Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30o at B. The height (in m) of the lamp-post is -

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45o from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30o, then the distance (in m) of the foot of the tower from the point A is :

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot–1 (3$$\sqrt{2}$$ ) and cosec–1 (2$$\sqrt{2}$$ ) respectively, then the height of the tower (in metres) is :

Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of 15º with ground. Then the distance (in m) between the poles, is :-

Two vertical poles of heights, 20 m and 80 m stand a part on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is :

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30o and the angle of depression of reflection of the cloud in the lake from P be 60o, then the height of the cloud (in meters) from the surface of the lake is :

The term independent of x in the expansion of \left( {{1 \over {60}} - {{{x^8}} \over {81}}} \right).{\left( {2{x^2} - {3 \over {{x^2}}}} \right)^6} is equal to :

If 20C1 + (22) 20C2 + (32) 20C3 + ..... + (202 ) 20C20 = A(2$$\beta$$), then the ordered pair (A, $$\beta$$) is equal to :

The coefficient of x18 in the product (1 + x) (1 – x)10 (1 + x + x2)9 is :

The smallest natural number n, such that the coefficient of x in the expansion of {\left( {{x^2} + {1 \over {{x^3}}}} \right)^n} is nC23, is :

If the coefficients of x2 and x3 are both zero, in the expansion of the expression (1 + ax + bx2 ) (1 – 3x)15 in powers of x, then the ordered pair (a,b) is equal to :

If some three consecutive in the binomial expansion of (x + 1)n is powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficient is :-

If the fourth term in the binomial expansion of {\left( {{2 \over x} + {x^{{{\log }_8}x}}} \right)^6} (x > 0) is 20 × 87, then a value of x is :

If the fourth term in the binomial expansion of {\left( {\sqrt {{x^{\left( {{1 \over {1 + {{\log }_{10}}x}}} \right)}}} + {x^{{1 \over {12}}}}} \right)^6} is equal to 200, and x > 1, then the value of x is :

The sum of the co-efficients of all even degree terms in x in the expansion of $${\left(x+\sqrt{x^3-1}\right)}^6$$ + $${\left(x-\sqrt{x^3-1}\right)}^6$$, (x > 1) is equal to:

The sum of the series 2.20C0 + 5.20C1 + 8.20C2 + 11.20C3 + ... +62.20C20 is equal to :

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of {\left( {{2^{1/3}} + {1 \over {2{{\left( 3 \right)}^{1/3}}}}} \right)^{10}} is :

If the fractional part of the number \left\{ {{{{2^{403}}} \over {15}}} \right\} is \, {k \over {15}}, then k is equal to :

The coefficient of t4 in the expansion of {\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3} is :

If {\sum\limits_{i = 1}^{20} {\left( {{{{}^{20}{C_{i - 1}}} \over {{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \right)} ^3} = {k \over {21}} then k is equal to