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

The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP

Write the n^th term of the sequence `3/(1^2 2^2), 5/(2^2 3^2), 7/(3^2 4^2), ...` as a difference of two terms

If t_k is the k^th term of a G.P., then show that t_{n – k}, t_n, t_{n + k} also form a GP for any positive integer k

If a, b, c are in geometric progression, and if `"a"^(1/x) = "b"^(1/y) = "C"^(1/z)`, then prove that x, y, z are in arithmetic progression

The AM of two numbers exceeds their GM by 10 and HM by 16. Find the numbers

If the roots of the equation (q – r)x² + (r – p)x + p – q = 0 are equal, then show that p, q and r are in AP

If a , b , c are respectively the p^th, q^th and r^th terms of a G . P show that (q – r) log a + (r – p) log b + (p – q) log c = 0

Choose the correct alternative:
If a, 8, b are in A.P, a, 4, b are in G.P, if a, x, b are in HP then x is

Choose the correct alternative:
The sequence = `1/sqrt(3), 1/(sqrt(3) + sqrt(2)), 1/(sqrt(3) + 2sqrt(2)) ...` form an

Choose the correct alternative:
The HM of two positive numbers whose AM and GM are 16, 8 respectively is

Choose the correct alternative:
The n^th term of the sequence 1, 2, 4, 7, 11, …… is

Choose the correct alternative:
The n^th term of the sequence `1/2, 3/4, 7/8, 15/16, ...` is

Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines

Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3

Find the distance between the line 4x + 3y + 4 = 0, and a point (−2, 4)

Find the distance between the line 4x + 3y + 4 = 0, and a point (7, −3)

Write the equation of the lines through the point (1, −1) parallel to x + 3y − 4 = 0

Write the equation of the lines through the point (1, −1) perpendicular to 3x + 4y = 6

If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal

Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and through the point (−1, 2)