Straight Line Class 11 Mock Test 01
: Question
1
of 30

The area enclosed within the curve |x|+|y|=1 is

The area enclosed within the curve |x|+|y|=1 is

1 Mark(s)

1 sq unit

2√2 sq units

√2 sq units

2 sq units

If the elevation of the sun is 30°, then the length of the shadow cast by a tower of 150 ft. height is

1. \(75\sqrt{3}ft.\)

2. \(200\sqrt{3}ft.\)

3. \(150\sqrt{3}ft.\)

4. \(\text{None of these}\)

If the elevation of the sun is 30°, then the length of the shadow cast by a tower of 150 ft. height is

1. \(75\sqrt{3}ft.\)

2. \(200\sqrt{3}ft.\)

3. \(150\sqrt{3}ft.\)

4. \(\text{None of these}\)

1 Mark(s)

1

2

3

4

If \(O'(4,\frac{8}{3})\) is the orthocentre of the triangle ABC the coordinates of whose vertices are O(0,0),A(8,0)and B(4,6), then the coordinates of the orthocentre of ∆O'AB are

If \(O'(4,\frac{8}{3})\) is the orthocentre of the triangle ABC the coordinates of whose vertices are O(0,0),A(8,0)and B(4,6), then the coordinates of the orthocentre of ∆O'AB are

1 Mark(s)

(0,0)

(8,0)

(4,6)

None of these

Let A(2,-3) and B(-2,1) be vertices of a triangleABC. If the centroid of this triangle moves on the line 2x+3y=1, then the locus of the vertex C is the line

Let A(2,-3) and B(-2,1) be vertices of a triangleABC. If the centroid of this triangle moves on the line 2x+3y=1, then the locus of the vertex C is the line

1 Mark(s)

2x+3y=9

2x-3y=7

3x+2y=5

3x-2y=3

If \(\text{ x=X cosθ - Y sinθ, y=X sinθ+ Y cosθ and } x^2+4xy+y^2=AX^2+BY^2,\) 0 ≤ θ ≤\( \frac{\pi}{2}\), then

If the sum of the distances from two perpendicular lines in a plane is 1, then its locus is

If the sum of the distances from two perpendicular lines in a plane is 1, then its locus is

1 Mark(s)

A square

A circle

A straight line

Two intersecting lines

A tower stands at the center of a circuit park. A and B are two points on the boundry of the park such that AB = a subtends an angles of \(60^o\) at the foot of the tower and the angle of elevation of the top of the tower from A or B is \(30^o\) . The height of the tower is

1. \(\frac{2a}{\sqrt{3}}\)

2. \(2a\sqrt{3}\)

3. \(\frac{a}{\sqrt{3}}\)

4.\(\sqrt{3}\)

A tower stands at the center of a circuit park. A and B are two points on the boundry of the park such that AB = a subtends an angles of \(60^o\) at the foot of the tower and the angle of elevation of the top of the tower from A or B is \(30^o\) . The height of the tower is

1. \(\frac{2a}{\sqrt{3}}\)

2. \(2a\sqrt{3}\)

3. \(\frac{a}{\sqrt{3}}\)

4.\(\sqrt{3}\)

1 Mark(s)

1

2

3

4

In ∆ABC, with usual notation, observe the two statements given below

If O(0,0),A(4,0) and B(0,3) are the vertices of a triangle OAB, then the coordinates of the excentre opposite to the vertex O(0,0) are

If O(0,0),A(4,0) and B(0,3) are the vertices of a triangle OAB, then the coordinates of the excentre opposite to the vertex O(0,0) are

1 Mark(s)

(12,12)

(6,6)

(3,3)

None of these

The coordinates axes are rotated through an angle 135°. If the coordinates of a point P in the new system are known to be (4,-3), then the coordinates of P in the original system are

The coordinates axes are rotated through an angle 135°. If the coordinates of a point P in the new system are known to be (4,-3), then the coordinates of P in the original system are

A flag staff is upon the top of a building. If at a distance of 40 m from the base of building the angles of elevation of the topes of the flag staff and building are \(60^o\) and \(30^o\) respectively, then the height of the flag staff is

A flag staff is upon the top of a building. If at a distance of 40 m from the base of building the angles of elevation of the topes of the flag staff and building are \(60^o\) and \(30^o\) respectively, then the height of the flag staff is

1 Mark(s)

46.19 m

50 m

25m

None of these

If in a ∆ABC, the altitudes from the vertices A,B,C on opposite sides are in HP, then sinA, sinB, sinC are in

If in a ∆ABC, the altitudes from the vertices A,B,C on opposite sides are in HP, then sinA, sinB, sinC are in

1 Mark(s)

HP

Arithmetico-Geometric Progression

AP

GP

From the top of a cliff 300 metres high, the top of a tower was observed at an angle of depression \(30^o\) and from the foot of the tower the top of the cliff was observed at an angle of elevation \(45^o\) the height of the tower is

1. \(50(3-\sqrt{3}) m\)

2. \(200(3-\sqrt{3}) m\)

