CBSE Question Paper 2019 (Set-1) Class 11 Mathematics Mahanhi Palanjall VidyaMandir, Prayagraj

Time: 3 Hr

1. 90

Total Pages: 3

General Instructions:

1. All questions are compulsory.

1. The question paper consists of 27 questions divided into 4 sections A, B, C and D. Section A comprises of 4 questions of one mark each. Section B comprises of 8 questions of two marks each. Section C comprises of 10 questions of four marks each. Section D comprises of 5 questions of six marks each

1. There is no overall choice. However internal choice has been provided in 3 questions of four marks and 2 questions of six marks.

Omission of essential working will result in loss of marks.

Section - A

1. Let <math>A = \{x : x^2 - 5x + 6 = 0\}, B = \{2, 4\}, C = \{4, 5\}.</math> Write <math>AX(B \cap C)</math>.
2. If A = {1,2,3,4,5}, then write the number of proper subsets of A.
3. If the arcs of same length in two circles subtend angles of 30° and 75° at their centres. Find the ratio of their radii.
4. Let f= {(1, 1),(2, 3),(0, -1).(-1,-3)} be a linear function from Z to Z, find f(x).

Section - B

1. If n arithmetic means are inserted belween 20 and 80 such that the ratio of first mean to the last mean is 1:3, find the value of n.

If in a triangle ABC, angle B= 60° and b: c = 5: 42, then find angle A.

1. Solve the equation <math>\sin x + \sin 3x + \sin x = 0</math>.
2. If one geometric mean 'G' and two arithmetic means 'p' and 'q' be inserted between two given quantities. prove that <math>G^2 = (2p - q)(2q - p)</math>.

1/3

1. Solve the equation <math>2x^2 + 3ix + 2 = 0</math> using general expression for a quadratic equation.
2. If <math>y = \sin\left(\frac{x}{2}\right) + \cos\left(\frac{x}{2}\right)^2</math>, find dydx at <math>x = \frac{\pi}{4}</math>.
3. Solve the inequation <math>\left|\frac{3x-4}{2}\right| = \frac{5}{12}</math>
4. Find the sum of n terms of the series <math>1^2 + 3^2 + 5^2 + 7^2 + \dots</math>

Section - C

Show by using principle of mathematical induction that for n∈N. <math>\cos \alpha \cdot \cos 2\alpha \cdot \cos 4\alpha \cdot \dots \cdot \cos(2^{n-1}\alpha) = \frac{\sin 2^n \alpha}{2^n \sin \alpha}</math>

1. Two cards are drawn at random from a pack of 52 cards. Find the probability that both the cards are of red colour or they are queen.
2. If <math>\frac{3}{2+\cos\theta-i\sin\theta}</math> = a + ib, prove that <math>a^2 + b^2 = 4a - 3</math>.

OR If <math>(1 + x)^n = a_0 + a_1x + a_2x^2 + a_3x^3 + \dots + a_nx^n</math>, prove that <math>2^n = (a_0 - a_2 + a_4 - \dots) + (a_1 - a_2)^n + a_1x + a_2x^2 + a_3x^3 + \dots</math> a₃ + a₅-.....).

1. Find the centre and radius of the circle

<math>(x \cos\alpha + y\sin\alpha - a)^2 + (x\sin\alpha - y\cos\alpha - b^2) = k^2</math>. If <math>\alpha</math> varies, show that the locus of its centre is again a circle.

1. Find the equation of the parabola whose focus is (1.1) and tangent the vertex is <math>x + y = 1</math>.
2. Find the locus of a point such that the sum of its distances from the points (0.2) and (0.-2) is 6.
3. Find <math>\lim_{x\to 0} \frac{\cot 2x - \csc 2x}{x}</math>

OR

Evaluate <math>\lim_{x\to 0} \frac{\sqrt{1+x^2}-\sqrt{1+x}}{x}</math>

1. Find the derivative of <math>tan(2x + 1)</math> with respect to x from the first principles
2. (i)
3. How many different words can be formed with the letters of the word HARYANA?
4. How many of these words begin with 11 and end with N?
5. In how many of these words have H and N are together?

2/3