If the degree of a polynomial AB is 15 and the degree of polynomial B is 5, then the degree of polynomial A is
(1) 3
(2) 8
(3) 4
(4) 10
The expression 21x2 + 11x – 2 equal to
(1) (x – 2) (7x + 1)
(2) (7x + 1) (3x – 2)
(3) (7x – 1) (3x – 1)
(4) (7x – 1) (3x + 2)
If the LCM and HCF of two polynomials are 90 m5a6b3x2 and m3 a5 respectively and also one of the monomial is 18 m5a6x2, then the other monomial is
(1) 5 m3a5b3
(2) 15 m5a3b2
(3) 5 m5a3b5
(4) 15 m3a5b4
The remainder when x3 – 3x2 + 5x – 1 is divided by x + 1 is ____________.
(1) –8
(2) –12
(3) –10
(4) –9
Which of the following is a homogeneous expression?
(1) 4x2 – 5xy + 5x2y + 10y2
(2) 5x + 10y + 100
(3) 14x3 + 15x2y + 16y2x + 24y3
(4) x2 + y2 + x + y + 1
Σx(y3 – z3) = __________.
(1) (x – y) (y – z) (z – x) (x + y + z)
(2) (x – y) (y – z) (x – z) (x – y – z)
(3) (x + y) (y + z) (z + x) (x + y + z)
(4) (x + y) (y + z) (z + x) (x – y – z)
The remainder when f(x) 4x3 – 3x2 + 2x – 1 is divided by 2x + 1 is ____________.
(1) 1
(2)
(3)
(4)
If the HCF of the polynomials 12a3b4c2, 18a4b3c3 and 24a6b2c4 is ________.
(1) 12a3b2c2
(2) 12a6b4c4
(3) 6a3b2c2
(4) 48a6b4c4
Find the value of a, if (x + 2) is a factor of the polynomial f(x) = x3 + 13x2 + ax + 20.
(1) –15
(2) 20
(3) 25
(4) 32
The polynomial x3 – 4x2 + x – 4 on factorization gives
(1) (x – 4) (x2 – 1)
(2) (x – 4) (x2 + 4)
(3) (x + 4) (x2 + 1)
(4) (x – 4) (x2 + 1)
If expression ax3 + 2x2y – bxy2 – 2y3 is symmetric, then (a, b) =
(1) (2, 2)
(2) (–2, 2)
(3) (–2, –2)
(4) (2, –2)
The square root of is
(1)
(2)
(3)
(4)
The product of the polynomial 2x3 – 3x2 + 6 and x2 – x is _________.
(1) 2x6 – 5x4 + 3x3 + 6x2 – 6x
(2) 2x5 – x4 + 3x3 – 6x2 + 6x
(3) 2x5 – 5x4 + 3x3 + 6x2 – 6x
(4) None of these
The LCM of x2 – 16 and 2x2 – 9x + 4 is
(1) (2x + 1) (x + 4) (x – 4)
(2) (x2 + 16) (2x + 1)
(3) 2(1 – 2x) (x + 4) (x – 4)
(4) (2x – 1) (x + 4) (x – 4)
If P = 3x3 – 5x + 9, Q = 4x3 + 5x2 – 11 and R = 5x3 + 4x2 – 3x + 7, then P – 2Q + R is
(1) 2(3x2 + 4x – 19)
(2) –6x2 – 5x + 38
(3) 2(3x2 + 4x + 19)
(4) – 2(3x2 + 4x – 19)
If g(x) = 3ax + 7a2b – 13ab2 + 9by is a homogeneous expression in terms of a and b, then the values of x and y respectively are _______.
(1) 2, 2
(2) 2, 1
(3) 3, 2
(4) 3, 3
The polynomial on factorization gives
(1)
(2)
(3)
(4)
If xn + 1 is divisible by x + 1, n must be.
(1) any natural number
(2) an odd natural number
(3) an even natural number
(4) None of these
What is the first degree expression to be subtracted from x6 + 8x4 + 2x3 + 16x2 + 4x + 5 in order to make it a perfect square?
(1) –4x – 4
(2) 4x + 4
(3) 4x – 4
(4) –4x + 4
Find the square root of .
