Archives

If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then (A) a = -7, b = -1 (B) a = 5, b = -1 (C) a = 2, b = – 6 (D) a = 0, b = – 6

Solution (D)a = 2, b = – 6 option (D) is the correct answer. Explanation: According to the given details we... View Article

A quadratic polynomial, whose zeroes are -3 and 4, is (A) x² – x + 12 (B) x² + x + 12 (C) (x²/2)-(x/2)-6 (D) 2x² + 2x -24

Solution (C) (x2/2)-(x/2)-6 option (C) is the correct answer. Explanation: Sum of zeroes, α+ β= -3+4 =1 Product of Zeroes,... View Article

If one of the zeroes of the quadratic polynomial (k-1) x² + k x + 1 is -3, then the value of k is (A) 4/3 (B) -4/3 (C) 2/3 (D) -2/3

Solution (A) 4/3 option (A) is the correct answer. Explanation: According to thegiven details -3 is one of the zeros of quadratic... View Article

Prove that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer.

Given that n, n + 2 and n + 4 three integer where n is any positive integer To Prove One and only one out of n, n + 2 and n + 4 is... View Article

Show that the cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.

Given that Positive integer of the form 6q + r, q is an integer To Prove The cube of a positive integer of the form 6q + r, q is an... View Article

Prove that if x and y are both odd positive integers, then x² + y² is even but not divisible by 4.

Given that x and y are both odd positive integers To Prove x2 + y2 is even but not divisible by 4 Proof Let the two odd positive... View Article

Show that the square of any odd integer is of the form 4q + 1, for some integer q.

Given that Any integer m To Prove We need to prove that the square of any odd integer is of the form 4q + 1, Proof Let a be any odd integer... View Article

Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

Given that Any integer m To Prove We need to prove that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any... View Article

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.

Given that Some integer q To Prove We need to prove that the square of any positive integer cannot be of the form 5q + 2 or 5q... View Article

Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

Given that Some integer m To Prove We need to prove that the cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some... View Article

Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

Given that Some integer q To Prove We need to prove that he square of any positive integer is either of the form 4q or 4q + 1 for some... View Article

A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify your answer.

Solution: No, its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m. Justification Consider the positive... View Article

Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

Solution: No, the square of any positive integer cannot be written in the form 3m + 2 where m is a natural number Justification: According to... View Article

M	T	W	T	F	S	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31

Archives

If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then (A) a = -7, b = -1 (B) a = 5, b = -1 (C) a = 2, b = – 6 (D) a = 0, b = – 6

A quadratic polynomial, whose zeroes are -3 and 4, is (A) x² – x + 12 (B) x² + x + 12 (C) (x²/2)-(x/2)-6 (D) 2x² + 2x -24

If one of the zeroes of the quadratic polynomial (k-1) x² + k x + 1 is -3, then the value of k is (A) 4/3 (B) -4/3 (C) 2/3 (D) -2/3

Prove that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer.

Show that the cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.

Prove that if x and y are both odd positive integers, then x² + y² is even but not divisible by 4.

Show that the square of any odd integer is of the form 4q + 1, for some integer q.

Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.

Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.

Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.

A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, i.e., 3m or 3m + 2 for some integer m? Justify your answer.

Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.

“The product of two consecutive positive integers is divisible by 2”. Is this statement true or false? Give reasons.

Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is (A) 4 (B) 2 (C) 1 (D) 3

n² – 1 is divisible by 8, if n is (A) an integer (B) a natural number (C) an odd integer (D) an even integer

For some integer q, every odd integer is of the form (A) q (B) q +1 (C) 2g (D) 2q +1

For some integer m, every even integer is of the form: (A) m (B) m +1 (C) 2m (D) 2m+1

Explain some harmful effects of agricultural practices on the environment.

FREE TEXTBOOK SOLUTIONS