(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

If A and B are complementary angles, prove that:

cot A cot B – sin A cos B – cos A sin B = 0

If A and B are complementary angles, prove that:

cosec² A + cosec² B = cosec² A cosec² B

If A and B are complementary angles, prove that:

`(sinA + sinB)/(sinA - sinB) + (cosB - cosA)/(cosB + cosA) = 2/(2sin^2A - 1)`

Find A, if 0° ≤ A ≤ 90° and 2 cos² A – 1 = 0

Find A, if 0° ≤ A ≤ 90° and sin 3A – 1 = 0

Find A, if 0° ≤ A ≤ 90° and 4 sin² A – 3 = 0

Find A, if 0° ≤ A ≤ 90° and cos² A – cos A = 0

Find A, if 0° ≤ A ≤ 90° and 2 cos² A + cos A – 1 = 0

If 0° < A < 90°; find A, if `sinA/(secA - 1) + sinA/(secA + 1) = 2`

Using remainder Theorem, factorise:

2x³ + 7x² − 8x – 28 Completely

Using the Reminder Theorem, factorise of the following completely.

2x³ + x² – 13x + 6

If x = −2 is a root of the equation 3x² + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x² + k(4x + k − 1) + p = 0 are equal.

Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`

Hence factorise the polynomial completely.

Using ruler and a compass only construct a semi-circle with diameter BC = 7cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.

Find the value of the discriminant in the following quadratic equation: 

2x² - 5x + 3 = 0 

Find the value of the discriminant in the following quadratic equation :

 x² +2x+4=0 

Find the value of the discriminant in the following quadratic equation: 

2x² - 3x + 1 = O 

Find the value of the discriminant in the following quadratic equation :

10 x - `1/x` = 3

Find the value of the discriminant in the following quadratic equation: 

x² +2x-2=0 

Find the value of the discriminant in the following quadratic equation :

`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`