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11th Maths – Study Material

XI STD (ENGLISH VERSION ) MARK: 90

TIME : 2.30HRS MATHEMATICS

PART –A 20 X 1 =20

1) Matrix A is of order 2 x 3 and B is of order 3 x 2 then order of matrix BA is

a) 3 x 3 b) 2 x 3 c) 2 x 2 d) 3 x 2

2) The order of matrix B = [1 2 5 7] is

a)1 x 4 b) 4 x 1 c) 2 x 1 d) 1 x 1

3) The solution of

= 0 is

a) x =1 b) x =2 c)x = 3 d) x =0

4) Given that the value of a third order determinant is 11 then the value of the determinat

Formed by the respective co- factors as its elements will be

a) 11 b) 121 c) 1331 d) 0

5) Let

be the vectors

,

determined by two adjacent sides of regular hexagon

ABCDEF . The vector represented by is

a) - b) + c)2 d) -

6) A polygon has 44 diagonals then number of its sides is

a) 11 b)1 c) 4 d) 8

7) The values of nc0 –nc1+nc2-nc3+……..(-1)n. ncn is

a)n b) 0 c) 2 n d) 2n+1.

8) When the terms of a G. P are written in reverse order the progression formed is

a) A.P. B) G.P. C) H.P. D) A.P AND H.P.

9)

is valid for

a) -1 < x < 1 b) -1 ≤x≤1 c) all real x d) x>0



10) Which of the following is a parallel line to 3x + 4y +5= 0?

a) 4x+3y+6=0 b) 3x-4y+6=0 c)4x-3y+9=0 d)3x+4y+6=0

11) T he graph of xy =0 is

a) a point b) a line c) a pair of intersecting lines d) a pair of parallel lines

12) The number of term in the series 101 + 99+ 97+…….+47 is

a) 25 b) 28 c) 30 d) 20

13) If the side of a right angled triangle are in A.P then the sides are proportional to

a) 1 2 : 3 b) 2 : 3 : 4 c) 3 : 4 : 5 d) 4: 5 : 6

14) If H is the harmonic mean between a and b, then

+

is =

a) 2 b) -2 c)

d)

15) Exactly one side of a tetrahedron is of length greater than 1, then max.volume

of the tetrahedron is

a) 1 b)

c)

d)

16) Between the number 2 and 20, 8 A.M' s are inserted, then their sum is

a) 88 b) 44 c)176 d)none of these

17) The number of point in which two circle touch each other internally is

a) 1 b) 2 c) 3 d) 4

18) The number of term in the expansion of ( a+ b+c)10 is

a) 11 b) 21 c) 55 d) 66

19) If f(x) =

, then f is=

a)x b) –x c)

d)

20) If x2-y2- 84y = 2012, x, y then x-3y =

a) 2 b) 3 c) 6 d) 7

PART-B



Answer any SEVEN questions. Q.NO 30 is compulsory.. 7 x 2 = 14

21) If A =

find A2 -7A -2 i .

22) Solve

= -3 .

23) Find the components along the coordinates of the position vector of P(-4,3).

24) Find the unit vectors parallel to the vector -3 + 4 .

25) Prove that the sum of n arithmetic means between two numbers is n times the

Single A.M between them .

26) If a, b, c are in A .P and a, mb,c are in G.P then prove that a, b ,c are in H.P .

27) Find the value of p if the line 3x +4y-p = 0 is a tangent to the circle x2 + y2 =16.

28) Solve f(X) = 2x2 -12x +50 ≤ 0 or find the domain of the function f(x).

29) Draw the graphs of the logarithmic function (1) f(x) = (2) f(X) = (3) f(X) =

30) IF y =3x + c is a tangent to circle x2 + y2 =9 , find the value of c .

PART –B

Answer any SEVEN questions. Q.NO 40 is compulsory.. 7 X 3 =21

31) If each element of a determinant ( ) is polynomial in x and if vanishes for x =a

Then ( x – a) is a factor of .

32) Evaluate

= xy

33) Vector addition is commutative i.e., if and are any vectors then .

34) Show that the points whose position vectors + -5 , arecollinear.

35) If b is the A.Mof a and c (a c) and (b-a) is the G.M of a and c-a, show that a b:c =1:3:5

36) Find the angle between the straight lines 3x -2y +9 =0 and 2x+y-9=0.

37) Find the equation of the circle with centre (2,-3) and radius 3 . show hat it passes through the point

(2,0).

38) Let A={1,2}, B={3,4}and C={5,6} and f:A→B and g: B→C SUCH that f(1) =3 , f(2) =4, g(3) =5, g(4)=6



Find gof.

39) solve the quadratic inequation 64x2 +48x +9 <0

40) Find 3 geometric means between 576 and 9 .

ANSWER THE ALL 7 QUESTIONS 7 X 5 = 35

41) Prove by factor method

= ( a –b) (b- a) ( c -a) (or)

Find n geometric means between two given number a and b and find their prouduct.

42) The medians of a triangle are concurrent. (or)

Find the equation of the circle passing through the point (1,0), (0, -1) ,and (0,1).

43) Solve

<

(or)

Find the coordinates of the orthocenter of triangle whose vertices are the points (-2,-1)

(6,-1) and (2,5).

44) Section formula – Internal division (or)

Find the sum of first n term of the series

.

45) Find the equation of the circle which passes through the point (1, 2) and cuts orthogonally each

Of the circles = 9 and .

(or)

If x is real, prove that

lies between

and 1 .

46) Find the narithmetic means between a and b and find their sum .

(or)

Show that the points given by the vectors + + , , + + , and + + are

coplanar.

47) Solve using factor method

=0 (or)

In the expansion find the coefficient of .

maths study material · pdf file11/12/2017 · 11th maths – study material xi...

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