Maths Sample Paper 4 (Part - B) for class Xth

 Maths Sample Paper 

Part - B

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Directions (Q. Nos. 21 - 26) These are very short answer type questions of 2 marks each.

21. If one root of the quadratic Equation 

2x² + kx - 6 = 0 is 2, find the value of k. Also, find the other root.

22. Vicky starts walking from his house to office. Instead of going to the office directly, he goes to a mall first, from there to his wife's office and then reaches the office. What is the extra distance travelled by Vicky in reaching his office? Assume that all distances covered are in straight lines, if the house is situated at (2, 4), mall at (5, 8), wife's office at (13, 14) and office at (13, 26) and coordinates are in kilometre.

23. Prove that 

(sin^8 ∅ - cos^8∅) = (sin²∅ - cos²∅)

 (1 - 2sin²∅cos²∅).

Or

Using the formula, 

sin (A - B) = sinAcosB - sinA sinB, find the value of sin 15°.

24. A letter is chosen at random from the letters of the word 'ASSASSINATION' . Find the probability that the letter chosen is a 

i. Vowel

ii. Consonant

Or

A jar contains 54 marbles which are blue, green or white. The probability of selecting a blue marble at random from the jar is 1/3, and the probability of selecting a green marbles at random is 4/9. How many white marbles does the jar contain?

25. Draw a circle of radius 6 cm. Take a point P on it. Without using the centre of the circle, draw a tangent to the circle at point P.

26. Prove that √3 + √7 is irrational.

Directions (Q. Nos. 27 - 33) These are short answer type questions of 3 marks each.

27. If alpha and beeta are the zeroes of the polynomial x² - 2x - 15, then form a quadratic polynomial whose zeroes are 2alpha and 2 beeta.

28. Find the values of k for which the following equation has equal roots.

(k - 12)x² + 2(k - 12)x + 2 = 0

29. Find the length of the median through vertex A of a ∆ABC, whose vertices are 

A(7 , -3), B(5, 3) and C(3, -1).

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Or

The two opposite vertices of a square are (-1, 2) and (3,2). Find the coordinates of the other two vertices.

30. Prove that the line segments joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle.

Or

In ∆PQR, PS is perpendicular QR and (PS)² = QS ×RS. Prove that ∆PQR is a right angled triangle.

31. If tanA = n tanB and sinA = m sinB, then prove that cos² A = m² - 1/ n² - 1.

32. Find the median for the following frequency distribution.

33. Find the zeroes of the polynomial f(x) 

x³ - 5x² -2x +24, if it is given that the product of it's two zeroes is 12.

Directions (Q. Nos. 34 - 36) These are long answer  type questions of 5 marks each.

34. Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6cm and measure it's length. Also, verify the measurement by actual calculation.

35. Draw the graphs of 2x + y = 6 and 

2x - y + 2 = 0. Shade the region bounded by these lines and X- axis. Find the area of the shaded region.

Or

Places P1 and P2 are 250 km apart from each other on a national highway. A car starts from P1 and another from P2 at the same time. If they go in the same direction then they meet in 5h and if they go in opposite directions they meet in 25/13h. Find their speeds.

36. The angle of the elevation of the top of a tower from certain point is 30° . If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

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Posted by - Anuranjan Gadekar

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