(1)
(2)
(3)
(4) None of there
What is the first degree expression to be added to 16x6 + 8x4 – 2x3 + x2 + 2x + 1 in order to make it a perfect square?
(1)
(2)
(3)
(4)
Factorize the polynomial
(1)
(2)
(3)
(4)
The product of polynomials 3x3 – 4x2 + 7 and x2 +1 is
(1) 3x5 – 4x4 + 3x3 + 3x2 + 7
(2) x5 + 4x2 – 2x + 3
(3) 3x5 – 4x4 – 3x3 + 4x + 8
(4) 3x5 – 5x4 + 8x2 + 2x + 1
If LCM and HCF of two monomials is 60x4y5a6b6 and 5x2y3 respectively. If one of the two monomials is 15x4y3a6, then the other monomial is
(1) 12x2y3a6b6
(2) 20x4y5b6
(3) 20x2y5b6
(4) 15x2y5b6
Which of the following is a factor of the polynomial f(x) = 2x3 – 5x2 + x + 2?
(1) x + 1
(2) x + 2
(3) 2x + 1
(4) 2x – 1
If 3x – 1 is a factor of the polynomial 81x3 – 45x2 + 3a – 6, then a is __________.
(1)
(2)
(3)
(4)
If A = 4x3 – 5x + 7, B = 2x3 – x2 + 3 and C = 5x3 – 8x2 + 10, then A – 2B – C is
(1) 5x3 – 2x2 + x + 4
(2) –5x3 + 10x2 – 5x – 9
(3) x3 + 10x2 – 5x + 9
(4) 5x3 – 8x2 + x – 1
The square root of is
(1) xm+n
(2)
(3)
(4)
x831 + y831 is always divisible by
(1) x – y
(2) x2 + y2
(3) x + y
(4) None of these
If (x + 1) (x + 2) (x + 3) (x + k) + 1 is a perfect square, then the value of k is
(1) 4
(2) 5
(3) 6
(4) 7
If A = 6x4 + 5x3 – 14x2 + 2x + 2 and B = 3x2 – 2x – 1, then the remainder when A ÷ B is
(1) x
(2) 2x
(3) 3x
(4) 4x
The polynomial x5 – a2x3 – x2y3 + a2y3 on factorization gives
(1) (x – y) (x – a) (x + a) (x2 – y2 + xy)
(2) (x + a) (x – y) (x – a) (x2 – y2 + xy)
(3) (x + a) (x – y) (x – a) (x2 + y2 + xy)
(4) None of these
The HCF of the polynomials x4 + 6x2 + 25, x3 – 63x2 + 7x – 5 and x2 + 5 – 2x is
(1) x2 – 2x – 5
(2) x2 – 2x + 5
(3) x – 1
(4) 3x2 + 2
The HCF of the polynomials (2x – 1) (5x2 – ax + 3) and (x – 3) (2x2 + x + b) is (2x –1) (x – 3). Then the values of a and b respectively are _______.
(1) 16, –1
(2) –16, 1
(3) –16, –1
(4) 16, 1
The remainder when x45 is divided by x2 – 1 is
(1) 2x
(2) –x
(3) 0
(4) x
Factorize .
(1) (a – b)2 (b – c)2 (c – a)2
(2) (a – b) (a + b) (b – c) (b + c) (c – a) (c + a)
(3) (a + b)2 (b + c)2 (c + a)2
(4) None of these
The polynomial 6y4 – 19y2 + 23y2 + 10y + 8 on factorization gives
(1) (y + 1) (y – 4) (3y + 2) (2y + 1)
(2) (y + 1) (y – 4) (3y – 2) (2y – 1)
(3) (y + 1) (y – 4) (3y – 2) (2y + 1)
(4) (y + 1) (y – 4) (3y + 2) (2y – 1)
If the LCM of the polynomials (y – 3)a (2y + 1)b (y + 13)7 and (y – 3)4 (2y +1)9 (y + 13)c is (y – 3)6 (2y +1)10 (y + 13)17, then the least value of a + b + c is
(1) 23
(2) 3
(3) 10
(4) 16
If the LCM of the polynomials 195(x + 3)2 (x – 2) (x + 1)2 and 221(x + 1)3 (x +3) (x + 4) is __________.
