HSC Science इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Prove that one of the straight lines given by ax² + 2hxy + by² = 0 will bisect the angle between the coordinate axes if (a + b)² = 4h²

If the pair of straight lines x² – 2kxy – y² = 0 bisect the angle between the pair of straight lines x² – 2lxy – y² = 0, Show that the later pair also bisects the angle between the former

Prove that the straight lines joining the origin to the points of intersection of 3x² + 5xy – 3y² + 2x + 3y = 0 and 3x – 2y – 1 = 0 are at right angles.

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Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter `4 + 2sqrt(2)` is

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The coordinates of the four vertices of a quadrilateral are (−2, 4), (−1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (−1, 2) and dividing the quadrilateral in the equal areas is

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If the equation of the base opposite to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length of a side is

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The image of the point (2, 3) in the line y = −x is

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The length of ⊥ from the origin to the line `x/3 - y/4` = 1 is

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The area of the triangle formed by the lines x² – 4y² = 0 and x = a is

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If one of the lines given by 6x² – xy – 4cy² = 0 is 3x + 4y = 0, then c equals to ______.

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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`