and C = `[(8, 3, 4),(1, -2, 3),(2, 4, -1)]` then verify that A + (B + C) = (A + B) + C
Find X and Y if X + Y = `[(7, 0),(3, 5)]` and X – Y = `[(3, 0),(0, 4)]`
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of B – 5A
If A = `[(0, 4, 9),(8, 3, 7)]`, B = `[(7, 3, 8),(1, 4, 9)]` find the value of 3A – 9B
Find the values of x, y, z if `[(x - 3, 3x - z),(x + y + 7, x + y + z)] = [(1, 0),(1, 6)]`
Find the values of x, y, z if `[(x), (y – z), (z + 3)] + [(y), (4), (3)] = [(4), (8), (16)]`
Find x and y if `x[(4),(-3)] + y[(-2),(3)] = [(4),(6)]`
Find the non-zero values of x satisfying the matrix equation
`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`
Solve for x, y : `[(x^2),(y^2)] + 2[(-2x),(-y)] = [(5),(8)]`
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.19 [Pages 153 - 154]
Find the order of the product matrix AB if
(i) | (ii) | (iii) | (iv) | (v) | |
Order of A | 3 × 3 | 4 × 3 | 4 × 2 | 4 × 5 | 1 × 1 |
Order of B | 3 × 3 | 3 × 2 | 2 × 2 | 5 × 1 | 1 × 3 |
If A is of order p × q and B is of order q × r what is the order of AB and BA?
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
If A = `[(2, 5),(4, 3)]`, B = `[(1, -3),(2, 5)]` find AB, BA and verify AB = BA?
Given that A = `[(1, 3),(5, -1)]`, B = `[(1, -1, 2),(3, 5, 2)]`, C = `[(1, 3, 2),(-4, 1, 3)]` verify that A(B + C) = AB + AC
Show that the matrices A = `[(1, 2),(3, 1)]`, B = `[(1, -2),(-3, 1)]` satisfy commutative property AB = BA
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that A(BC) = (AB)C
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that (A – B)C = AC – BC
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that (A – B)^{T} = A^{T} – B^{T}
If A = `[(costheta, theta),(0, costheta)]`, B = `[(sintheta, 0),(0, sintheta)]` then show that A^{2} + B^{2} = I
If A = `[(costheta, sintheta),(-sintheta, costheta)]` prove that AA^{T} = I
Verify that A^{2} = I when A = `[(5, -4),(6, -5)]`
If A = `[("a", "b"),("c", "d")]` and I = `[(1, 0),(0, 1)]` show that A^{2} – (a + d)A = (bc – ad)I_{2}
If A = `[(5, 2, 9),(1, 2, 8)]`, B = `[(1, 7),(1, 2),(5, -1)]` verify that (AB)^{T} = B^{T} A^{T}
If A = `[(3, 1),(-1, 2)]` show that A^{2} – 5A + 7I_{2} = 0
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Exercise 3.20 [Pages 154 - 156]
Multiple choice questions
A system of three linear equation in three variables is inconsistent if their planes
intersect only at a point
intersect in a line
coincides with each other
do not intersect
The solution of the system x + y – 3z = – 6, – 7y + 7z = 7, 3z = 9 is
x = 1, y = 2, z = 3
x = – 1, y = 2, z = 3
x = – 1, y = – 2, z = 3
x = 1, y = − 2, z = 3
If (x – 6) is the HCF of x^{2} – 2x – 24 and x^{2} – kx – 6 then the value of k is
3
5
6
8
`(3y - 3)/y ÷ (7y - 7)/(3y^2)` is
`(9y)/7`
`(9y^3)/((21y - 21))`
`(21y^2 - 42y + 21)/(3y^3)`
`(7(y^2 - 2y + 1))/(y^2)`
`y^2 + 1/y^2` is not equal to
`(y^4 + 1)/(y^2)`
`(y + 1/y)^2`
`(y - 1/y)^2 + 2`
`(y + 1/2)^2 - 2`
`x/(x^2 - 25) - 8/(x^2 + 6x + 5)` gives
`(x^2 - 7x + 40)/((x - 5)(x + 5))`
`(x^2 + 7x + 40)/((x - 5)(x + 5)(x + 1))`
`(x^2 - 7x + 40)/((x^2 - 25)(x + 1))`
`(x^2 + 10)/((x^2 - 25)(x + 1))`
The square root of `(256x^8y^4z^10)/(25x^6y^6z^6)` is equal to
`16/5|(x^2z^4)/y^2|`
`16|y^2/(x^2z^4)|`
`16/5|y/(xz^2)|`
`16/5|(xz^2)/y|`
Which of the following should be added to make x^{4} + 64 a perfect square
4x^{2}
16x^{2}
8x^{2}
– 8x^{2}
The solution of (2x – 1)^{2} = 9 is equal to
– 1
2
– 1, 2
None of these
The values of a and b if 4x^{4} – 24x^{3} + 76x^{2} + ax + b is a perfect square are
100, 120
10, 12
– 120, 100
12, 10
If the roots of the equation q^{2}x^{2} + p^{2}x + r^{2} = 0 are the squares of the roots of the equation qx^{2} + px + r = 0, then q, p, r are in __________
A.P.
G.P.
