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A particle has an initial velocity $3i^+4j^ $ and an acceleration of $0.4i^+0.30j^ $. Its speed after 10s is

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If p and q are positive real numbers such that $p_{2}+q_{2}=1$, then the maximum value of $(p+q)$ is

The function $f:R{0}R$given by $f(x)=x1 −e_{2x}−12 $can be made continuous at x = 0 by defining f(0) as

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

In the binomial expansion of $(a−b)_{n},n≥5,$the sum of 5th and 6th terms is zero, then $ba $equals

Statement 1: The variance of first n even natural numbers is $4n_{2}−1 $Statement 2: The sum of first n natural numbers is $(n2n+1 $and the sum of squares of first n natural numbers is $(n(n+1)62n+1 $

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire -2 has cross-sectional area 3A. If the length of wire 1 increases by $Δx$ on applying force F, how much force is needed to stretch wire 2 by the same amount ?

If A, B and C are three sets such that $A∩B=A∩C$and $A∪B=A∪C$, then

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being