QUESTION 03 \(\cos 30^{\text{o}} \sin 45^{\text{o}} \tan 60^{\text{o}} + \cos 135^{\text{o}} \sin 120^{\text{o}} \tan 150^{\text{o}} = \sqrt{m}\). The value...

QUESTION 02 When \(a = 3+2 \sqrt{2}\) and \(b = 3 - 2 \sqrt{2}\), then \(a^2 + b^2 =\)...

QUESTION 01 When \(\dfrac {a + b}{4} = \dfrac {b+c}{5} = \dfrac{c+a}{6}\), then ratio \(a : b : c...

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QUESTION 10B A triangle \(ABC\) on a plane satisfies \(AC = BC\) and \(\angle ACB = 90^{\circ}, DC =...

QUESTION 10A A triangle \(ABC\) on a plane satisfies \(AC = BC\) and \(\angle ACB = 90^{\circ}, DC =...

QUESTION 09 The equation of the tangent to the curve \(f(x) = -x^2 + x + 2\) at the...

QUESTION 08 Let M denote the midpoint of side BC of a triangle ABC. When \(BC = 8, CA...

QUESTION 07 Let \(\vec a = (1,0,-1), \vec b = (-2,2,1), \vec c = (x,y,z) \quad x > 0\)...

QUESTION 06 Let the sequence \(a_n\) (\(n = 1, 2, 3, \dots\)) be a geometric progression satisfying \(a_1 +...