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

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)`

Integrate the following with respect to x:

`4 cos(5 - 2x) + 9"e"^(3x  - 6) + 24/(6 - 4x)`

Integrate the following with respect to x:

`sec^2  x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)`

Integrate the following with respect to x:

`8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)`

Integrate the following with respect to x:

`6/(1 + (3x + 2)^2) - 12/sqrt(1 - (3 - 4x)^2`

Integrate the following with respect to x:

`1/3 cos(x/3 - 4) + 7/(7x + 9) + "e"^(x/5 + 3)`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"(bar"A")`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"("A" ∪ "B")`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"(bar"A" ∩ "B")`

If A and B are mutually exclusive events P(A) = `3/8` and P(B) = `1/8`, then find `"P"(bar"A" ∪ bar"B")`

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only B)

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find `"P"(bar"B")` 

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only A) 

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event, ‘second
die shows 5’. Find P(A ∪ B)