English Medium इयत्ता १० - CBSE Question Bank Solutions

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Evaluate

`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`

 Evaluate sin25° cos65° + cos25° sin65°

9 sec² A − 9 tan² A = ______.

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.

(secA + tanA) (1 − sinA) = ______.

`(1+tan^2A)/(1+cot^2A)` = ______.

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(cosec  θ  – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

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

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`

[Hint: Write the expression in terms of sinθ and cosθ]

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(1+ secA)/sec A = (sin^2A)/(1-cosA)` 

[Hint : Simplify LHS and RHS separately.]

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`sqrt((1+sinA)/(1-sinA)) = secA + tanA`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec² A = 1 cot² A.

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`

Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)`  and `(2 - sqrt3)`

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

`p(x) = x^2 + 2sqrt2x + 6`

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

`q(x) = sqrt(3)x^2 + 10x + 7sqrt(3)`