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

In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being 5 particles on the first day. Find the day when the infectious virus particles just grow over 1,50,000 units?

Choose the correct alternative:
If ⁿC₁₀ > ⁿC_r for all possible r, then a value of n is

Choose the correct alternative:
The sum up to n terms of the series `sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) + ...` is

Find the combined equation of the straight lines whose separate equations are x − 2y − 3 = 0 and x + y + 5 = 0

Show that 4x² + 4xy + y² − 6x − 3y − 4 = 0 represents a pair of parallel lines

Show that 2x² + 3xy − 2y² + 3x + y + 1 = 0 represents a pair of perpendicular lines

Show that the equation 2x² − xy − 3y² − 6x + 19y − 20 = 0 represents a pair of intersecting lines. Show further that the angle between them is tan⁻¹(5)

Prove that the equation to the straight lines through the origin, each of which makes an angle α with the straight line y = x is x² – 2xy sec 2α + y² = 0

Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x − 3y + 1 = 0 and 5x + y − 3 = 0

Find the separate equation of the following pair of straight lines
3x² + 2xy – y² = 0

Find the separate equation of the following pair of straight lines
6(x – 1)² + 5(x – 1)(y – 2) – 4(y – 3)² = 0

Find the separate equation of the following pair of straight lines
2x² – xy – 3y² – 6x + 19y – 20 = 0

The slope of one of the straight lines ax² + 2hxy + by² = 0 is twice that of the other, show that 8h² = 9ab

The slope of one of the straight lines ax² + 2hxy + by² = 0 is three times the other, show that 3h² = 4ab

A ∆OPQ is formed by the pair of straight lines x² – 4xy + y² = 0 and the line PQ. The equation of PQ is x + y – 2 = 0, Find the equation of the median of the triangle ∆ OPQ drawn from the origin O

Find p and q, if the following equation represents a pair of perpendicular lines
6x² + 5xy – py² + 7x + qy – 5 = 0

Find the value of k, if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting, 12x² + 7xy − 12y² − x + 7y + k = 0

For what values of k does the equation 12x² + 2kxy + 2y² +11x – 5y + 2 = 0 represent two straight lines

Show that the equation 9x² – 24xy + 16y² – 12x + 16y – 12 = 0 represents a pair of parallel lines. Find the distance between them

Show that the equation 4x² + 4xy + y² – 6x – 3y – 4 = 0 represents a pair of parallel lines. Find the distance between them