Both A.P. and G.P.
none of these
Graph of a linear equation is a _______
straight line
circle
parabola
hyperbola
The number of points of intersection of the quadratic polynomial x^{2} + 4x + 4 with the X axis is
0
1
0 or 1
2
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix A^{T} is
2 × 3
3 × 2
3 × 4
4 × 3
If A is a 2 × 3 matrix and B is a 3 × 4 matrix, how many columns does AB have
3
4
2
5
If the number of columns and rows are not equal in a matrix then it is said to be a
diagonal matrix
rectangular matrix
square matrix
identity matrix
Transpose of a column matrix is
unit matrix
diagonal matrix
column matrix
row matrix
Find the matrix X if 2X + `[(1, 3),(5, 7)] = [(5, 7),(9, 5)]`
`[(-2, -2),(2, -1)]`
`[(2, 2),(2, -1)]`
`[(1, 2),(2, 2)]`
`[(2, 1),(2, 2)]`
Which of the following can be calculated from the given matrices A = `[(1, 2),(3, 4),(5, 6)]`, B = `[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`,
(i) A^{2}
(ii) B^{2}
(iii) AB
(iv) BA
(i) and (ii) only
(ii) and (iii) only
(ii) and (iv) only
all of these
If A = `[(1, 2, 3),(3, 2, 1)]`, B = `[(1, 0),(2, -1),(0, 2)]` and C = `[(0, 1),(-2, 5)]` Which of the following statements are correct?
(i) AB + C = `[(5, 5),(5, 5)]`
(ii) BC = `[(0, 1),(2, -3),(-4, 10)]`
(iii) BA + C = `[(2, 5),(3, 0)]`
(iv) (AB)C = `[(-8, 20),(-8, 13)]`
(i) and (ii) only
(ii) and (iii) only
(iii) and (iv) only
all of these
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board Chapter 3 Algebra Unit Exercise – 3 [Pages 156 - 157]
Solve `1/3` (x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)
One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections
In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number
Find the least common multiple of xy(k^{2} + 1) + k(x^{2} + y^{2}) and xy(k^{2} – 1) + k(x^{2} – y^{2})
Find the GCD of the following by division algorithm
2x^{4} + 13x^{3} + 27x^{2} + 23x + 7, x^{3} + 3x^{2} + 3x + 1, x^{2} + 2x + 1
Reduce the given Rational expression to its lowest form
`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4)`
Reduce the given Rational expression to its lowest form
`(10x^3 - 25x^2 + 4x - 10)/(-4 - 10x^2)`
Simplify `(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`
Arul, Madan and Ram working together can clean a store in 6 hours. Working alone, Madan takes twice as long to clean the store as Arul does. Ram needs three times as long as Arul does. How long would it take each if they are working alone?
Find the square root of 289x^{4} – 612x^{3} + 970x^{2} – 684x + 361
Solve `sqrt(y + 1) + sqrt(2y - 5)` = 3
A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hr, what is the speed of the boat in still water?
Is it possible to design a rectangular park of perimeter 320 m and area 4800 m^{2}? If so find its length and breadth.
At t minutes past 2 pm, the time needed to 3 pm is 3 minutes less than `("t"^2)/4`. Find t.
The number of seats in a row is equal to the total number of rows in a hall. The total number of seats in the hall will increase by 375 if the number of rows is doubled and the number of seats in each row is reduced by 5. Find the number of rows in the hall at the beginning.
If α and β are the roots of the polynomial f(x) = x^{2} – 2x + 3, find the polynomial whose roots are α + 2, β + 2
If α and β are the roots of the polynomial f(x) = x^{2} – 2x + 3, find the polynomial whose roots are `(alpha - 1)/(alpha + 1), (beta - 1)/(beta + 1)`
If – 4 is a root of the equation x^{2} + px – 4 = 0 and if the equation x^{2} + px + q = 0 has equal roots, find the values of p and q.
Two farmers Thilagan and Kausigan cultivates three varieties of grains namely rice, wheat and ragi. If the sale (in ₹) of three varieties of grains by both the farmers in the month of April is given by the matrix.
`{:("April sale in" ₹)/("rice" "wheat" "ragi"):}`
A = `[(500, 1000, 1500),(2500, 1500, 500)]"Thilagan"/"Kausigan"`
and the May month sale (in ₹) is exactly twice as that of the April month sale for each variety.
What is the average sales for the months of April and May
Two farmers Thilagan and Kausigan cultivates three varieties of grains namely rice, wheat and ragi. If the sale (in ₹) of three varieties of grains by both the farmers in the month of April is given by the matrix.
`{:"April sale in" ₹)/("rice" "wheat" "ragi":}`
A = `[(500, 1000, 1500),(2500, 1500, 500)]"Thilagan"/"Kausigan"`
and the May month sale (in ₹) is exactly twice as that of the April month sale for each variety.
If the sales continue to increase in the same way in the successive months, what will be sales in the month of August?
If `cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta[(x, -cos theta),(cos theta, x)]` = I_{2}, find x.
Given A = `[("p", 0),(0, 2)]`, B = `[(0, -"q"),(1, 0)]`, C = `[(2, -2),(2, 2)]` and if BA = C^{2}, find p and q.
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
Chapter 3: Algebra
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 3 - Algebra
Samacheer Kalvi solutions for Mathematics Class 10 SSLC Tamil Nadu State Board chapter 3 (Algebra) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Mathematics Class 10 SSLC Tamil Nadu State Board solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Mathematics Class 10 SSLC Tamil Nadu State Board chapter 3 Algebra are Introduction to Algebra, Simultaneous Linear Equations in Three Variables, GCD and LCM of Polynomials, Rational Expressions, Square Root of Polynomials, Quadratic Equations, Graph of Variations, Quadratic Graphs, Matrices.
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