The angle of depression of a boat from a \(50\sqrt { 3 } \) m high bridge is 30^o. The horizontal distance of the boat from the bridge is ___________

(sec A + tan A)(1 - sin A) is equal to ___________

If the probability of non-happening of an event is, then probability of happening of the event is ___________

The angle of elevation of a cloud from a point h metres above a lake is b. The angle of depression of its reflection in the lake is 45^o. The height of location of the cloud from the lake is ___________

Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the triangle is ____________

If \(\\ \\ \\ \\ \\ \\ \\ \left[ \begin{matrix} 4 & 3 & 2 \end{matrix} \right] \left[ \begin{matrix} 1 \\ -2 \\ x \end{matrix} \right] =\left[ 6 \right] \),then x is ___________

For what set of values \(\frac { { x }^{ 2 }+5x+6 }{ { x }^{ 2 }+8x+15 } \) is undefined ___________

Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

If a and b are the two positive integers when a > b and b is a factor of a then HCF (a, b) is ____________

If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

IF the probability of the non-happening of a event is q, then the probability of happening of that event is 

The value of the expression \(\left[ \frac { { sin }^{ 2 }{ 22 }^{ o }+{ sin }^{ 2 }{ 68 }^{ o } }{ { cos }^{ 2 }{ 22 }^{ 0 }+{ cos }^{ 2 }{ 68 }^{ 0 } } +{ sin }^{ 2 }{ 63 }^{ o+ }{ cos }63^{ 0 }{ sin27 }^{ 0 } \right] \)is ___________

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

7^4k \(\equiv \) ________ (mod 100)

A straight line has equation 8y = 4x + 21. Which of the following is true

If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

In the given figure, PR = 26 cm, QR = 24 cm, \(\angle PAQ\) = 90^o, PA = 6 cm and QA = 8 cm. Find \(\angle\)PQR

In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

The total surface area of a cylinder whose radius is \(\frac{1}{3}\)of its height is

Let f and g be two functions given by
f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

Graph of a linear equation is a ____________

The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is