Q.15. The square of the distance of the point from the line along the line is equal to:

Q.3. Let be a complex number such that and . Then is equal to :

Q.12. is equal to :

Q.18. The area of the region bounded by the curves x + 3y= 0 and x + 4y = 1 is equal to :

Q.25. Let f be a twice differentiable function such that , . Then is equal to ________.

Q.23. Let A, B be points on the two half-lines x-, a > 0 at a distance of a from their point of intersection P. The line

Q.9. Let a focus of the ellipse E: be S(4,0) and its eccentricity be . If the point P(3, ) lies on E and O is the origi

Q.11. In an equilateral triangle PQR, let the vertex P be at (3, 5) and the side QR be along the line . If the orthocent

Q.47. Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the

Q.51. The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g)

Q.52. The first and second ionization constants of a weak dibasic acid are and respectively. 0.1 mol of was dissolve

Q.53. is isostructural with : Choose the correct answer from the options given below:

Q.56. At , 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the st

Q.57. Consider the reaction , for which the rate constant at is . Which of the following statements are true? A. When c