NEB Class 11 Mathematics Model Set 2 | NepaliEducate

Time: 3:00 Hrs

Class : 11

Subject: Mathematics (4011)    

F.M:- 75

 P.M:- 30 

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicates full marks.

Attempt all questions.

Group-A                                                                (11x1=11)  Rewrite the correct Option in your answer sheet:

1.      A compound statement which is always true is called 

a)      Converse  b) Contradiction           c) Conditional d) Tautology

2.      If x, y, z are in G.P. then logx, logy, logz are in

a)      A.P.                       b) G.P.             c) H.P.             d) None of above

3.      In a triangle ABC B= 120⁰ , a=1, c=1 then other angles and sides are

a)      35, 45, 2    b) 10, 50 , 3     c) 20, 40, 2      d) 30, 30, 3

4.      For what value of m are the two vectors  = -2 +4  and   = 2+ 7 + m orthogonal?

a)      3    b) -     c) 2                  d) None of these

5.      The equation of parabola with the vertex at origin and directrix  y+a = 0 is 

a)      y²= 4ax      b) x²= 4ay       c) (y-k)²=4a(x-h)                     d) (x-h)²= 4a(y-k)

6.      
What is the probability that a leap year selected at random contained 53 Sundays? 

a)1/7               b) 2/7                  c) 1                  d) 1/53 

7.       is equal to

a)      0    b) 1                  c) infinity                 d) can’t be said

8.      xsinx + cosx is _______ function.

a)      Even          b) Odd             c) neither even nor odd                       d) none of above 

9.      A particle moves in a straight line so that its distance in meters from a given point in the line after t seconds is given by  s = 3+ 5t +t³. What is the average velocity during the 5^th second.

a)      65              b) 66    c) 67    d) none of the above 

10.  How many negative roots does the function 2x³-5x+2=0 have,

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

11.  If supply: P=Q²+40 and demand P= 240-Q² what is the market equilibrium price?

a)      140            b) 130              c) 135              d) 145

                                                                                                         Group-B                       (8x5=40)                                         

 

12.  Define domain and range of the function. Find the domain and range of         f(x)= 

13.  Prove that A.M., G.M. and H.M. between unequal positive number satisfy the following  a) A.M.x H.M.=G.M²

b) A.M>G.M>H.M

14.  a) In any Triangle ABC, if a⁴+b⁴+c⁴=2c²(a²+b²), Prove that C= 45⁰ or 135⁰.                     [3] b) Express =(4,7) as the linear combination at = (5, -4 ) and = (-2, 5)                                 [2]

 

15.  Calculate the coefficient of variation from the following data:    

Class	0-10	10-20	20-30	30-40	40-50
FREQUENCY	8	13	16	8	5

16.  Determine whether the function f(x)= 2x³-3x²-36x+49 is increasing or decreasing at x=5 and x=-3. Also obtain the Critical point and point of inflection.

17.  Evaluate 

18.  Evaluate, using composite trapezoidal rule the integral,   n=3

Also find the error of approximation from its actual value.

19.  The demand and supply function for goods are given by P_d: 120- 2Q_d and P_s= 30+ Q_s

i)           Calculate the equilibrium price and quantity.                                                                [3]   

ii)     Calculate the excess of supply(Q_s-Q_d)                                                                                [1] 

.iii)   Calculate the excess of demand (Q_d-Q_s) when p=42                                                          [1]                           

 

                                    Group-C                                         (3x8=24)

 

20.  a) Prove that  =  4a^2 b^2 c^2                       [4] 

      b)  If (x+iy)(3+2i)= 1+i , show that                                                    [2]

c)      Test the periodicity and find the period of f(x)=sinbx                                                         [2]

21.  a)  Write the general equation of circle.                                                                                    [1] 

      b)  Write the equation of tangent to the circle x²+y²=a² at a point (x₁,y₁)   c         [1]

c)      Find the equation of the tangent of the circle x²+y²+6x+4y-12 =0. Which is parallel to the line 4x+3y+12=0.                                                                                                                [4]

d)      Does the normal passes through the center of circle.                                                        [1]            

e)      What is the length of tangent from the point (6,4)  to the circle x²+y²+6x+4y-12 =0.   [1]                     

 

22.  a)   From the first principle, find the derivative of y=                                     [4]

.         b) Find the area of ellipse,                                                                          [4]

Best of Luck