All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
821
In an arithmetic progression with first term 10 and common difference 5, find the sum of the first 13 terms.
Answer:
520
Step-by-step solution: 1. Use S_n = n/2 [2a + (n-1)d]. 2. S_n = 13/2 [2*10 + (13-1)*5]. 3. S_n = 520.
822
In an arithmetic progression with first term 5 and common difference 7, find the sum of the first 19 terms.
Answer:
1292
Step-by-step solution: 1. Use S_n = n/2 [2a + (n-1)d]. 2. S_n = 19/2 [2*5 + (19-1)*7]. 3. S_n = 1292.
823
In an arithmetic progression with first term 10 and common difference 3, find the sum of the first 15 terms.
Answer:
465
Step-by-step solution: 1. Use S_n = n/2 [2a + (n-1)d]. 2. S_n = 15/2 [2*10 + (15-1)*3]. 3. S_n = 465.
824
In an arithmetic progression with first term 10 and common difference 5, find the sum of the first 18 terms.
Answer:
945
Step-by-step solution: 1. Use S_n = n/2 [2a + (n-1)d]. 2. S_n = 18/2 [2*10 + (18-1)*5]. 3. S_n = 945.
825
Find the roots of x² -7x +10 = 0.
Answer:
5 and 2
Step-by-step solution: 1. Factor the quadratic using sum and product of roots. 2. Sum of roots = -b = 7. 3. Product of roots = c = 10. 4. Roots are 5 and 2.
826
Find the roots of x² -10x +16 = 0.
Answer:
8 and 2
Step-by-step solution: 1. Factor the quadratic using sum and product of roots. 2. Sum of roots = -b = 10. 3. Product of roots = c = 16. 4. Roots are 8 and 2.
827
Find the roots of x² -8x +16 = 0.
Answer:
4 and 4
Step-by-step solution: 1. Factor the quadratic using sum and product of roots. 2. Sum of roots = -b = 8. 3. Product of roots = c = 16. 4. Roots are 4 and 4.
828
Find the roots of x² -14x +49 = 0.
Answer:
7 and 7
Step-by-step solution: 1. Factor the quadratic using sum and product of roots. 2. Sum of roots = -b = 14. 3. Product of roots = c = 49. 4. Roots are 7 and 7.
829
Find the roots of x² -10x +25 = 0.
Answer:
5 and 5
Step-by-step solution: 1. Factor the quadratic using sum and product of roots. 2. Sum of roots = -b = 10. 3. Product of roots = c = 25. 4. Roots are 5 and 5.
830
Find the roots of x² -7x +12 = 0.
Answer:
3 and 4
Step-by-step solution: 1. Factor the quadratic using sum and product of roots. 2. Sum of roots = -b = 7. 3. Product of roots = c = 12. 4. Roots are 3 and 4.