quadratic equations mcq pdf Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

ibps rrb so officer sclae 2 3 single exam 2024 SYLLABUS WISE SUBJECTS MCQs

Number System

Lcm & Hcf

Ratio & Proportion

Percentage

Time & Work

Mensuration

Advance Math

Trigonometric Ratios & Identities

Average

Profit & Loss

Alligation & Mixtures

Compound Interest

Linear Equations

Quadratic Equations

Click To More Exercise For Quadratic Equations
Question :11

For what value of c the quadratic equation $x^2$ – (c + 6) x + 2(2c – 1) = 0 has sum of the roots as half of their product?

Answer: (a)

(c + 6) = 1/2 × 2(2c – 1) ⇒ c + 6 = 2c – 1 ⇒c = 7

Question :12

Which is not true?

Answer: (d)

(a) is clearly true.

(b) $x^2$ + 1 is a quadratic polynomial which has no real value of x for which $x^2$ + 1 is zero.

[∴ $x^2 ≥ 0 ⇒ x^2$ + 1 > 0 for all real x]

∴ (b) is true.

(c) The quadratic polynomial

$x^2 – 2x + 1 = (x – 1)^2$ has only one zero i.e. 1

∴ (c) is true.

[∵ $(x – 1)^2$ > 0 at x ≠ 1 and for x = 1, $(x – 1)^2$ = 0]

(d) is false [∵ of (b), (c)]

Hence (d) holds.

Question :13

  1. $x^2$ + 13x = - 42
  2. $y^2$ + 16y + 63 = 0

Answer: (b)

Question :14

If $√{3x^2 + x + 5} = x – 3$, then the given equator has ...... solution/solutions.

Answer: (d)

Square both sides, we shall get x = – 4, $1/2$.

But both of them do not satisfy the given equation.

Question :15

Solve the simultaneous equations $√{x/y} + √{y/x} = 5/2$; x + y = 10

Answer: (b)

We have $√{x/y} + √{y/x} = 5/2$ ...(1)

and x + y = 10 ...(2)

Now, $√{x/y} + √{y/x} - 5/2 ⇒ {x + y}/√{xy} = 5/2$

⇒ $10/√{xy} = 5/2$ [using eq. (2)]

⇒ $√{xy}$ = 4 ⇒ xy = 16

Thus, the given system of simultaneous equations reduces to

x + y = 10 and xy = 16

⇒ y = 10 – x

and xy = 16

⇒ x(10 – x) = 16

⇒ $x^2$ – 10x + 16 = 0

⇒ (x – 2) (x – 8) = 0 ⇒ x = 2 or x = 8

Now, x = 2 and x + y = 10 ⇒ y = 8

and x = 8 and x + y = 10 ⇒ y = 2

Hence, the required solution are x = 2, y = 8

and x = 8, y = 2

Click To More Exercise For Quadratic Equations
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