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

Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%.

Calculate:

1. The dividend that Ajay will get.
2. The rate of interest on his investment, if Ajay had paid Rs. 30 for each share.

Points (3, 0) and (−1, 0) are invarient points under reflection in the line L₁; point (0, −3) and (0, 1) are invarient points on reflection in line L₂.

1. Write the equation of the line L₁ and L₂.
2. Write down the images of points P(3, 4) and Q(−5, −2) on reflection in L₁. Name the images as P' and Q' respectively.
3. Write down the images of P and Q on reflection in L₂. Name the image as P'' and Q'' respectively.

Use remainder theorem and find the remainder when the polynomial g(x) = x³ + x² – 2x + 1 is divided by x – 3.

When x³ + 3x² – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.

Find the value of p if the division of px³ + 9x² + 4x - 10 by (x + 3) leaves the remainder 5.

Find the remainder when the polynomial f(x) = 2x⁴ - 6x³ + 2x² - x + 2 is divided by x + 2.

If p(x) = 4x³ - 3x² + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4

If p(x) = 4x³ - 3x² + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2

If p(x) = 4x³ - 3x² + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.

If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x² + y² + z² = r². 

Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.

Prove that tan²Φ + cot²Φ + 2 = sec²Φ.cosec²Φ.

Prove that sin² θ + cos⁴ θ = cos² θ + sin⁴ θ.

Prove that sin⁴θ - cos⁴θ = sin²θ - cos²θ
= 2sin²θ - 1
= 1 - 2 cos²θ

Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.

`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A

Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.

Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`

Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`

Prove that: `(sec θ - tan θ)/(sec θ + tan θ ) = 1 - 2 sec θ.tan θ + 2 tan^2θ`