Grade 10 Revision Questions Set I

Fast track revision

 Q1 Find the largest four-digit number which when divided by 4,7 and 13 leaves a remainder 3 in each case.

Q2 Show that $\frac{2+3 \sqrt{2}}{7}$ is not a rational number, given that $\sqrt{2}$ is an irrational number.

Q3 Write the number of real roots of the equation $x^{2}+3|x|+2=0$

Q4 Solve for $\mathrm{x}$ $\frac{x+1}{x-1}+\frac{x-2}{x+2}=4-\frac{2 x+3}{x-2} ; x \neq 1,-2,2$

Q5 The longer side of a rectangular hall is $24 \mathrm{m}$ and the length of its diagonal is $26 \mathrm{m}$. Find the area of the hall.

Q6 Prove the trigonometric identity:

$\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta$

Q7 If $A=B=60^{\circ},$ verify that $\cos (A-B)=\cos A \cos B+\sin A \sin B$

Q8 From a point $\mathrm{P}$ on the ground the angle of elevation of the top of a $10 \mathrm{m}$ tall building is $30^{\circ} . \mathrm{A}$ flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from $\mathrm{P}$ is $45^{\circ} .$ Find the length of the flagstaff and distance of building from point $\mathrm{P}$. $\sqrt{3}=1.732]$

Q9 A pole casts a shadow of length $2 \sqrt{3} \mathrm{m}$ on the ground, when the Sun's elevation is $60^{\circ} .$ Find the height of the pole.

Q10 Find the values of $\mathrm{k}$ for which the given equation has real and equal roots:

$x^{2}-2 x(1+3 k)+7(3+2 k)=0$

Q11 If $\tan \theta=\frac{12}{13},$ evaluate $\frac{2 \sin \theta \cos \theta}{\cos ^{2} \theta-\sin ^{2} \theta}$

Q12 A solid metal cone with radius of base $12 \mathrm{cm}$ and height $24 \mathrm{cm}$ is melted to form solid spherical balls of diameter $6 \mathrm{cm}$ each. Find the number of balls formed.