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ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories
Examples:
The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term.
Ans: a4= 0
⇒ a + 3d = 0
T.P a25= 3 (a11)
⇒ a + 24d = 3 (a + 10d)
⇒ a + 24d = 3a + 30d
RHS sub a = - 3d
- 3d + 24d = 21d
LHS 3a + 30d
- 9d + 30d = 21d
LHS = RHS Hence proved
How do you traverse a Binary Tree? Describe Preorder, Inorder and Postorder traversals with example. Ans: Traversal of tree means tree searching for a aim. The aim may be
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot
find the area bounded by the curve y=5x^2-4x+3 from the limit x=0 to x=5
We now focus on the use of Datalog for defining properties and queries m graphs. (a) Suppose that P is some property of graphs definable in Datalog. Show drat P is preserved und
-7-5
1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
Independent and Dependent Events Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event
For inequalities we contain a similar notation. Based on the complexity of the inequality the solution set might be a single number or it might be a range of numbers. If it is jus
Explain Linear Equations ? Set of ordered pairs of numbers A set is an undefined term and we describe it as a "well defined" collection. We use the symbol "{ }" to denote "a se
i needed help with algebra
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