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

ssc steno grade c d 2024 SYLLABUS WISE SUBJECTS MCQs

Question :1

\$9/?\$ × 33824 = 63

\${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:

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.

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)}\$

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)= ?

? = 350 × 4 × 50 = 70000

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