(1) 221(x + 3)2 (x – 1)2 (x – 2) (x – 14)
(2) 13(x + 3) (x + 1)2
(3) 3315(x + 3)2 (x + 1)3 (x – 2) (x + 4)
(4) None of these
The what value of k the HCF of x2 + x + (5k – 1) and x2 – 6x + (3k +11) is (x – 2)?
(1) 2
(2) 2
(3) – 2
(4) – 1
The HCF of the polynomials 9(x + a)p (x – b)q (x + c)r and 12(x + a)p + 3 (x – b)q – 3 (x + c)r + 2 is 3(x + a)6 (x – b)6 (x + c)6 , then the value of p + q – r is
(1) 21
(2) 9
(3) 15
(4) 6
The remainders obtained when the polynomial x3 + x2 – 9x – 9 divided by x, x + 1 and x + 2 respectively are __________.
(1) – 9, 0, – 15
(2) – 9, – 16, 5
(3) 0, 0, 5
(4) – 9, 0, 5
Find the value of
(1) – 1
(2) 0
(3) 1
(4) 2
Find the square root of the expression
(1)
(2)
(3)
(4)
Factorize the expression
(1)
(2)
(3)
(4)
The following are the steps involved in factorizing 64x6 – y6. Arrange them in sequential order.
(A) {(2x)3 + y3}{(2x)3 – y3}
(B) (8x3)2 – (y3)2
(C) (8x3 + y3) (8x3 – y3)
(D) (2x + y) (4x2 – 2xy + y2) (2x – y) (4x2 + 2xy + y2)
(1) BADC
(2) BDAC
(3) BCAD
(4) BACD
If a + b + c = 0, show that a3 + b3 + c3 = 3abc. The following are the steps involved in showing the above result. Arrange them in sequential order.
(A) a3 + b3 + 3ab(–c) = –c3
(B) (a + b)3 = (–c)3
(C) a3 + b3 + 3ab(a + c) = –c3
(D) a3 + b3 + c3 = 3abc
(1) ABDCE
(2) BCDAE
(3) CBDAE
(4) CADBE
If the HCF of 8x3 ya and 12xby2 is 4xa yb, then find the maximum value of a + b.
(1) 2
(2) 4
(3) 6
(4) Cannot be determined
The polynomial 5x5 – 3x3 + 2x2 – k gives a remainder 1, when divided by x + 1. Find the value of k.
(1) 5
(2) –1
(3) 2
(4) 1
Factorize: a3 + b3 + 3abc – 1.
(1) (a + b – 1) (a2 + b2 + a + b + 1 – ab)
(2) (a + b – 1) (a2 + b2 + a + b – 1 + ab)
(3) (a + b – 1) (a2 + b2 – a – b + 1 + ab)
(4) None of these
If f and g are two polynomials of degrees 3 and 4 respectively, then what is the degree of f – g?
(1) 1
(2) 3
(3) 4
(4) Cannot be determined
Find the square root of .
(1)
(2)
(3)
(4)
The Square root of (xy + xz – yz)2 – 4xyz (x – y) is ____________.
(1) xy – yz – 2xyz
(2) (x + y – 2xy)
(3) (xy + 3 – y)
(4) ( xy + yz –zx)
_________.
(1)
(2)
(3)
(4)
= ______.
(1)
(2)
(3)
(4)
If , then which of he following is true?
(1) 2b = a – c
(2) 2a = b + c
(3) 2b = a + c
(4) 2x = c – a
Find the square root of the algebraic expression which is the average of the following expressions
(1)
(2)
(3)
(4) None of these
Find the square root of
(1)
(2)
(3)
(4)
_________.
(1) x3 – y3
(2) (x – y)3
(3) 2x3– 3x2y
(4) x3– 6xy2
Find the square root of (4a + 5b + 5c)2 – (5a + 4b + 4c)2 + 9a2.
(1)
(2) 3(b + c – a)
(3) 3(b + c)
(4) 3(b + c – a)
__________.
(1) a3 – b3
(2) (a + b)3
(3) a3 + b3
(4) (a – b)3
The square root of (3a + 2b + 3c)2 – (2a + 3b + 2c)2 + 5b2 is
(1)
(2)
(3)
(4)