problem archive
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Find the domain and the range of the real function f defined by f(x) = \sqrt{x - 1}. -
Find the domain and the range of the real function f defined by f(x) = |x - 1|. -
Let f = \left\{ \left( x, \frac{x^2}{1 + x^2} \right) : x \in \mathbb{R} \right\} be a function from \mathbb{R} into \mathbb{R}. Determine the range o... -
Let A = \{1, 2, 3, 4\}, B = \{1, 5, 9, 11, 15, 16\} and f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}. Are the following true? (i) f is a relation f... -
For functions f: X → R and g: X → R, we have (f + g)(x) = f(x) + g(x), x ∈ X (f - g)(x) = f(x) - g(x), x ∈ X (fg)(x) = f(x) . g(x), x ∈ X (kf)(x) = k ... -
Convert 40° 20' into radian measure. -
Convert 6 radians into degree measure. -
Find the radius of the circle in which a central angle of 60° intercepts an arc of length 37.4 cm (use π = 22/7). -
The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes? (Use π = 3.14). -
If the arcs of the same lengths in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii. -
Find the radian measures corresponding to the following degree measures: (i) 25° (ii) -47°30' (iii) 240° (iv) 520° -
Find the degree measures corresponding to the following radian measures (Use \(\pi = \frac{22}{7}\)). (i) \(\frac{11}{16}\) (ii) \(-4\) (iii) \(\frac{... -
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? -
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use \(\pi = \frac{22}{7}\)). -
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord. -
If in two circles, arcs of the same length subtend angles \(60^\circ\) and \(75^\circ\) at the centre, find the ratio of their radii. -
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 c... -
If \( \cos x = -\frac{3}{5} \), \( x \) lies in the third quadrant, find the values of other five trigonometric functions. -
If \( \cot x = - \frac{5}{12} \), \( x \) lies in second quadrant, find the values of other five trigonometric functions. -
Find the value of \( \sin \frac{31\pi}{3} \).