In how many ways can the letters of the word ENGINEERING be arranged?

There are 11 letters in the word ENGINEERING and E occurs 3 times, I occurs 2 times, N occurs 3 times and G occurs 2 times Thus, the required number of arrangements = (11!)/(3! x 2! x 2! x 3!) = 2,77,200 ways

If 1 + sin 2θ = p

^{2}and sin^{3}θ + cos^{3}θ = q then Which of the following is true ?The Value of (sin38˚)/(cos52˚)+ (cos12˚)/(sin78˚)- 4cos²60˚ is

tan 4˚ × tan 43˚ × tan 47˚ × tan 86˚ = ?

If P, Q, R, S are the vertex of a cyclic quadrilateral. Find the value of

`1/sec p` +`1/sec q` +`1/sec r` +`1/sec s`

...If A + B = 45

^{0}, then the value of 2(1 + tanA) (1 + tanB) is:If 7sin²θ + 3cos²θ = 4, then find the value of θ?

If SecA + TanA = 2√2 + 9, then find the value of Sin A + Cos A.

If secθ + tanθ = 3+√10, then the value of sinθ+cosθ is

If 4sin² θ = 3(1+ cos θ), 0° < θ < 90°, then what is the value of (2tan θ + 4sinθ - secθ)?

What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

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