simplification Model Questions & Answers, Practice Test for ssc steno grade c d 2024

Question :1

$9/?$ × 33824 = 63

Answer: (b)

${9/?}×33824=63$

or ? = ${9×33824}/63$=4832

Question :2

One of the factors of the polynomial $x^4 – 7x^3 + 5x^2$ – 6x + 81 is:

Answer: (d)

Let f(x) = $x^4 – 7x^3 + 5x^2$ – 6x + 81

By hit and trial method,

$x^4 – 7x^3 + 5x^2$ – 6x + 81

= $x^3 (x – 3) – 4x^2(x – 3)$ – 7x(x – 3) – 27(x – 3)

= (x – 3) ($x^3 – 4x^2$ – 7x – 27)

(x – 3) is one of the factor of the given polynomial.

Question :3

If , $a/b = b/c = c/d$ then which of the following is/are correct?
1. ${b^3 + c^3 + d^3}/{a^3 + b^3 + c^3} = d/a$
2.${a^2 + b^2 + c^2}/{b^2 + c^2 + d^2} = a/d$
Select the correct answer using the code given below.

Answer: (c)

Let $a/b = b/c = c/d$ = k

⇒a = bk, c = ck, c = dk

⇒abc = $bcdk^3$

⇒a = $dk^3$

(1) ${b^3 + c^3 + d^3}/{a^3 + b^3 + c^3} = d/a$

(2) ${a^2 + b^2 + c^2}/{b^2 + c^2 + d^2} = a/d$

⇒${b^3 + c^3 + d^3}/{b^3k^3 + c^3k^3 + d^3k^3} = d/a$

⇒${b^2k^2 + c^2k^2 + d^2k^2}/{b^2 + c^2 + d^2} = a/d$

⇒${b^3 + c^3 + d^3}/{(b^3 + c^3 + d^3)k^3} = d/a$

⇒${(b^2 + c^2 + d^2)k^2}/{b^2 + c^2 + a^2} = a/d$

⇒$1/{k^3} = d/a$

⇒$k^2 = a/d$

⇒$k^2 – k^3$

⇒$1/{a/d} = d/a$

which is not possible

⇒$d/a = d/a$

⇒only (1) is true.

∴ Option (a) is correct.

Question :4

If ab + bc + ca = 0, then the value of ${(b^2 - ca) (c^2 - ab) + (a^2 - bc) (c^2 - ab) + (a^2 - bc) (b^2 - ca)}/{(a^2 - bc) (b^2 - ca) (c^2 - ab)}$

Answer: (a)

ab + bc + ca = 0

– ab = c(b + a).........(i)

– bc = a(b + c) .........(i)

– ca = b(a + c) .........(i)

ATQ,

${(b^2 - ca) (c^2 - ab) + (a^2 - bc) (c^2 - ab) + (a^2 - bc) (b^2 - ca)}/{(a^2 - bc) (b^2 - ca) (c^2 - ab)}$

$1/{a^2 - bc} + 1/{b^2 - ca} + 1/{c^2 - ab}$

$1/{a(a + b + c)} + 1/{b(a + b + c)} + 1/{c(a + b + c)}$

From (i)

${bc + ac + ab}/{(a + b + c) abc}$ = 0

Question :5

(331 + 19) × (15 – 11) × (37 + 13)= ?

Answer: (c)

? = 350 × 4 × 50 = 70000

ssc steno grade c d 2024 IMPORTANT QUESTION AND ANSWERS

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