List of practice Questions

$x^ 2 + xy + 8x + 8y$
$15xy - 6x + 5y - 2 $
$ax + bx - ay - by$
$15pq + 15 + 9q + 25p$
$z - 7 + 7xy - xyz$

The amount of solute (molar mass $ 60\text{ }g\text{ }mo{{l}^{-1}} $ ) that must be added to $180\, g$ of water so that the vapour pressure of water is lowered by $10\%$, is

If p=–2,find the value of: (i)4p+7 (ii) –3p²+4p+7 (iii)–2p³–3p²+4p+7

Why was the Moral Rearmament Army welcomed at the Studios?

Simplify these expressions and find their values if x = 3, a = – 1, b = – 2. (i) 3x – 5 – x + 9 (ii) 2 – 8x + 4x + 4 (iii) 3a + 5 – 8a + 1 (iv) 10 – 3b – 4 – 5b (v) 2a – 2b – 4 – 5 + a

Write equations of the following reactions:
(i)Friedel-Crafts reaction–alkylation of anisole.
(ii)Nitration of anisole.

(iii)Bromination of anisole in ethanoic acid medium.
(iv)Friedel-Craft’s acetylation of anisole.

Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then

Among two discs $A$ and $B$, first has radius $10 \,cm$ and charge $ 10^{-6} \mu C$ and second has radius $30 \,cm$ and charge $10^{-5}C$ . When they are touched, charges on both are, $q_{A}$ and $q_{B}$ respectively, will be

The graphs shows, angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

Find the value of:
(i) -4÷$\frac{2}{3}$
(ii) -$\frac{3}{5}$÷2
(iii) -$\frac{4}{5}$÷(-3)
(iv) -$\frac{1}{8}$÷$\frac{3}{4}$
(v) -$\frac{2}{13}$÷$\frac{1}{7}$
(vi) -$\frac{7}{12}$÷(-$\frac{2}{13}$)
(vii) $\frac{3}{13}$÷(-$\frac{4}{65}$)

Give reasons.

Water is not used to control fires involving electrical equipment.
LPG is a better domestic fuel than wood.
Paper by itself catches fire easily whereas a piece of paper wrapped around an aluminium pipe does not.

The author has used gentle humour to point out human foibles. Pick out instances of this to show how this serves to make the piece interesting.

Explain why objects moving in fluids must have special shapes.

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

402
1989
3250
825
4000

Classify into monomials, binomials and trinomials.
(i) 4y – 7z (ii) y² (iii) x + y – xy (iv) 100 (v) ab – a – b (vi) 5 – 3t (vii) 4p²q – 4pq² (viii) 7mn (ix) z² – 3z + 8 (x) a² + b²(xi) z²+ z (xii) 1 + x + x²

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.

252
2925
396
2645
2800
1620

$\log ( \tan 18\degree) + \log ( \tan 36\degree) + \log ( \tan 54\degree) + \log (\tan 72\degree) =$

If $ x^{1/3} + y^{1/3} = 1 $, find $ \frac{dy}{dx} $ at the point $ \left( \frac{1}{8}, \frac{1}{8} \right) $.

Integrate the function: $\frac {1}{\sqrt {8+3x-x^2}}$

The ratio of the respective de Broglie wavelengths associated with electrons accelerated from rest with the voltages 100 V, 200 V and 300 V is

A merchant made a profit of 5 on the sale of a sweater that cost the merchant $15. What is the profit expressed as a percent of the merchant's cost?
Give your answer to the nearest whole percent.

For the large cars sold at an auction that is summarized in the table above, what was the average sale price per car?

One pen costs 0.25 and one marker costs $0.35. At those prices, what is the total cost of 18 pens and 100 markers?