Class 11th

A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1). If ∠BAC = 90°, and ar(?ABC) = 5√5 sq. units, then the abscissa of the vertex C is:

A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1). If ∠BAC = 90°, and ar(?ABC) = 5√5 sq. units, then the abscissa of the vertex C is:

Let u = (2z+i)/(z-ki), z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is:

Given the following two statements:
(S₁): (q∨p) → (p ↔~ q) is a tautology.
(S₂): ~ q∧ (~ p ↔ q) is a fallacy. Then:

If 1 + (1 − 2² . 1) + (1 − 4² • 3) + (1 − 6² · 5) + … . + (1 − 20² · 19) = α − 220β, then an ordered pair (α, β) is equal to:

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m ) above the line AC is:

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15, then the absolute difference of the remaining two observations is:

Let x²/a² + y²/b² = 1(a > b) be given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, φ(t) = 5/12 + t − t², then a² + b² is equal to:

Let α and β be roots of x² – 3x + p = 0 and y and δ be the roots of x² – 6x + q = 0. If α, β, γ, δ, form a geometric progression. Then ratio (2q + p): (2q – p) is:

A circular disc of mass M and radius R is rotating about its axis with angular speed ω₁. If another stationary disc having radius R/2 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω₂. The energy lost in the process is p% of the initial energy. Value of p is
(Rotational)