3. \(100(3-\sqrt{3}) m\)

4. \(\text{None of these}\)

From the top of a cliff 300 metres high, the top of a tower was observed at an angle of depression \(30^o\) and from the foot of the tower the top of the cliff was observed at an angle of elevation \(45^o\) the height of the tower is

1. \(50(3-\sqrt{3}) m\)

2. \(200(3-\sqrt{3}) m\)

3. \(100(3-\sqrt{3}) m\)

4. \(\text{None of these}\)

1 Mark(s)

1

2

3

4

The x-coordinate of the incentre of the triangle where the mid points of the sides are (0, 1), (1, 1)and (1, 0) is

If the points \((x+1,2),(1,x+2),(\frac{1}{x+1},\frac{2}{x+1})\) are collinear, then \(x\) is

If the points \((x+1,2),(1,x+2),(\frac{1}{x+1},\frac{2}{x+1})\) are collinear, then \(x\) is

1 Mark(s)

4

5

-4

None of these

A vertical pole (more than 100 m high) consists of two portions, the lower being-one third of the whole, if the upper portion subtends an angle \(tan^{-1}\frac{1}{2}\) at a point in a horizontal plane through the foot of the pole and distance 40 ft from it, then the height of the pole is

A vertical pole (more than 100 m high) consists of two portions, the lower being-one third of the whole, if the upper portion subtends an angle \(tan^{-1}\frac{1}{2}\) at a point in a horizontal plane through the foot of the pole and distance 40 ft from it, then the height of the pole is

1 Mark(s)

100 ft

120 ft

150 ft

None of these

If \(A\) is the area and \( 2s\) the sum of three sides of a triangle, then

\(1. A≤\frac{s^2}{3\sqrt{3}}\\ 2. A≤\frac{s^2}{2}\\ 3. A>\frac{s^2}{\sqrt{3}}\\ 4. \text{None of these}\)

If \(A\) is the area and \( 2s\) the sum of three sides of a triangle, then

\(1. A≤\frac{s^2}{3\sqrt{3}}\\ 2. A≤\frac{s^2}{2}\\ 3. A>\frac{s^2}{\sqrt{3}}\\ 4. \text{None of these}\)

1 Mark(s)

1

2

3

4

A vertical tower stands on a declivity which is inclined at \(15^o\) to the horizon. From the foot of the tower a man ascends the declivity for 80 ft and then, finds that the tower subtends an angle of \(30^o\). The height of tower is

\(\text{1. }20(\sqrt{6}-√2)ft \\ \text{2. } 40(\sqrt{6}-√2)ft \\ \text{3. } 40(\sqrt{6}+√2)ft \\ \text{4. } \text{None of these
}\)

A vertical tower stands on a declivity which is inclined at \(15^o\) to the horizon. From the foot of the tower a man ascends the declivity for 80 ft and then, finds that the tower subtends an angle of \(30^o\). The height of tower is

\(\text{1. }20(\sqrt{6}-√2)ft \\ \text{2. } 40(\sqrt{6}-√2)ft \\ \text{3. } 40(\sqrt{6}+√2)ft \\ \text{4. } \text{None of these
}\)

1 Mark(s)

1

2

3

4

The image of the centre of the circle \( x^2+y^2=a^2 \) with respect to the mirror image , is

A vertical pole PS has two marks Q and R such that the portions PQ,PR and PS subtend angles α,β,γ at a point on the ground distance \(x\) from the pole. If PQ = a, PR = b, PS = c and α+ β+ γ =180° then \(x^{2}\) is equal to

A vertical pole PS has two marks Q and R such that the portions PQ,PR and PS subtend angles α,β,γ at a point on the ground distance \(x\) from the pole. If PQ = a, PR = b, PS = c and α+ β+ γ =180° then \(x^{2}\) is equal to

The upper \((\frac{3}{4})\text{th}\) portion of a vertical pole subtends an angle \(tan^{-1}(\frac{3}{4})\) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

The upper \((\frac{3}{4})\text{th}\) portion of a vertical pole subtends an angle \(tan^{-1}(\frac{3}{4})\) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

1 Mark(s)

20 m

40 m

60 m

80 m

The straight lines\(\text{ x = y, x-2y= 3 and x+2y= -3 }\) form a triangle, which is

The straight lines\(\text{ x = y, x-2y= 3 and x+2y= -3 }\) form a triangle, which is

1 Mark(s)

Isosceles

Equilateral

Right angled

None of these

From the top of a cliff \(h\) metres above sea level an observer notices that angles of depression of an object and its image B are complementary. If the angle of depression at A is \(\theta\) . The height of A above sea level is

From the top of a cliff \(h\) metres above sea level an observer notices that angles of depression of an object and its image B are complementary. If the angle of depression at A is \(\theta\) . The height of A above sea level is

1 Mark(s)

h sinθ

h cosθ

h sin2θ

h cos2θ

If A(-a,0) and B(a,0) are two fixed points, then the locus of the point at which AB subtends a right angle, is