Orthocenter

Q.

Shows that the locus of point of intersection of the lines xcosa+ycosa=p, xsina-ycosa=q, a is parameter, is a circle.

Q. The equation to the normal to the curve y = sin x at (0, 0) is

(a) x = 0
(b) y = 0
(c) x + y = 0
(d) x − y = 0

Q. If x, y, z are the distances of the vertices of triangle ABC from its orthocenter, then x+y+z = .

1. r+R
2. 2(r+R)
3. 2r+R
4. r+2R

Q. The equation of the normal to the curve y = x + sin x cos x at x = π/2 is

(a) x = 2
(b) x = π
(c) x + π = 0
(d) 2x = π

Q. The area bounded by the curve y = f (x), x-axis, and the ordinates x = 1 and x = b is
(b −1) sin (3b + 4). Then, f (x) is
(a) (x − 1) cos (3x + 4)
(b) sin (3x + 4)
(c) sin (3x + 4) + 3 (x − 1) cos (3x +4)
(d) none of these

Q. If x, y, z are the distances of the vertices of triangle ABC from its orthocenter, then x+y+z = .

1. r+R
2. 2(r+R)
3. 2r+R
4. r+2R

Q. If x, y, z are the distances of the vertices of triangle ABC from its orthocenter, then x+y+z = .

1. r+R
2. 2(r+R)
3. 2r+R
4. r+2R

Q. Find the equation of the tangent to the curve x = sin 3t, y = cos 2t at $t=\frac{\mathrm{\pi }}{4}$.

Q. The area bounded by the curve y = f (x), x-axis, and the ordinates x = 1 and x = b is
(b −1) sin (3b + 4). Then, f (x) is
(a) (x − 1) cos (3x + 4)
(b) sin (3x + 4)
(c) sin (3x + 4) + 3 (x − 1) cos (3x +4)
(d) none of these

Q. If $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}.$

Q. Show that the points A (1, −2, −8), B (5, 0, −2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Q. The equation of the normal to the curve y = x + sin x cos x at x = π/2 is

(a) x = 2
(b) x = π
(c) x + π = 0
(d) 2x = π

Q. The magnitudes of vectors A, B and C are 3, 4, and 5 units respectively. If vector A+B=C, the angle between vector A and B are A) pi/2 B)cos-1(0.6) C)tan-1(7/5) D)pi/4