Mathematics
Saket wrote four different algebraic expressions in his notebook. These are . (1) Which of these expressions is/are binomials ? 1. f(x), g(x), h(x) only 2. f(x), g(x), k(y) only 3. f(x), h(x), k(y) only 4. f(x), h(x) only (2) Which of these expressions is/are not polynomials ? 1. f(x), g(x), h(x) only 2. f(x), h(x) only 3. g(x), h(x) only 4. h(x) only (3) Which of these expressions is/are polynomials in two variables ? 1. f(x) only 2. k(y) only 3. f(x), k(y) only 4. None of these (4) The degree of the polynomial f (x) is : 1. 0 2. 1 3. 2 4. 3
Related Questions
Fill in the blanks :
(i) The highest power of the …………… in a polynomial is called its degree.
(ii) The degree of the polynomial 75 is …………… .
(iii) Several parts of an algebraic expression separated by + or - signs are called the …………… of the expression.
(iv) Any number is a polynomial of degree …………… .
(v) Terms having the same …………… are called like terms.
(vi) The algebraic expression for the statement ‘the number of times b is contained in x' is …………… .
(vii) 1 + x + y + xy is a polynomial having …………… terms and degree ………….. .
(viii) The length of a side of a square having perimeter 8x2 - 2y + 16xy is …………… .
(ix) In a polynomial, the exponents of the variables are always …………… .
(x) If the length of a rectangle having perimeter (6 m2 - 2 mn + 2 m2n - 4n2) units, is (3m2 + m2n - 2 mn) units, then its breadth is equal to …………… units.
Write true (T) or false (F) :
(i) A literal can take on various numerical values.
(ii) 2a3b - a2b - 3a2b2 + 7ba2 - ba3 is a trinomial.
(iii) 3mn is a factor of -9mn2.
(iv) If we add a monomial and a trinomial, the answer can be a monomial.
(v) The coefficient of a2b in - 9a2b2c is -9bc.
(vi) The degree of the monomial 33 is 3.
Vasu has a rectangular farmland A. The length of this farmland is x2y - 2xy + 3x2 and its perimeter is 2x2y + 6x2 - 2xy - 4y2. Today he purchased the adjacent farmland B and combined the two farmlands into one. The length of his farmland now increased by x2 + xy, while the breadth remained the same.
(1) Find the breadth of farmland A :
- x2y + 3x2 - 4y2
- xy - 2y2
- 12x2 - 4xy
- 6x2 + xy - 2y2
(2) Find the length of the combined farmland owned by Vasu :
- x2 + 2xy - 2y2
- 4x2 - 3xy + x2y
- 4x2 - xy + x2y
- 2x2 - 3xy + x2y
(3) The perimeter of Vasu's combined farmland is :
- 8x2 + 2x2y - 4y2
- 4y2 + 4xy + 2x2y + 8x2
- 4x2 - 2x2y + 4y2
- 4x2 + 4xy - 2x2y - 8x2
(4) The change in the perimeter after combining farmlands A and B is :
- 4x2 + 2xy + 4x2y - y2
- 2x2 - 2xy + y2
- 4x2 + 2xy - y2
- 2x2 + 2xy
Assertion: The expression x + y - 2x is a trinomial.
Reason: An algebraic expression containing three terms is called a trinomial.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.