If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

• 601

• 600

• 602

• 602

12.

The value  of 

• 
• 
• 
• 

If A =  and I =  , then which one of the following holds for all n ≥ 1, by the principle of mathematical induction

• Aⁿ = n^A – (n – 1)I

• Aⁿ = 2^n-1A – (n – 1)I

• Aⁿ = nA + (n – 1)I

• Aⁿ = nA + (n – 1)I

If the coefficient of x⁷  in equals the coefficient of x^-7 inthen a and b satisfy the relation

• a – b = 1

• a + b = 1

• a/b =1

• a/b =1

If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z2| then argz₁ – argz₂ is equal to

• π/2

• -π

• 0

• 0

• an ellipse

• a circle

• a straight line

• a straight line

Let α and β be the distinct roots of ax2 + bx + c = 0, then  equal to

• 

• 0

• 
• 

If x is so small that x³ and higher powers of x may be neglected, then may be approximated as

If  where a, b, c are in A.P. and |a| < 1, |b|<1, |c|< 1, then x, y, z are in

• G.P.

• A.P.

• Arithmetic − Geometric Progression

• Arithmetic − Geometric Progression

In a triangle, ABC, let ∠C = π/2 . If r is the in radius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

• b + c

• a+b

• a + b + c

• a + b + c