Class 12th

A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of any ellipse with eccentricity 1/3 and the distance of the nearer focus from this directrix is 8/√53, then the equation of the other directrix can be:

Three moles of AgCl get precipitated when one mole of an octahedral co-ordination compound with empirical formula CrCl?·3NH?·3H?O reacts with excess of silver nitrate. The number of chloride ions satisfying the secondary valency of the metal ion is ______.

Let X be a random variable such that the probability function of a distribution is given by P(X=0) = 1/2, P(X = j) = (1/3)? (j = 1,2,3,.∞). Then the mean of the distribution and P(X is positive and even) respectively are:

Let y = y(x) be solution of the differential equation logₑ(dy/dx) = 3x + 4y, with y(0) = 0.
If y(-2/3 logₑ2) = α logₑ2, then the value of α is equal to:

Let f: [-π/4, π/4] → R be defined as
f(x) = { (1 + |sin x|)³ᵃ/|sin x|, -π/4 < x < 0; b, x = 0; e^(cot 4x / cot 2x), 0 < x < /4 }
If f is continuous at x = 0, then the value of 6a + b² is equal to:

Consider the cell at 25°C
Zn | Zn²?(aq), (1M) Fe³?(aq), Fe²?(aq) | Pt(s)
The fraction of total iron present as Fe³? ion at the cell potential of 1.500V is x * 10?². The value of x is ______ (Nearest integer).
(Given: E?(Fe³?/Fe²?) = 0.77V, E?(Zn²?/Zn) = -0.76V)

Let the plane passing through the point (-1, 0, -2) and perpendicular to each of the planes 2x + y - z = 2 and x - y - z = 3 be ax + by + cz + 8 = 0. Then the value of a + b + c is equal to:

When 10 ml of an aqueous solution of Fe²? ions was titrated in the presence of dil H?SO? using diphenylamine indicator, 15 mL of 0.02 M solution of K?Cr?O? was required to get the end point. The molarity of the solution containing Fe²? ions is x * 10?²M. The value of x is ______. (Nearest integer)

If |a| = 2, |b| = 5 and |a * b| = 8, then a . b is equal to:

Let a = i + j + 2k and b = -i + 2j + 3k. Then the vector product (a + b) * ((a * ((a - b) * b)) * b) is equal to: