`3/4:1/2 27 y : ?` `12\ y` b. `18\ y` c. `21\ y` d. `24\ y` e. none of these

If 8% of x=4% of y, t h e n 20 % of x is a.10 % of y b. 80 % of y c. 16 % of y d. none of these

If earths rotational motion increases by 12% then the relation between a day and hours will be 12 hou r s=1 d a y b. 20 5/7 hou r s=1 d a y c. 21 3/7hou r s=1 d a y d. None of these

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

The solution of the differential equation y_1y_3=y_2^2 is a. x=C_1e^(C_2 \ y)+C_3 b. y=C_1e^(C_(2) \ x)+C_3 c. 2x=C_1e^(C_(2) \ y)+C_3 d. none of these

If (x,3) and (3,5) are the extremities of a diameter of a circle with centre at (2,y) then the values of x and y are a.(3,1) b.x=4,y=1 c.x=8,y=2d .none of these

The equations of the sides A B ,\ B C\ a n d\ C A\ of\ "Delta"A B C\ a r e\ y-x=2,\ x+2y=1\ a n d\ 3x+y+5=0 respectively. The equation of the altitude through B is x-3y+1=0 b. x-3y+4=0 c. 3x-y+2=0 d. none of these

If (x_1-x_2)^2+(y_1-y_2)^2=a^2, (x_2-x_3)^2+(y_2-y_3)^2=b^2, (x_3-x_1)^2+(y_3-y_1)^2=c^2, and k|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|=(a+b+c)(b+c-b)(c+a-b)xx(a+b-c) , then the value of k is 1 b. 2 c. 4 d. none of these

If y=sinm x , then the value of the determinant |y y_1y_2y_3y_4y_5y_6y_7y_8|,w h e r ey_n=(d^n y)/(dx^n) is m^9 b. m^2 c.m^3 d. none of these

If xy-log_(e)y=1 satisfies the equation x(yy_(2)+y_(1)^(2))-y_(2)+lambda yy_(1)=0, then lambda=-3 (b) 1 (c) 3 (d) none of these

If y=sinp xa n dy_n is the n t h derivative of y , then |[y, y_1,y_2],[y_3,y_4,y_5],[y_6,y_7,y_8]|i s (a)1 (b) 0 (c) -1 (d) none of these