Karnataka 1st PUC Advance Maths Model Paper 2024: Kannada Medium and English Medium PDF
Karnataka 1st PUC Advance Maths Model Paper 2024: KSEAB, DPUE has recently published Karnataka 1st PUC Advance Maths Model Question Paper 2024 in its official portal. In this page we have given Karnataka Class 11 Advance Maths Model Question Paper in PDF. The Board has also published Blue Print of I PUC on dpue-exam.karnataka.gov.in.
Karnataka 1st PUC Advance Maths Model Question Paper 2024: Overview
- Board – Karnataka State Board.
- Class – Class 11.
- Topic – Karnataka 1st PUC Model Paper.
- Subject – Advance Maths.
- Year – 2023 – 24.
Part – A
(I) Answer all the multiple choice questions:
(1) The interval form of {x : x ∈ R, – 4 < x ≤ 6} is
(a) [–4, 6]
(b) (–4, 6]
(c) (–4, 6)
(d) [–4, 6)
(2) If (x + 1, y –2) = (3, 1) then
(a) x = 2, y = 3
(b) x = 2, y = –3
(c) x = –2, y = 3
(d) x = 2, y = –1
(3) The degree measure of 5π/3 radians is equal to
(a) 225°
(b) 300°
(c) 420°
(d) 135°
(4) The conjugate of i – 2 is
(a) i + 2
(b) –2 + i
(c) -2 – i
(d) – i + 2
(5) a > b implies
(a) – a < – b
(b) –a > b
(c) –a < b
(d) a < –b
(6)
(a) 1
(b) 17
(c) 7
(d) 10
(7) The number of terms in the expansion of (a + b)6 is
(a) 6
(b) 5
(c) 7
(d) 8
(8) If a sequence is defined as an = 2n + 5, then the first term is
(a) 5
(b) 6
(c) 7
(d) 8
(9) The equation of x – axis is
(a) x = 0
(b) y = 0
(c) xy = 0
(d) x = y
(10) The centre of the circle (x + 2)2 + (x – 3)2 = 16 is
(a) (2, 3)
(b) (–2, 3)
(c) (–2, –3)
(d) (2, – 3)
(11) The length of transverse axis of the hyperbola x2/9 – y2/16 = 1 is
(a) 4
(b) 6
(c) 9
(d) 16
(12) The octant in which the point (–3, 1, 2) lies is
(a) First
(b) Second
(c) Third
(d) fourth
(13) The derivative of 2x – 3/4 with respect to x is
(a) 2
(b) – 3/4
(c) -2
(d) 0
(14) The Median of the data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 is
(a) 18
(b) 9
(c) 12
(d) 10
(15) The probability of drawing a diamond card from a well shuffled deck of 52 cards is
(a) 1/4
(b) 1/52
(c) 1/13
(d) 1/2
(II) Fill in the blanks by choosing the appropriate answer from those given in the bracket (-1, 16, 0, 20, 42, 1).
(16) If A = {1, 2} and B = {3, 4}, then the number of relations from A to B is _______.
(17) The value of cos3π is ___________.
(18) The value of 7!/5! is ________.
(19) The slope of the line passing through the points (3, –2) and (7, –2) is ________.
(20) The derivative of x2 – 2 at x = 10 is _________.
Part – B
Answer any six questions
(21) Let A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8}. Find A – B and B – A
(22) List all the the subsets of the set {a, b}
(23) Prove that 3 sin π/6 . sec π/3 – 4 sin 5π/6 . cot π/4 = 1
(24) Find the multiplicative inverse of 2 – 3i
(25) If x + iy = a+ib/a-ib, prove that x2+y2 = 1
(26) Solve inequality 5x –3 < 3x + 1 and show the graph of the solutions on number line.
(27) How many 3–digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
(28) Expand (1 – 2x)5, using Binomial theorem
(29) Find the equation of the line intersecting the x– axis at a distance of 3 units to the left of origin with slope -2.
(30) Evaluate
(31) A die is thrown. Describe the following events
(1) A number less than 4
(2) A number not less than 3
Part – C
Answer any six questions:
(32) Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5} prove that (A ∪ B)1 = A1∩B1
(33) Let f(x) = x2 and g (x) = 2x + 1 be two real functions.
Find that cos3 = 4 cos3x-3 cosx
(35) If cosx = – 1/2, x lies in third quadrant, find the values of other five trigonometric functions.
(36) Express 5+√2i/1-√2i in the form a + ib
(37) Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
(38) The sum of first three terms of a G.P. is 13/12 and their product is –1. Find the common ratio and the terms.
(39) Derive the equation a line with x-intercept ‘a’ and y-intercept ‘b’ in the form x/a + y/b = 1
(40) Find the equation of the Parabola with vertex (0,0), passing through the point (2,–3) and symmetric about y – axis.
(41) show that the points (0, 7, 10), (–1, 6, 6 ) and (– 4, 9, 6) are the vertices of a right angled triangle.
(42) Find the derivative of sinx with respect to x form first principle.
Part – D
Answer any four questions
(43) Define Greatest integer function, draw the graph. Write the domain and range
(44) Prove that sin5x – 2sin3x + sinx/cos5x-cosx = tanx
(45) Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements,
(1) do the words start with P?
(2) do the words begin with I and end in P?
(46) Prove that for every positive integer n
(47) Derive the formula to find the distance of a point P (x1, y1) from the line Ax + By + C = 0
(48) Prove geometrically that , x being measured in radians
(49) Find mean deviation about the mean for the following data
xi |
2 | 5 | 6 | 8 | 10 | 12 |
fi | 2 | 8 | 10 | 7 | 8 |
5 |
(50) A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be
(i) red
(ii) yellow
(iii) blue
(iv) not blue
Part – E
Answer the following questions
(51) Prove geometrically that cos (x + y) = cosx cosy – sinx siny
Or
Derive the equation of ellipse in the standard form x2/a2 + y2/b2 = 1
(52) Find the sum of the sequence 7, 77, 777, 7777, – – – – – – – to n terms
Or
Find the derivative of x5-cosx/sinx with respect to x
Click Here to Download this PDF: Advance Maths Model Question Paper
You can download more Karnataka Board 1st PUC model question papers here – Karnataka Class 11 Model Paper
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