English Medium इयत्ता ९ - CBSE Question Bank Solutions

Find the remainder when x³ + 3x² + 3x + 1 is divided by x + π.

Find the remainder when x³ + 3x² + 3x + 1 is divided by 5 + 2x.

Find the remainder when x³ – ax² + 6x – a is divided by x – a.

Check whether 7 + 3x is a factor of 3x³ + 7x.

In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.

Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (See the given figure). Prove that

1. ΔABD ≅ ΔBAC
2. BD = AC
3. ∠ABD = ∠BAC.

AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.

l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.

Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:

1. ΔAPB ≅ ΔAQB
2. BP = BQ or B is equidistant from the arms of ∠A.

In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that

1. ΔDAP ≅ ΔEBP
2. AD = BE

In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:

1. ΔAMC ≅ ΔBMD
2. ∠DBC is a right angle.
3. ΔDBC ≅ ΔACB
4. CM = `1/2` AB

The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.