The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is
75
A.
Let AB be the tower and BC be the distance between tower and car. Let be the angle of depression of the car.
According to the given information,
Two different dice are tossed together. Find the probability
(i) That the number on each die is even.
(ii) That the sum of numbers appearing on the two dice is 5.
The total number of outcomes when two dice are tossed together is 36.
The sample space is as follows
(i). Favourable outcomes = { (2,2) (2,4) (2,6) (4,2) (4,4)
(6,4) (6,2) (6,4) (6,6) }
Porbability that the number on each dice is even
=
(ii) Favourable outcomes = { (1,4) (2,3) (3,2) (4,1) }
Probability that the sum of the number appearing on the two dice is 5
=
In a family of 3 children, the probability of having at least one boy is
A.
There are in all 23 = 8 combinations or outcomes for the gender of the 3 children
The 8 combinations are as follows
BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG
Thus the probability of having at least one boy in a family is
ABCD is a rectangle whose three vertices are B (4, 0), C(4,3) and D(0, 3). The length of one of its diagonals is
5
4
3
25
A.
5
We se that AB= 4 units and BC=3 units
Using pythagoras theorem
AC2 = AB2 + BC2
= 42 + 32
AC2 = 25
Thus AC= 5 Units
Hence length of the diagonal of the rectangle is 5 units
In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is
4
3
2
1
C.
2
It is given that AB = 5 and BC = 12
Using pythagoras theorem
We know that two tangents drwan to a circlefrom the same point that is exterior to
the circle are of equal iengths.
Thus AM = AQ = a
Similarly MB = BP = b and PC = CQ = c
We know AB = a+b = 5
BC = b+c = 12 and AC = a+c = 13
Solving simultaneously we get a = 3, b =2, c = 10
We also know that the tangent is perpendicular to the radius.
Thus OMBP is a square with side b
Hence the length of the radius of the circle inscribed in the right angled triangle is 2 cm.
A chord of a circle of radius 10 cm subtends a right angleat its centre. The length of the chord (in cm) is
5
10
10
B.
10
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 isa multiple of 4, is
C.
Two circles touch each other externally at P. AB is a common tangent to the circlestouching them at A and B. The value of APB is
D.
The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.
Given: is an isosceles triangle with a circle inscribed in the triangle.
To prove: BD=DC
Proof:
AF and AE are tangents drawn to the circle from point A.
Since two tangents drwan to a circle from the same exterior point are equal.
AF=AE=a
Similarly BF=BD=b and CD=CE=c
We also know that is an isosceles triangle
Thus AB=AC
a+b=a+c
Thus b=c
Therefore, BD=DC
Hence proved.
Severity: Notice
Message: Undefined variable: question_book_id
Filename: features/flexipad.php
Line Number: 469
Backtrace:
File: /var/www/html/public_html/application/views/features/flexipad.php
Line: 469
Function: _error_handler
File: /var/www/html/public_html/application/views/previous_year_papers/paper.php
Line: 163
Function: view
File: /var/www/html/public_html/application/controllers/Study.php
Line: 2109
Function: view
File: /var/www/html/public_html/index.php
Line: 315
Function: require_once
Severity: Notice
Message: Undefined variable: chapter_number
Filename: features/flexipad.php
Line Number: 469
Backtrace:
File: /var/www/html/public_html/application/views/features/flexipad.php
Line: 469
Function: _error_handler
File: /var/www/html/public_html/application/views/previous_year_papers/paper.php
Line: 163
Function: view
File: /var/www/html/public_html/application/controllers/Study.php
Line: 2109
Function: view
File: /var/www/html/public_html/index.php
Line: 315
Function: require_once