Archives

If A, B where 0° < A, B < 180° and Sin A+ Sin B = √(3/2), cos A + cos B = √(1/2), then what is the value of (A+B) ?

Given, Sin A + Sin B = √(3/2) 2 sin(A+B)/2 cos(A-B)/2 = √(3/2) ..........(i) Also, given, cos A + cos B =... View Article

A cardboard of size 18 cm x 18 cm, two colour papers say pink and blue, pair of dice, empty box, pair of scissors, sketch pens, fevicol, etc.

Given, A cardboard of size 18 cm x 18 cm, two colour papers say pink and blue, pair of dice, empty box, pair of scissors, sketch pens,... View Article

Suppose is a 3 × 3 matrix. If for every column vector X, X^T AX=0 and a_23 =−1008,then the sum of the digits of a_32 is:

XTAX = 0 XTAX = (XTAX)T = XTATX = -XTAX = XTAX = 0 Therefore, XTATX = -XTAX AT = -A a23 = -a32 or a32 = -a23 a32 = - (-1008) = 1008 Sum... View Article

The value of 4(cos² 60° + cos²45°-sin 30°) is:

4(cos² 60° + cos²45°)-sin2 30° = 4(1/2)2 + 4(1/√2)² - (√3/2)² = 1 + 2 - 3/4 = 3 - 3/4 = 9/4... View Article

Find all three-digit numbers with different digits, with each digits odd.

Total number of digits are 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Total number of odd digits = 5 A three digit number is 100a+10b+c Here, a = 5, b... View Article

Let A and B be two non-singular matrices such that A⁶ = I and AB² = BA (B ≠ I). If B^m = I (where I is the identity matrix), then the least value of m is:

Answer: A square matrix (m = n) that is not invertible is called singular or degenerate. A square matrix is singular if and only if its... View Article

The edges of a triangular board are 3m, 4m and 5m. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 10 per sq m.

Length, breadth and height of a room are 5m, 4m and 3m, respectively. Area of four walls of the room = 2h(l+b) = 2 × 3(5+4) =... View Article

If I1, I2, I3 are excentres of the triangle with vertices (0,0), (5,12), (16, 12) then find the orthocentre of ∆I1I2I3.

Given, I1, I2, I3 are the excentres of a triangle ABC. The vertices of ∆ABC are (0,0), (5,12) and (16, 12). Orthocenter... View Article

Two poles of height 6m and 11m stand on a plane ground of the distance between their feet 12m, find the distance between their tops.

Given, Heights of the poles are 6m and 11m respectively. Distance between their foot = 12m Suppose AB and CD are two poles of 11 m and 6 m... View Article

M	T	W	T	F	S	S
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17	18	19	20	21	22	23
24	25	26	27	28	29	30
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Archives

If A, B where 0° < A, B < 180° and Sin A+ Sin B = √(3/2), cos A + cos B = √(1/2), then what is the value of (A+B) ?

A cardboard of size 18 cm x 18 cm, two colour papers say pink and blue, pair of dice, empty box, pair of scissors, sketch pens, fevicol, etc.

Suppose is a 3 × 3 matrix. If for every column vector X, X^T AX=0 and a_23 =−1008,then the sum of the digits of a_32 is:

The value of 4(cos² 60° + cos²45°-sin 30°) is:

Find all three-digit numbers with different digits, with each digits odd.

Let A and B be two non-singular matrices such that A⁶ = I and AB² = BA (B ≠ I). If B^m = I (where I is the identity matrix), then the least value of m is:

The edges of a triangular board are 3m, 4m and 5m. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 10 per sq m.

If I1, I2, I3 are excentres of the triangle with vertices (0,0), (5,12), (16, 12) then find the orthocentre of ∆I1I2I3.

Two poles of height 6m and 11m stand on a plane ground of the distance between their feet 12m, find the distance between their tops.

If ƒ(x) = a(x² – 1)(ax b), a ≠ 0 has local maximum and minimum at x1 and x2 respectively, then f'(x) is:

arctan x/√(a² – x²) = ?

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