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

Integrate the following functions with respect to x:

`"e"^(8 - 7x)`

Integrate the following functions with respect to x:

`1/(6 - 4x)`

Integrate the following functions with respect to x:

`sec^2  x/5`

Integrate the following functions with respect to x:

cosec(5x + 3) cot(5x + 3)

Integrate the following functions with respect to x:

30 sec(2 – 15x) tan(2 – 15x)

Integrate the following functions with respect to x:

`1/sqrt(1 - (4x)^2`

Integrate the following functions with respect to x:

`1/sqrt(1 - 81x^2)`

Integrate the following functions with respect to x:

`1/sqrt(1 + 36x^2)`

Choose the correct alternative:

If `int f"'"(x)"e"^(x^2) "d"x = (x - 1)"e"^(x^2) + "c"`, then`f(x)` is

Construct a quadratic equation with roots 7 and −3

A quadratic polynomial has one of its zeros `1 + sqrt(5)` and it satisfies p(1) = 2. Find the quadratic polynomial

If α and β are the roots of the quadratic equation `x^2 + sqrt(2)x + 3` = 0, form a quadratic polynomial with zeroes `1/α, 1/β`

If one root of k(x − 1)² = 5x − 7 is double the other root, show that k = 2 or −25

If the difference of the roots of the equation 2x² − (a + 1)x + a − 1 = 0 is equal to their product, then prove that a = 2

Find the condition that one of the roots of ax² + bx + c may be negative of the other

Find the condition that one of the roots of ax² + bx + c may be thrice the other

Find the condition that one of the roots of ax² + bx + c may be reciprocal of the other

If the equations x² − ax + b = 0 and x² − ex + f = 0 have one root in common and if the second equation has equal roots, then prove that ae = 2(b + f)

Discuss the nature of roots of − x² + 3x + 1 = 0

Discuss the nature of roots of 4x² − x − 2 = 0