- This is an assessment test.
- These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
- Kindly take the tests in this series with a pre-defined schedule.
Geometry and Mensuration: Test 25
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Question 1 |
R and S are two points on the sides PT and QT respectively of ΔPQR such that RS= 18 cm, TS= 5 cm and ÐRST= 90o. If tan ÐPQR= 3.6, then PT: TR =
QT: 2 TS | |
2 TS: QT | |
2 QT: TS | |
TS: 2 QT |
Question 1 Explanation:
$ \displaystyle \begin{array}{l}\angle \,RST={{90}^{o}}\\RS=18\,cm\\TS=5\,cm\\\therefore \,\,\tan \,T=\frac{RS}{TS}=\frac{18}{5}=3.6\\\tan \,\angle PQR=3.6\\\therefore \angle T=\angle Q\\\therefore PT=PQ\\\angle T+\angle R={{90}^{o}}\\\Rightarrow 2\,\angle T+2\,\angle R={{180}^{o}}\\\angle T+\angle P+\angle Q={{180}^{o}}\\\Rightarrow \,2T+\angle P={{180}^{o}}\\\therefore \,\,\angle P=2\,\angle R\\\therefore \,\frac{PT}{TQ}=\frac{2TR}{TS}\end{array}$
Question 2 |
BL and CM are medians of ΔABC right-angled at A and BC= 5cm. If BL = 8cm, then the length of CM is
√61/2cm | |
√48/2cm | |
10√2cm | |
4 cm |
Question 3 |
ABCD is a rectangle where the ratio of the lengths of AB and BC is 3: 2. If P is the mid-point of AB, then the value of sin ∠CPB is
3/5 | |
2/5 | |
3/4 | |
4/5 |
Question 4 |
PQRS is a square, T is the mid-point of PQ and M is the mid-point of QR. PM and ST are joined and they meet at L. Then which of the following is correct?
TP: TL= 1: 2 | |
PM = TS | |
∠PMS = ∠PMQ | |
∠PTS = ∠QPM |
Question 5 |
If the sums of the interior angles of a regular polygon be 1080o, the number of sides of the polygon is
6 | |
8 | |
10 | |
12 |
Question 5 Explanation:
Let the number of sides be x.
180(x-2)= 1080,
=> x - 2 = 6=> x = 8
Thus the correct option is (b)
180(x-2)= 1080,
=> x - 2 = 6=> x = 8
Thus the correct option is (b)
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