Maths Set-1 MCQ Online Practice Test | Class 10

Q1. A ladder of length $8\,$ m leans against a vertical wall making an angle of $60^\circ$ with the horizontal. How high above the ground does the ladder touch the wall?

(A)

$4\ \text{m}$

(B)

$4\sqrt{3}\ \text{m}$

(C)

$2\sqrt{3}\ \text{m}$

(D)

$6\ \text{m}$

Q2. Points $P$ and $Q$ are on the same straight line on one side of a tower. Point $Q$ is $20\,$ m closer to the tower than $P$ . From $P$ the angle of elevation of the top of the tower is $30^\circ$ and from $Q$ it is $45^\circ$ . Find the height of the tower.

(A)

$10(\sqrt{3}-1)\ \text{m}$

(B)

$20\sqrt{3}\ \text{m}$

(C)

$10(\sqrt{3}+1)\ \text{m}$

(D)

$5(3+\sqrt{3})\ \text{m}$

Q3. A vertical tree casts a shadow $15\,$ m long when the angle of elevation of the Sun is $30^\circ$ . Later, when the angle of elevation becomes $60^\circ$ , what will be the length of the shadow of the same tree?

(A)

$5\ \text{m}$

(B)

$15\sqrt{3}\ \text{m}$

(C)

$7.5\ \text{m}$

(D)

$10\ \text{m}$

Q4. Two vertical poles of heights $10\,$ m and $6\,$ m stand on level ground $8\,$ m apart. From a point on the ground between them, the angles of elevation to the tops of the two poles are equal. How far is this point from the taller pole?

(A)

$3\ \text{m}$

(B)

$8\ \text{m}$

(C)

$4\ \text{m}$

(D)

$5\ \text{m}$

Q5. A man whose eyes are $1.5\,$ m above the water of a still pond observes the top of a vertical tower across the pond at an angle of elevation $30^\circ$ and observes the reflection of the top of the tower in the pond at an angle of depression $60^\circ$ . What is the height of the tower?

(A)

$2\ \text{m}$

(B)

$3\ \text{m}$

(C)

$4.5\ \text{m}$

(D)

$1.5\ \text{m}$

Q6. From a point on level ground, the angle of elevation to the top of a vertical tower is $30^\circ$ . If the point is $30\ \text{m}$ away from the base of the tower, the height of the tower is

(A)

(A) $15\ \text{m}$

(B)

(B) $10\sqrt{3}\ \text{m}$

(C)

(C) $10\ \text{m}$

(D)

(D) $5\sqrt{3}\ \text{m}$

Q7. A ladder of length $13\ \text{m}$ rests against a vertical wall. Initially the ladder makes an angle of $60^\circ$ with the ground. It is then slid down so that its top now makes an angle of $30^\circ$ with the ground. By how much (in metres) has the top of the ladder moved vertically?

(A)

(A) $4.258\ \text{m (approx)}$

(B)

(B) $6.5\ \text{m}$

(C)

(C) $11.258\ \text{m}$

(D)

(D) $\dfrac{13(\sqrt{3}-1)}{2}\ \text{m}$

Q8. Two points on the same straight line from the base of a tower are $40\ \text{m}$ apart. From the nearer point the angle of elevation of the top of the tower is $60^\circ$ and from the farther point it is $30^\circ$ . The height of the tower is

(A)

(A) $20\sqrt{3}\ \text{m}$

(B)

(B) $10\sqrt{3}\ \text{m}$

(C)

(C) $40\sqrt{3}\ \text{m}$

(D)

(D) $20\ \text{m}$

Q9. From two points $A$ and $B$ on the same side of a vertical tower, the angles of elevation of its top are $45^\circ$ and $60^\circ$ respectively. If $A$ is $10\ \text{m}$ farther from the base of the tower than $B$ , the height of the tower equals

(A)

(A) $10(\sqrt{3}+1)\ \text{m}$

(B)

(B) $5(\sqrt{3}-1)\ \text{m}$

(C)

(C) $15+5\sqrt{3}\ \text{m}$

(D)

(D) $5(3-\sqrt{3})\ \text{m}$

Q10. From a point on level ground the angle of elevation of the top of a vertical tower is $30^\circ$ . After walking $10\ \text{m}$ straight towards the tower, the angle of elevation becomes $60^\circ$ . The height of the tower is

(A)

(A) $10\ \text{m}$

(B)

(B) $5\sqrt{3}\ \text{m}$

(C)

(C) $15\ \text{m}$

(D)

(D) $5\ \text{m}$

Q11. A ladder leans against a vertical wall such that the top of the ladder reaches a height of $4\ \text{m}$ above the ground when its foot is $3\ \text{m}$ away from the wall. The angle between the ladder and the ground is

(A)

$36.87^\circ$

(B)

$53^\circ$

(C)

$53.13^\circ$

(D)

$37^\circ$

Q12. From two points $A$ and $B$ on the same straight line from the base of a tower, the angles of elevation of the top of the tower are $30^\circ$ and $45^\circ$ respectively. If $B$ is $20\ \text{m}$ closer to the tower than $A$ , the height of the tower is

(A)

$10\bigl(\sqrt{3}+1\bigr)\ \text{m}$

(B)

$10\bigl(\sqrt{3}-1\bigr)\ \text{m}$

(C)

$\dfrac{20}{\sqrt{3}}\ \text{m}$

(D)

$10\sqrt{3}\ \text{m}$

Q13. Two identical vertical towers are $40\ \text{m}$ apart. From a point $P$ between them the angles of elevation to their tops are $30^\circ$ and $60^\circ$ . The height of each tower is

(A)

$20\ \text{m}$

(B)

$30\sqrt{3}\ \text{m}$

(C)

$\dfrac{40}{\sqrt{3}}\ \text{m}$

(D)

$10\sqrt{3}\ \text{m}$

Q14. From the top of a lighthouse $50\ \text{m}$ high, the angles of depression to two ships on the same side of the lighthouse are $30^\circ$ and $45^\circ$ . The distance between the two ships is

(A)

$50\bigl(\sqrt{3}+1\bigr)\ \text{m}$

(B)

$50\bigl(\sqrt{3}-1\bigr)\ \text{m}$

(C)

$100\bigl(\sqrt{3}-1\bigr)\ \text{m}$

(D)

$25\bigl(\sqrt{3}-1\bigr)\ \text{m}$

Q15. An observer stands at a point between two vertical towers of heights $20\ \text{m}$ and $30\ \text{m}$ . The angles of elevation to the tops of the two towers are $45^\circ$ and $60^\circ$ respectively. If the observer is between the towers (so distances to the towers add to the separation), the distance between the towers is

(A)

$20+10\sqrt{3}\ \text{m}$

(B)

$10\sqrt{3}-20\ \text{m}$

(C)

$50\ \text{m}$

(D)

$30+\dfrac{20}{\sqrt{3}}\ \text{m}$

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Maths Set-1

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