Let S=a,b,c∈N×N×N:a+b+c=21,a≤b≤c and T=a,b,c∈N×N×N:a,b,c are in A.P where N is the set of all natural numbers. Then the number of elements in the set S∩T is.
A differentiable function f is satisfying the relation f(x+y)=f(x)+f(y)+2xy(x+y)−13∀x,y∈R and limh→03f(h)−16h=23. Then the value of [f(2)] is (where [x] represent the greatest integer function)______
Let S=θ∈(0,2π):7cos2θ-3sin2θ-2cos22θ=2. Then, the sum of roots of all the equations x2-2tan2θ+cot2θx+6sin2θ=0,θ∈S is_____.
Let the mean and the variance of 20 observations x1,x2,…,x20 be 15 and 9, respectively. For α∈R, if the mean of x1+α2,x2+α2,….,x20+α2 is 178, then the square of the maximum value of α is equal to______.
Let S={4,6,9} and T={9,10,11,…,1000}. If A=a1+a2+…+ak:k∈N,a1,a2,a3,…,ak∈S, then the sum of all the elements in the set T-A is equal to______.
Let W denote the words in the English dictionary. Define the relation R by : R=x,y∈W×W the words x and y have atleast one letter in common} then R is
If [.] denotes the greatest integer function then the number of points where f(x)=[x]+x+13+x+23 is discontinuous for x∈(0,3) are