List of practice Questions

Find the area of the triangle whose vertices are (-5, -1), (3, -5) and (5, 2).
Divide \(x^3 + 1\) by \(x + 1\).
Using Euclid's division algorithm, find the H.C.F. of 504 and 1188.
Find the discriminant of the quadratic equation \(2x^2 + 5x - 3 = 0\) and find the nature of the roots also.
Find two consecutive positive integers, sum of whose squares is 365.
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Write the equation for this statement.
In a triangle PQR, two points S and T are on the sides PQ and PR respectively such that \(\frac{PS}{SQ} = \frac{PT}{TR}\) and \(\angle PST = \angle PRQ\), then prove that \(\triangle PQR\) is an isosceles triangle.
If the radius of base of a cone is 7 cm and its height is 24 cm then find its curved surface area.
The length of the minute hand for a clock is 7 cm. Find the area swept by it in 40 minutes.
Prove that \(\tan 7^\circ \cdot \tan 60^\circ \cdot \tan 83^\circ = \sqrt{3}\).
Sides AB and BC and median AD of a \(\triangle ABC\) are respectively proportional to sides PQ and QR and median PM of another \(\triangle PQR\). Then prove that \(\triangle ABC \sim \triangle PQR\).
\(\triangle ABC\) and \(\triangle DEF\) are similar and their areas are 9 cm\(^2\) and 64 cm\(^2\) respectively. If DE = 5.1 cm then find AB.
Prove that \(\sqrt{\frac{1+\cos\theta}{1-\cos\theta}} = \frac{1+\cos\theta}{\sin\theta}\)
Prove that \(\tan 9^\circ \cdot \tan 27^\circ = \cot 63^\circ \cdot \cot 81^\circ\).
If \(\cos A = \frac{4}{5}\), then find the values of \(\cot A\) and \(\csc A\).
If \(\tan\theta = \frac{5}{12}\), then find the value of \(\sin\theta + \cos\theta\).
If \(\sin 3A = \cos(A - 26^\circ)\), where 3A is an acute angle, then find the value of A.
The sum of two numbers is 50 and one number is \(\frac{7}{3}\) times of the other; then find the numbers.
The ratio of the circumferences of two circles is 5:7; then the ratio of their radii is
\(7 \sec^2 A - 7 \tan^2 A =\)
If \(x = a \cos \theta\) and \(y = b \sin \theta\) then \(b^2x^2 + a^2y^2 =\)
The angle of elevation of the top of a tower at a distance of 10 m from its base is 60\(^\circ\); then the height of the tower is
A kite is at a height of 30 m from the earth and its string makes an angle 60\(^\circ\) with the earth. Then the length of the string is
E is a point on side CB produced of an isosceles \(\triangle ABC\) with AB = AC. If AD \(\perp\) BC and EF \(\perp\) AC, prove that \(\triangle ABD \sim \triangle ECF\).
If one zero of the quadratic polynomial \((k-1)x^2 + kx + 1\) is -4 then the value of k is