Competitive Exam PYQ
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Q. What will be the result after subtracting -3 from -3 ? (-ā§Š-ā§° āĻĒā§°āĻž -ā§Š āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻŋāĻ˛ā§ āĻĢāĻ˛āĻžāĻĢāĻ˛ āĻāĻŋ āĻš'āĻŦ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 0 B) 2 C) 6 D) 3
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
−3 − (−3) ing a positive.
= −3 + 3 =
Rule / āĻ¨āĻŋāĻ¯āĻŧāĻŽ: Subtracting a negative number is the same as adding a positive number. (āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ āĻ¸āĻāĻā§āĻ¯āĻž āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻžāĻā§ āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻ¸āĻāĻā§āĻ¯āĻž āĻ¯ā§āĻ āĻā§°āĻžā§° āĻ¸āĻŽāĻžāĻ¨āĨ¤)
Formula / āĻ¸ā§āĻ¤ā§ā§°: a − (−b) = a + b
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Q. What will be the result after adding 2 to -2 ? (-ā§¨-āĻ¤ ā§¨ āĻ¯ā§āĻ āĻā§°āĻŋāĻ˛ā§ āĻĢāĻ˛āĻžāĻĢāĻ˛ āĻāĻŋ āĻš'āĻŦ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 2 B) 0 C) 4 D) 6
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
−2 + 2 = 0
Rule / āĻ¨āĻŋāĻ¯āĻŧāĻŽ: When two numbers have opposite signs, subtract the smaller number from the larger number and keep the sign of the larger number. Here, 2 and -2 have the same value, so the result is 0. (āĻĻā§āĻāĻž āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻāĻŋāĻšā§āĻ¨ āĻŦāĻŋāĻĒā§°ā§āĻ¤ āĻš'āĻ˛ā§, āĻĄāĻžāĻā§° āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻĒā§°āĻž āĻ¸ā§°ā§ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻž āĻšāĻ¯āĻŧ āĻā§°ā§ āĻĄāĻžāĻā§° āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻāĻŋāĻšā§āĻ¨ āĻ˛ā§ā§ąāĻž āĻšāĻ¯āĻŧāĨ¤ āĻāĻ¯āĻŧāĻžāĻ¤ +ā§¨ āĻā§°ā§ -ā§¨ āĻ¸āĻŽāĻžāĻ¨ āĻŽāĻžāĻ¨ā§°, āĻ¸ā§āĻ¯āĻŧā§āĻšā§ āĻĢāĻ˛āĻžāĻĢāĻ˛ ā§ĻāĨ¤)
Ans / āĻāĻ¤ā§āĻ¤ā§°: B) 0
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Q. What will be the result after subtracting -1 from 1 ? (ā§§ā§° āĻĒā§°āĻž -ā§§ āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻŋāĻ˛ā§ āĻĢāĻ˛āĻžāĻĢāĻ˛ āĻāĻŋ āĻš'āĻŦ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A) 0 B) -2 C) 2 D) 1
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
1- (-1) = 1+1 = 2
Rule / āĻ¨āĻŋāĻ¯āĻŧāĻŽ : Subtracting a negative number is the same as adding a positive number. ("−" × "−" = +)
āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ āĻ¸āĻāĻā§āĻ¯āĻž āĻŦāĻŋāĻ¯āĻŧā§āĻ āĻā§°āĻžāĻā§ āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻ¸āĻāĻā§āĻ¯āĻž āĻ¯ā§āĻ āĻā§°āĻžā§° āĻ¸āĻŽāĻžāĻ¨āĨ¤ ("−" × "−" = +)
Ans / āĻāĻ¤ā§āĻ¤ā§°: C) 2
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Q. Which of the following numbers is not a perfect square ? āĻĒā§ā§°āĻļā§āĻ¨: āĻ¤āĻ˛ā§° āĻā§āĻ¨āĻā§ āĻ¸āĻāĻā§āĻ¯āĻž āĻŦā§°ā§āĻ āĻ¸āĻāĻā§āĻ¯āĻž (Perfect Square) āĻ¨āĻšāĻ¯āĻŧ ?
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: A. 1225 B. 2025 C. 2525 D. 4225
Short Trick
A perfect square ending in 25 must have its first part multiplied consecutively.·
- 1225 = 35² (3 × 4 = 12)
- 2025 = 45² (4 × 5 = 20)
- 4225 = 65² (6 × 7 = 42)
- 2525 For a square ending in 25, if last digit is 5, check: 5 × 6 = 30 ≠ 25
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Q. How many perfect squares are there between 100 and 200 ? (100 āĻā§°ā§ 200ā§° āĻŽāĻžāĻāĻ¤ āĻāĻŋāĻŽāĻžāĻ¨āĻāĻž āĻĒā§ā§°ā§āĻŖ āĻŦā§°ā§āĻ (Perfect Square) āĻāĻā§ ?)
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒāĻ¸āĻŽā§āĻš: (a) 7 (b) 4 (c) 6 (d) 5
Tricks: √100 = 10, √200 ≈ 14.14
Now count the integers between 10 and 14.14: (āĻāĻ¤āĻŋāĻ¯āĻŧāĻž 10 āĻā§°ā§ 14.14ā§° āĻŽāĻžāĻāĻ¤ āĻĨāĻāĻž āĻĒā§ā§°ā§āĻŖ āĻ¸āĻāĻā§āĻ¯āĻžāĻŦā§ā§° āĻāĻŖāĻ¨āĻž āĻā§°ā§āĻ: 11, 12, 13, 14
Total integers = 4 (āĻŽā§āĻ āĻĒā§ā§°ā§āĻŖ āĻ¸āĻāĻā§āĻ¯āĻž = 4)
Therefore, the perfect squares are: āĻ¸ā§āĻ¯āĻŧā§ āĻĒā§ā§°ā§āĻŖ āĻŦā§°ā§āĻāĻ¸āĻŽā§āĻš āĻš'āĻ˛ - 11² = 121, 12² = 144, 13² = 169, 14² = 196
Total / āĻŽā§āĻ = 4
Ans / āĻāĻ¤ā§āĻ¤ā§°: (b) 4
Q. A, B, C, and D are four consecutive even numbers. If A + D = 120, then what is the sum of all four numbers ? (āĻĒā§ā§°āĻļā§āĻ¨: A, B, C, D āĻāĻžā§°āĻŋāĻāĻž āĻā§ā§°āĻŽāĻžāĻāĻ¤ āĻā§ā§° āĻ¸āĻāĻā§āĻ¯āĻžāĨ¤ āĻ¯āĻĻāĻŋ A + D = 120, āĻ¤ā§āĻ¨ā§āĻ¤ā§ āĻāĻžā§°āĻŋāĻāĻāĻž āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻŽā§āĻ āĻ¯ā§āĻāĻĢāĻ˛ āĻāĻŋāĻŽāĻžāĻ¨ ?)
Trick:
For 4 consecutive even numbers: A + B + C + D = 2(A+D)
Given: A + D = 120
Therefore,
Sum = 2 × 120 = 240
Ans: 240
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Q. 1AB + CCA = 895, then B = ?
Options: A) 9 B) 8 C) 5 D) 3
Explanation :
- First, 1 + C = 8, so C = 7.
- Next, A + 7 = 9, so A = 2.
- Finally, 2 + B = 5, so B = 3.
Ans: D) 3