List of practice Questions

A straight line \(y = x - 1\) intersects a circle with center at \(x = 1, y = 1\) and radius of magnitude 1 at two points. The length of the chord formed by this intersection is ________. (rounded off to three decimal places)

If the straight lines given by the following two equations are parallel to each other, the value of \(a\) is _____. (answer in integer) \[ 4x + 7y = 6; \quad 3ax + 42y = 24 \]

If the slope of the straight line joining the points \((2,3)\) and \((5,7)\) is \(m\), then \(9m^2=\)

If the point \(P(a,b)\) divides the line joining the points \(A(-3,4)\), \(B(5,2)\) internally in the ratio \(2:3\), then \(b-a=\)

If angles of a triangle are \((x+10)^\circ\), \((2x+5)^\circ\) and \((3x-15)^\circ\), then the value of \(x\) is

Among the following, the point that does not lie on the circle with centre at origin and radius \(3\) cm is

The radii of two concentric circles with centre \(O\) are \(10\) cm and \(6\) cm. If chord \(AB\) of the larger circle is tangent to the smaller circle, then the distance (in cm) of chord \(AB\) from centre \(O\) is

Which of the following cannot be the sides of a triangle ?

For which of the following figures, diagonals don't bisect each other?

The angle which makes a linear pair with an angle of \(61^{\circ}\) is :

If \(\triangle ABC \sim \triangle DEF\) such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then the perimeter of \(\triangle ABC\) is :

In \(\triangle ABC\) & \(\triangle PQR\), if \(AB = QR\), \(BC = PR\) and \(CA = PQ\), then :

In the proof of BPT (\(DE \parallel BC\) in \(\triangle ABC\)), since \(\triangle BDE\) and \(\triangle CDE\) have equal areas, the ratio AD/DB is shown to be equal to ________.

In \(\triangle ABC\), D lies on AB and E lies on AC such that AD = 2 cm, DB = 3 cm, AE = 4 cm and EC = 6 cm. By the converse of the Basic Proportionality Theorem, ________.

In \(\triangle ABC\) and \(\triangle PQR\), \(\angle A = \angle P\) and \(\angle B = \angle Q\). If AB = 4 cm, BC = 6 cm and PQ = 8 cm, then QR is

In \(\triangle ABC\) and \(\triangle DEF\), \(\angle A = \angle D\). For \(\triangle ABC \sim \triangle DEF\) by the SAS similarity criterion, the additional condition required is

In the proof of the Basic Proportionality theorem for \(\triangle ABC\) with \(DE \parallel BC\) (on AB, E on AC), the construction made is to join ________.

In the given figure, O is the centre of the circle and PQ & PR are the tangents to the circle such that OQ = 8 cm and OP = 17 cm, then the length of the tangent PQ is :

Match the postulates in List-I with List-II.

Kartik has three solid objects — a cone, a hemisphere, and a cylinder. All three have the same base radius and the same height. He completely immerses each solid in a bucket full of water. What is the ratio of the volumes of the cylinder: cone: hemisphere?

Kritika has three solid objects cone, hemisphere, cylinder. All have same base radius and height. Then the ratio of volume of cylinder : cone : hemisphere is

In the adjoining figure, the slant height of the conical part is :

A rectangular field is to be fenced on three sides leaving one side measuring 20 feet uncovered by fencing. If the area of the field is 680 sq ft, how many feet of fencing is required?

A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is \(10\sqrt{3}\) m away from the base of the tower, is :

If TP and TQ are two tangents to a circle with centre O from an external point T so that \(\angle POQ = 120^\circ\), then \(\angle PTQ\) is equal to :