Municipality Examination
Mathematics - Grade XI
Examination - 2079 (2022)
Regular Students
Time - 3 hrs
Full Marks - 75
Pass Marks - 27
Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.
Also Check:-
Note: Don't use Dark mode
Attempt all the question
Group 'A'
Choose the correct alternative. [11x1=11]
1) A compound statement that is always true, whatever may be the truth values of its components, is known as
a) tautology
b) contradiction
c) inverse
d) contrapositive
2) The sum of three cube roots of unity is equal to
a) 0
b) 1
c) 2
d) None of the above
3) Which one of the following is a projection law?
a) cosA=b2+c2-a2/2bc
b) sinA/2=√(s-b)(s-c)/bc
c) a/sinA=b/sinb=c/sinc=2R
d) a= b cosC+c cosB
4) The length of the perpendicular drawn from the point (2,3) to the line 8x+15y+24=0 is
a) 4
b) 20
c) 1
d) 5
5) The equation of a tangent to the circle x2+y2=25 at the point (3,4) is
a) 3x-4y=25
b) 3x+4y=25
c) 4x-3y=25
d) 4x+3y=25
6) If a -->=(5,3) b-->=(-2,-3), then find the unit vector along 2a-->+3b--> is
a) (4,6)
b) (2,-3)
c) (2/5,11/5)
d) (4/5,-3/5)
7) The probability that a leap-year selected at random contains 53 Sundays is
a) 1/7
b) 3/7
c) 2/7
d) None of the above
8) The value of limx-->01-cos9x/x2 is equal to
a) 81/2
b) 81/8
c) 1/2
d) None of the above
9) The derivative of log(ax+b) is
a) 1/ ax+b
b) x/ ax+b
c) a/ ax+b
d) b/ ax+b
10) For the inequality of the type Ax<=b, the new introduced non-negative variable 'r' such that Ax+r=b is called
a) Surplus variable
b) slack variable
c) both of the above
d) none of the above
11) If the total cost of producing Q units of items is C(Q)= 25000+50Q, then the fixed cost is
a) 20000
b) 22000
c) 25000
d) 30000
Group 'B'
b) If G is the geometric mean between two distinct positive numbers a and b, then show that 1/G2-a+1/G2-b=1/G2
13) a) Show that ∣ 1 1 1 ∣ = (a - b) (b -c) (c - a)
∣ a b c ∣
∣ aˆ3 bˆ3 cˆ3 ∣
b) Express the equation 4+4√3 I in polar form and calculate the multiplicative inverse of 3-2i.
14) a) Find the equation of the parabola whose vertex is at (3,2) and focus is at (5,2).
b) Prove by vector method: b = c cosA + a cosC
15) Following is the information about the marks of two students A and B:
| A | B | |
| Average marks (x) | 84 | 92 |
| Variance (s.d.)ˆ2 | 16 | 25 |
Examine who has got the uniform marks.
b) The probability that a boy will get a scholarship is 0.75 and that a girl will get is 0.72. What is the probability that at least one of them gets the scholarship?
16) Define the continuity of a function at a point. A function f(x) is defined as follows:
f(x)= {kx + 3 for x ≥ 2
{3x - 1 for x < 2
Find the value of k so that f(x) is continuous at x=2.
17) Find the local maxima, local minima, and the point of inflection of the function:
f(x)=3x3-2x2-36x.
18) Evaluate using the trapezoidal rule: ∫ 2 1 dx/1+x, n=4, also, estimate the error.
19) The fixed cost of the new product is Rs.4000 and the variable cost per unit of output is Rs.8. Find the total cost function. Also, find the total cost of producing 47 units of items.
Group 'C'
20) a) Let p and q be any two statements, prove that (p ∧ q) => (p ∨ q) is a tautology.
b) State De-Morgan's law. Prove that AUB ― = A― n B―
21) a) Prove that the equation 2x2+7xy+3y2-4x-7y+2=0 represents a pair of straight lines.
b) In any tringle, prove that
a3(sin3B-sin3C)+b3(sin3C-sin3A)+c3(sin3A-sin3B)=0
22) a) Evaluate: ∫ log(ax+b)/ax+b dx.
Also, find the Area of the circle x 2+y2=25
THE END
Photos:-
Also Check:-
If you want to ask anything, please contact us by Messaging us on Social Media.
Social Media links:-
.post-body{
line-height:1.5; }If you want to ask anything, please contact us by Messaging us on Social Media.
Social Media links:-
