NEB — CLASS 11
Model Question
Answer each question in your own words as far as practicable. The figures in the margin indicate full marks.
सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)
Which of the following is a statement?
(a) The fishes are beautiful
(b) Study mathematics.
(c) x is a capital of country y.
(d) Water is essential for health.
The value of √(-16) × √(-25) is
(a) -20
(b) -20i
(c) 20i
(d) 20
If ∠C = 60°, b = 5 cm and a = 4 cm of △ABC, what is the value of c?
(a) 3.58 cm
(b) 4.58 cm
(c) 4.89 cm
(d) 4.56
In a triangle ABC, B = 120°, a = 1, c = 1 then the other angles and sides are
(a) 35, 45, √2
(b) 10, 50, √3
(c) 20, 40, 2
(d) 30, 30, √3
The cosine of the angle between the vectors a=i−2j+3k and b=i+3j+3k is
(a) 1/14
(b) 14
(c) √14
(d) 196
The equation of parabola with the vertex at the origin and the directrix y - 2 = 0 is
(a) x² - 8y = 0
(b) y² + 8y = 0
(c) x² + 8y = 0
(d) y² - 8y = 0
A mathematical problem is given to three students Sumit, Sujan and Rakesh whose chance of solving it are 1/2, 1/3 and 1/a respectively. The probability that the problem is solved is 3/4. The possible values of a are
(a) 9/2
(b) 4
(c) 1/4
(d) 1/8
lim (θ→0) (sin θ)/θ is equal to
(a) 0
(b) ∞
(c) 1
(d) 0/0
The derivatives of (4x² + 3)/(3x² - 2) is
(a) -34x / (3x² - 2)²
(b) 30x² / (3x² - 2)
(c) -32x / (3x² - 2)³
(d) -31x / (3x - 2)²
By Newton’s Raphson, the positive root of x³ - 18 = 0 in (2, 3) is
(a) 2.666
(b) 2.621
(c) 2.620
(d) 2.622
Two forces acting at an angle of 45° have a resultant equal to √10 N, if one of the forces be √2 N, what is the other force.
(a) 1N
(b) 2N
(c) 3N
(d) 4N
A function f(x) = x² is given. Answer the following question for the function f(x).
(i) What is the algebraic nature of the function?
(ii) Write the name of the locus of the curve.
(iii) Write the vertex of the function.
(iv) Write any one property for sketching the curve.
(v) Write the domain of the function.
Compare the sum of n terms of the series: 1 + 2a + 3a² + 4a³ + ……… and a + 2a + 3a + 4a … up to n terms.
In any triangle, prove that: (b + c) Sin(A/2) = a Sin(A/2 + B)
Express r=(4,7) as the linear combination of a=(5,−4) and b=(−2,5)
Calculate the appropriate measure of Skewness for the data below.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|---|
| No of workers | 10 | 12 | 25 | 35 | 40 | 50 |
Define different types of discontinuity of a function. Also write the condition for increasing, decreasing and concavity of function. (2+3)
Evaluate: ∫ (x² dx) / √(a² - x²)
Define Trapezoidal rule. Evaluate using Trapezoidal rule for ∫₀¹ dx/(1 + x) , n = 4.
State sine law and use it to prove Lami’s theorem.
The factor of expression ω3 - 1 are ω - 1 and ω2 + ω + 1. If ω3 - 1 = 0
(i) Find the possible values of ω and write the real and imaginary roots of ω.
(ii) Prove that:
| 1 ωn ω2n |
| ω2n 1 ωn | = 0. Where n is positive integer.
| ωn ω2n 1 |
Verify that: |x + y| ≤ |x| + |y| with x = 2 and y = -3
The single equation of pair of lines is 2x2 + 3xy + y2 + 5x + 2y - 3 = 0
(i) Find the equation of pair straight lines represented by the single equation.
(ii) Are the pair of lines represented by the given equation passes through origin? Write with reason.
(iii) Find the point of intersection of the pair of lines.
If three vectors a, b and c are mutually perpendicular unit vectors in space then write a relation between them.
(i) Distinguish between derivative and anti-derivative of a function. Write their physical meanings and illustrate with example in your context. Find the differential coefficient of log(sin x) with respect to x. (1+2+2)
(ii) Find the area bounded by the y-axis, the curve x² = 4(y - 2) and the line y = 11.