TCS NQT Equations Questions and Answers Quiz 1

Given,

Total question = 26,

Let x be the number of questions which are correct,

⇒ The number of questions that are incorrect = 26 - x,

Now, five points were deducted for each wrong answer and eight points were added for every correct answer,

Thus, the total score = 8x - 5(26-x)

According to the question,

8x - 5(26-x) = 0

⇒ 8x - 130 + 5x = 0

⇒ 13x = 130

⇒ x = 10

Hence, 10 questions are correctly answered



Video solution:

first equate 4x+1 and 5y-1

4x+1=5y-1

5y-4x=2

now try different values of x and y to satisfy above eqn.

these values are

y=2 and x=2 i.e number is 9

y=6 and x=7 i.e number is 29

y=10 and x=12 i.e number is 49

y=14 and x=17 i.e number is 69

y=18 and x=22 i.e number is 89

among these numbers 29 and 89 are prime

Let the age of elder person be x

Let the age of younger person be x - 25

9 years before

∴ x - 9 = 6( x - 25 )

x - 9 = 6x - 150

150 - 9 = 6x - x

141 = 5x

28 = x

x - 25 = 28 - 25 = 3

Addition = 28 + 3 = 31



Video solution:

Let f(x) = x³ – 3x² + kx – 10

Now, f(x) at (x = 5)

⇒   f(x) = (5)³ – 3(5)² + 5k – 10 = 0

⇒   125 – 3 × 25 + 5k – 10 = 0

⇒   125 – 75 – 10 + 5k = 0

⇒   40 + 5k = 0   ⇒   5k = –40   ⇒   k = –8.



Video solution:

Let the two digit number be 10x+y
Adding 2 after doubling the number is reverse of the number.
So 2(10x+y)+2 = 10y+x
19x -8y +2=0
Above equation satisfies for the value, x=2, y=5
So the number is 10*2+5= 25

Alternate solution : Option verification-

take
22 , 22*2+2 =46 wrong
24, 24*2+2=50 wrong
25, 25*2+2=52 correct
27 , 27*2+2=56 wrong

So answer is 25



Video solution:

Let f(x) = x³ + 6x² + 11x + 6

f(x) = 0. So, put x = – 1, –2 and –3

f(–1) = (–1)³ + 6(–1)² + 11(–1) + 6 = –1 + 6 – 11 + 6

= –12 + 12 = 0.

f(–2) = (–2)³ + 6(–2)² + 11(–2) + 6 = –8 + 24 – 22 + 6

= –30 + 30 = 0.

f(–3) = (–3)³ + 6(–3)² + 11(–3) + 6 = –27 + 54 – 33 + 6

= –60 + 60 = 0.

Hence, (x + 1), (x + 2) and (x + 3) are the factors of f(x).



Video solution:

f(x) = (1 – x)(1 + x²) = 1 + x² – x – x³

So,  2x³ – x² + x – 1  is added to  1 + x² – x – x³  to obtain x³.



Video solution:

{(x² + y²) (x – y) – (x – y)³} / (x²y – xy²)

= {x³ + xy² – x²y – y³ – (x³ – y³ –3x²y + 3xy²)} / x²y – xy²

= (x³ + xy² – x²y – y³ – x³ + y³ + 3x²y – 3xy²) / x²y – xy²

= (2x²y – 2xy²) / x²y – xy² = 2(x²y – 2xy²) / x²y – xy² = 2



Video solution:

Put x = –3 in equation x³ + 2x² + 3x + 8
= (–3)³ + 2(–3)² + 3(–3) + 8
= –10 ≠ 0
So, (x + 3) is not the factor of x³ + 2x² + 3x + 8
Similarly, put x = 2 in above equation
= (2)³ + 2(2)² + 3(2) + 8
= 30 ≠ 0
So, (x – 2) is also not the factor of x³ + 2x² + 3x + 8.



Video solution:

{a + (1 / a)}² = 3

⇒ a + (1 / a) = 3

On cubing both sides, we get

⇒ {a + (1 / a)}³ = (3)³

⇒ a³ + (1 / a³) + 3 {a + (1 /a)} = 33

⇒ a³ + (1 /a³) + 33 = 33

⇒ a³ + (1 / a³) = 33 – 33 = 0



Video solution: