जिल्हा परिषद माध्यमिक विद्यालय, विडूळ ता . उमरखेड जि. यवतमाळ
Online Exam
Class - 10th, Sub - Mathematics- II , Marks - 40, Time - 2 Hours
Date - 07 / 04 / 2021 , Timing - 12 : 00 ते 2 : 15
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Q. 1 (A) For every subquestion 4 alternative answers are given. Choose the correct answer and write the alphabet of it: 04
i. Out of given triplets, which is not a Pythagoras triplet ?
(A) (5,12,13) (B) (8,15,17)
(C) (7,8,15) (D) (24,25,7)
ii. If ∆ABC~ ∆LMN and ⦟A = 60° then ⦟L =?
A) 45⁰ B) 60⁰
C)25⁰ D) 40⁰
iii. In ⛶ PQRS if ∠RSP = 80° then find ∠RQT ?
(A) 100⁰ (B) 80⁰ (C) 70⁰ (D) 110⁰
iv. The tangents drawn at the end of a diameter of a circle are…………..
A) Perpendicular B) parallel
C) congruent D) can’t say
Q.1. B. Solve the following subquestions: 04
i. Write the X-coordinate and Y-coordinate of point P(- 5 , 4).
ii. If tan θ = 1 then sin θ . cos θ = ?
iii. Are triangles in figure similar ? If yes then write the test of similarity.
iv. From given figure, In ∆ ABC, AB⊥BC, AB =BC, AC = 5√2 then
what is the height of ∆ ABC ?
Q.2. A. Complete and write any two activities from the following: 04
i)
ii) From given figure, In ∆ ABC, If ABC = 900 CAB=300
iii) If O is the center of the circle in the figure alongside , then complete the table from the given information.
The type of arc
Q.2. B. Solve any four subquestions from the following: 08
i. Prove that sec²θ − cos²θ = tan²θ + sin²θ .
ii. Show that the point(11, -2) is equidistant from (4, -3) and (6, 3).
iii. Draw seg AB = 6.8 cm. Draw a circle with diameter AB. Draw points C on the circle apart
from A and B. Draw line AC and line CB Write the measure of angle ACB.
iv. Length of a tangent segment drawn from a point which is at a distance 1
v. Areas of two similar triangles are 225 𝑐𝑚² and ,81 𝑐𝑚² if side of smaller triangle is 12cm. find corresponding side of major triangle
प्र. 3 A. खालीलपैकी कोणतीही एक कृती सोडवा. 03
i. tan²θ − sin²θ = tan²θ X sin²θ .
For proof of this complete the
activity given below.
ii. Tangent segments drawn from an external point to a circle are congruent .
prove this theorem.Complete the following activity.
प्र. 3. B . पुढील कोणतेही दोन उपप्रश्न सोडवा. 06
i. In triangle ABC point D is on side BC (B-D-C) such that ⦟BAC = ⦟ADC then prove that CA² = CB x CD.
ii. A congruent side of an isosceles right angled triangle is 7 cm ,Find
its perimetre .
iii. Prove the following theorem.
'Opposite angles of a cyclic quadrilateral are supplementry.'
iv. Construct an equilateral △ ABC with side 5cm. △ ABC ~ △ LMN, ratio the corresponding sides of triangle is 6:7 then construct ∆LMN 𝑎𝑛𝑑 ∆ABC
Q.4. Attempt any two subquestions from the following: 08
i. Prove that
sin²A . tan A + cos²A . cot A + 2 sin A . cos A = tan A + cot A
ii. ∆AMT. ~∆AHE, 𝐼𝑛 ∆AMT AM=6.3 cm, ∠TAM=500
,AT=5.6cm, 𝐴𝑀 / 𝐴𝐻 = 7/5
, then construct △AMT and ∆AHE.
iii. As shwon in figure, LK = 6 √2 then
1) MK = ? 2) ML = ? 3) MN = ?
Q.5. Attempt any one subquestion from the following: 03
i. An architecture have model of building, length of building is 1m then length of model is 0.75cm then find length & height of model building whose actual length is 22.5m& heght is 10m.
ii. Using distance formula decide whether the points (4, 3), (5, 1) and
(1, 9) are collinear or not ?
