ABHYAS | Self Learning | Testing Platform

Q.1

The area of the trriangle formed by the points A (2,0), B (6,0) and C (4,6) is

A.

24 Sq. units

B.

12 Sq. units

C.

10 Sq. units

D.

None of these

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Q.2

The area of the triangle formad by the points (0 , 0) , (0 , 6) and (-5 , 5) is

A.

-15 sq. units

B.

30 sq. units

C.

$frac{5}{2}sq. units$

D.

15 sq. units

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Q.3

The area of the triangle formed by the points P (0 , 1) , Q (0 , 5) and R ( 3 , 4) is

A.

16 Sq. units

B.

8 Sq. units

C.

4 Sq. units

D.

6 Sq. units

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Q.4

Points (-6 , - 5) , (0 , b) and $large (2,frac{5}{3})$ are colliner. What is the value of b ?

A.

-3

B.

$large frac{-5}{2}$

C.

$large frac{10}{3}$

D.

0

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Q.5

Point P (x, y) divides the line segment joining points (2, 1) and (3, 2), internally, in the ratio 2 : 3. What is the value of y ?

A.

0

B.

$large frac{-2}{5}$

C.

$large frac{12}{5}$

D.

$large frac{7}{5}$

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Q.6

Find the distance between A(a,b) and B(-b, a).

A.

$large 2(a^{2}+b^{2});units$

B.

$large sqrt{2(a^{2}+b^{2})};units$

C.

$large sqrt{2(a^{2}-b^{2})};units$

D.

$large sqrt{2(2a^{2}+b^{2})};units$

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Q.7

Distance between point $(a,b)$ and $(-a,-b)$ is

A.

$large sqrt {2a^{2}+2b^{2}}$

B.

$large 2sqrt {a^{2}-b^{2}}$

C.

$large 2sqrt {a^{2}+b^{2}}$

D.

$large 4sqrt {a^{2}+b^{2}}$

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Q.8

If a is the length of one of the sides of an equilateral triangle ABC whose base BC lies on the x-axis with vertex B at the origin, find the coordinates of the vertices of triangle ABC.

A.

$large left ( frac{a}{2},pm frac{sqrt{3}}{2}a right )$

B.

$large left ( frac{a}{2},pm frac{sqrt{2}}{3}a right )$

C.

$large left ( frac{3a}{2},pm frac{sqrt{3}}{2}a right )$

D.

None of these

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Q.9

The distance between the points A(2,3) and C whose abscissa is two times the ordinate of point A and the ordinate is three times the abscissa of A

A.

$large sqrt{32}$

B.

$large sqrt{25}$

C.

$large 2sqrt{5}$

D.

$large sqrt{10}$

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Q.10

Assertion : The points $large (k,2-2k), (-k+1, 2k) : : and, , ( -4 -k, 6 - 2k)$ are collinear if $large k=frac {1}{2}.$

Reason : Three points A,B and C are collinear in same straight line, if AB + BC = AC.

A.

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B.

If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

C.

If Assertion is correct but Reason is incorrect.

D.

If Assertion is incorrect but Reason is correct.

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