If roots of `x^2-(a-3)x+a=0` are such that at least one of them is greater than 2, then `a in [7,9]` b. `a in [7,oo]` c. `a in [9,oo]` d. `a in [7,9]`

If no solution of 3siny+12sin^3x=a lies on the line y=3x , then (a) a in (-oo,-9)uu(9,oo) (b) a in [-9,9] (c) a in {-9,9} (d) none of these

If no solution of 3siny+12sin^3x=a lies on the line y=3x , then a in (-oo,-9)uu(9,oo) a a in [-9,9] a a in {-9,9} non eoft h e s e

For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is (-oo,-7]uu[1,oo) b. (-3,oo) c. (-oo,-7) d. [1,oo)

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

Show that 3x^9-10x^5+3x^4+2x^2+7=0 has at least 6 imaginary roots.

Which is greater: (9+7) xx 1000 or 9 + 7 xx 1000?

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

If alpha, beta, gamma are the roots of 9x^3 - 7x + 6 = 0 , then alpha beta gamma is …………

One diagonal of a square is along the line 8x-15 y=0 and one of its vertex is (1, 2). Then the equations of the sides of the square passing through this vertex are a. 23 x+7y=9,7x+23 y=53 b. 23 x-7y+9=0,7x+23 y+53=0 c. 23 x-7y-9=0,7x+23 y-53=0 d.none of these

If lim_(xrarr0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a) a=-3 and b=9/2 (b) a=3 and b=9/2 (c) a=-3 and b=-9/2 (d) a=3 and b=-9/2