HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:
One of the equation of the lines given by x² + 2xy cot θ – y² = 0 is

Prove that the relation R defined on the set V of all vectors by `vec"a"  "R"  vec"b"`  if  `vec"a" = vec"b"` is an equivalence relation on V

Let `vec"a"` and `vec"b"` be the position vectors of the points A and B. Prove that the position vectors of the points which trisects the line segment AB are `(vec"a" + 2vec"b")/3` and `(vec"b" + 2vec"a")/3`

If D and E are the midpoints of the sides AB and AC of a triangle ABC, prove that `vec"BE" + vec"DC" = 3/2vec"BC"`

Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side whose length is half of the length of the third side

Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram

If `vec"a"` and `vec"b"` represent a side and a diagonal of a parallelogram, find the other sides and the other diagonal

If `vec"PO" + vec"OQ" = vec"QO" + vec"OR"`, prove that the points P, Q, R are collinear

If D is the midpoint of the aide BC of a triangle ABC, prove that `vec"AB" + vec"AC" = 2vec"AD"`

If G is the centroid of a triangle ABC, prove that `vec"GA" + vec"GB" + vec"GC" = vec0`

Let A, B, and C be the vertices of a triangle. Let D, E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that `vec"AD" + vec"BE" + vec"CF" = vec0`

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then Prove that `vec"AB" + vec"AD" + vec"CB" + vec"CD" = 4vec"EF"`

The position vectors of the vertices of a triangle are `hat"i" + 2hat"j" + 3hat"k", 3hat"i" - 4hat"j" + 5hat"k"` and `-2hat"i" + 3hat"j" - 7hat"k"`. Find the perimeter of the triangle

Show that the points A(1, 1, 1), B(1, 2, 3) and C(2, – 1, 1) are vertices of an isosceles triangle

Choose the correct alternative:
The value of `vec"AB" + vec"BC" + vec"DA" + vec"CD"` is

Choose the correct alternative:
If `vec"BA" = 3hat"i" + 2hat"j" + hat"k"` and the position vector of is `hat"i" + 3hat"j" - hat"k"`, then the position vector A is

Choose the correct alternative:
If `vec"a", vec"b"` are the position vectors A and B, then which one of the following points whose position vector lies on AB, is

Choose the correct alternative:
If `vec"r" = (9vec"a" + 7vec"b")/16`, then the point P whose position vector `vec"r"` divides the line joining the points with position vectors `vec"a"` and `vec"b"` in the ratio

Choose the correct alternative:
Two vertices of a triangle have position vectors `3hat"i" + 4hat"j" - 4hat"k"` and `2hat"i" + 3hat"j" + 4hat"k"`. If the position vector of the centroid is `hat"i" + 2hat"j" + 3hat"k"`, then the position vector of the third vertex is

Integrate the following with respect to x:

`(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)`