SSLC (English Medium) इयत्ता १० - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Given the LCM and GCD of the two polynomials p(x) and q(x) find the unknown polynomial in the following table

If (x – 6) is the HCF of x² – 2x – 24 and x² – kx – 6 then the value of k is 

Find the least common multiple of xy(k² + 1) + k(x² + y²) and xy(k² – 1) + k(x² – y²)

Find the GCD of the following by division algorithm

2x⁴ + 13x³ + 27x² + 23x + 7, x³ + 3x² + 3x + 1, x² + 2x + 1

In ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC

If `"AD"/"DB" = 3/4` and AC = 15 cm find AE

In ∆ABC, D and E are points on the sides AB and AC respectively such that DE || BC

If AD = 8x – 7, DB = 5x – 3, AE = 4x – 3 and EC = 3x – 1, find the value of x

ABCD is a trapezium in which AB || DC and P, Q are points on AD and BC respectively, such that PQ || DC if PD = 18 cm, BQ = 35 cm and QC = 15 cm, find AD

In ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC

AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm

In ΔABC, D and E are points on the sides AB and AC respectively. For the following case show that DE || BC

AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm.

If PQ || BC and PR || CD prove that `"AR"/"AD" = "AQ"/"AB"`

If PQ || BC and PR || CD prove that `"QB"/"AQ" = "DR"/"AR"`

Rhombus PQRB is inscribed in ΔABC such that ∠B is one of its angle. P, Q and R lie on AB, AC and BC respectively. If AB = 12 cm and BC = 6 cm, find the sides PQ, RB of the rhombus.

In trapezium ABCD, AB || DC, E and F are points on non-parallel sides AD and BC respectively, such that EF || AB. Show that = `"AE"/"ED" = "BF"/"FC"`

DE || BC and CD || EE Prove that AD² = AB × AF

Check whether AD is bisector of ∠A of ∆ABC of the following
AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm

Check whether AD is bisector of ∠A of ∆ABC of the following

AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm.

∠QPR = 90°, PS is its bisector. If ST ⊥ PR, prove that ST × (PQ + PR) = PQ × PR

ABCD is a quadrilateral in which AB = AD, the bisector of ∠BAC and ∠CAD intersect the sides BC and CD at the points E and F, respectively. Prove that EF || BD.

Construct a ∆PQR in which the base PQ = 4.5 cm, ∠R = 35° and the median from R to RG is 6 cm.

Construct a ∆PQR in which QR = 5 cm, ∠P = 40° and the median PG from P to QR is 4.4 cm. Find the length of the altitude from P to QR.