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1 SCT H.S.C/SCI/MATHS-I

H.S.C

Batch :

Date : 01/01/2013

SHRI CHANDRA TUTORIALSSCIENCE DEPARTMENT

PRILIMINARY EXAMINATION

MATHS & STATS - I

MARKS : 40

TIME : 1.45 HRS

Note : 1) All questions are compulsory.

2) Answer to every question must be written on a new page.3) Figures to the right indicate full marks.

SECTION - I

Q.1) (A) Select and write most appropriate answer from the given alternative for each

sub question : (6)

1) The two statements

i) I do not respect time or I am punctual.

ii) If I am punctual then I respect time, are

a) Duals of each other b) negations of each otherc) inverse statements d) converse of each other

2) The vectors and represent sides AB and BC of regular hexagon ABCDEF. Thevector representing side CD is .

a) b) c) d) 3) The length of transversal axis of the hyperbola is .

a) b) c) d)

Q.1) (B) Attempt any three of the following: (6)

1) show that 2) If and are tangents to the same circle then find radius

of the circle.

3) Find the angle between the pairs of line represented by

4) if

* + [

]and

then find values of x and y.

5) Find the value of p if the points arecoplanar.

Q.2) (A) Attempt any two of the following: (6)

1) Prove the following by truth table Also write the dual ofthe statements

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2) Find the joint equation of the pairs of lines passing through andperpendicular to the lines and , find the acute anglebetween them.

3) Show that the lines ( ) ( ) and ( ) ( )intersect each other and find the position vector of their point of intersection.

Q.2) (B) Attempt any two of the following: (8)

i) Using vectors, show that the angle bisectors of a triangle are concurrent.

ii) Satish wants to invests C 24000 in public provident fund[PPF] and in National

bond. He has to invest at least C1000 in PPF and at least C 2000 in bonds. If the

rates of interest on PPF and the bonds are respectively 9% p.a. and 8% p.a., how

should he invests his money to earn maximum annual income? Also find

maximum annual income.

iii) Find the inverse of the following matrix by adjoint method *

+

iv) Solve the following system of equations by reduction method.

Q.3) (A) Attempt any two of the following: (6)

i) Write a negation of following statements:

a) A person is rich if and only if he is a software engineer.

b) All quadrilaterals are not rectangles.

ii) The tangents at point P on the parabola intersects the directrix in F.Show that segments PF subtends a right angle at the focus S.

iii) Show that line touches the circle . Find thepoint of contact.

Q.2) (B) Attempt any two of the following: (8)

i) The normal to the ellipse

at the point (-3,-2) touches the parabola

. Find the value of a . Also find the point of contact.ii) a) In find 1)

, 2) .

b) In show that ABC is a right angled triangle.iii) Find the equation of the plane passing through the line of intersection of the

planes and parallel to the line

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