Class 11th

Reaction of an inorganic sulphite X with dilute H₂SO₄ generates compound Y. Reaction of Y with NaOH gives X. Further, the reaction of X with Y and water affords compound Z. Y and Z respectively, are:

If the variance of the following frequency distribution :
Class : 10 – 20 20 – 30 30 – 40
Frequency : 2 x 2
is 50, then x is equal to:

Let PQ be a diameter of the circle x² + y² = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is.

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

Let a₁, a₂, . aₙ be a given A.P. whose common difference is an integer and Sₙ = a₁ + a₂ + … + aₙ. If a₁ = 1, aₙ = 300 and 15 ≤ n ≤ 50, then the ordered pair (Sₙ−₄, aₙ−₄) is equal to:

If the perpendicular bisector of the line segment joining the points P(1,4) and Q(k, 3) has y-intercept equal to -4, then a value of k is:

Let U(i=1 to n)Xᵢ = U(i=1 to 50)Yᵢ = T, where each Xᵢ contains 10 elements and each Yᵢ contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xᵢ 's and exactly 6 of sets Yᵢ 's then n is equal to:

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1/2. If P(1, β), β > 0 is a point on this ellipse, then the equation of the normal to it at P is:

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°, then PC (in m ) is equal to

Let f: (0,∞) → (0,∞) be a differentiable function such that f(1) = e and lim(t→x) (t²f²(x)-x²f²(t))/(t-x) = 0. If f(x) = 1, then x is equal to: