Mathematical Tools | Set-1

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Q 1. Find the distance of point (–12, 5) from the origin.

Ans: 13

Q 2. Find the value of a if the distance between (a, 3) cm and (–2, 6) cm is 5 cm.

Ans: -6 or 2

Q 3. The two shorter sides of a right-angled triangle are 5 cm and 12 cm. Let θ denote the angle opposite to the 5 cm side. Find sin θ, cos θ, and tan θ.

Ans: 5/13, 12/13, and 5/12

Q 4. Find x, y, and the perimeter of the triangle shown:

Ans: 3, 4 and 12

Q 5. Find the value of:

  1. sin 30º + cos 60º
  2. sin 0º – cos 0º
  3. tan 45º – tan 37º
  4. cos 180º
  5. sin 150º
  6. cos 120º
  7. tan 135º
  8. sin (–30º)
  9. cos (–60º)
  10. tan (45º)

Ans: (i) 1, (ii) -1, (iii) ¼, (iv) -1, (v) ½, (vi) -½, (vii) -1, (viii) -½, (ix) ½, (x) 1

Q 6. Evaluate:

  1. sin (210º)
  2. cos 120º
  3. sin (330º)
  4. tan (300º)

Ans: (i) -½, (ii) -½, (iii) -½, (iv) –3

Q 7. The equation of the line making an angle of 135º with the positive x-axis and passing through the point (2, 3) will be:

  1. y – x = 5y – x = 5y – x = 5 
  2. y = x – 5y = x – 5y = x – 5
  3. y – x = 1y – x = 1y – x =1
  4. y = –x+ 5y = –x + 5y = –x + 5

Ans: 4

Q 8. Statement I: Line 3x + 5y = 103x + 5y = 103x + 5y = 10 is parallel to the line 5x + 3y = 95x + 3y = 95x + 3y = 9. 

Statement II: The slope of the line joining the points (2, 3) and (4, –1) is –2.

  1. Both Statement I and Statement II are true, and Statement II is the correct explanation of Statement I.
  2. Both Statement I and Statement II are true, but Statement II is not the correct explanation of Statement I.
  3. Statement I is true, but Statement II is false.
  4. Statement I is false, but Statement II is true.

Ans: 4

Q 9. The equation of the line is 2y = 3x – 62y = 3x – 62y = 3x – 6. Its x and y intercepts are:

  1. –3, 2
  2. 3, –2
  3. 2, –3
  4. –2, 3

Ans: 3

Q 10. The distance between points (2, 3, –7) and (–2, 0, 5) is:

  1. 5
  2. 13
  3. 145
  4. 119

Ans: 2

Q 11. Find sum of 1 + 3 + 5 + 7 + … + 51.

Ans: 676

Q 12. Find 20th term of series 1 + 5 + 9 + 13 + …..

Ans: 77

Q 13. Find the sum of the first 20 natural numbers.

  1. 210 
  2. 200
  3. 220 
  4. 230

Ans: 1

Q 14. The sum of the first five multiples of 3 is:

  1. 45 
  2. 55
  3. 65 
  4. 75

Ans: 1

Q 15. Find the sum of the geometric series: 

4 – 12 + 36 – 108 + ………… to 10 terms.

  1. 59048 
  2. –30421
  3. –59048
  4. 30421

Ans: 3

Q 16. Find the sum to n terms of the sequence, 8, 88, 888, 8888…..

Ans: 

Q 17. If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.

Ans: 5, 8, 11, or 11, 8, 5

Q 18. Find the sum of the following series: 0.6 + 0.66 + 0.666 + … to n terms.

Ans: 

Q 19. Find the sum of the following arithmetic progressions: 50, 46, 42, … to 10 terms.

Ans: 320

Q 20. log 25 + log 4 – log 5 is equal to:

  1. log 20 
  2. log 25
  3. log 15 
  4. log 10

Ans: 1

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