Author admin Posted on Categories Uncategorized   Leave a comment on Q. If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2 )^n and B denotes the sum of all the coefficients in the expansion of (1+x^2 )^n, then : (1) A=B^3 (2) 3A=B (3) B=A^3 (4) A=3B

Q. If A denotes the sum of all the coefficients in the expansion of (1-3x+10x^2 )^n and B denotes the sum of all the coefficients in the expansion of (1+x^2 )^n, then : (1) A=B^3 (2) 3A=B (3) B=A^3 (4) A=3B

Ans: (1) Solution: Sum of coefficients in the expansion of(1-3x+10x^2 )^n=Athen A=(1-3+10)^n=8^n ( put x=1)and sum of coefficients in the expansion of (1+x^2 )^n=Bthen B=(1+1)^n=2^nA=B^3

Author admin Posted on Categories Uncategorized   Leave a comment on Q. The number of common terms in the progressions 4,9,14,19,……. , up to 25th term and 3,6,9,12, up to 37th term is : (1) 9 (2) 5 (3) 7 (4) 8

Q. The number of common terms in the progressions 4,9,14,19,……. , up to 25th term and 3,6,9,12, up to 37th term is : (1) 9 (2) 5 (3) 7 (4) 8

Ans. (3)Sol. 4,9,14,19,…, up to 25th termT_25=4+(25-1)5=4+120=1243,6,9,12,…, up to 37th termT_37=3+(37-1)3=3+108=111Common difference of 1st series d_1=5Common difference of 2nd series d_2=3First common term =9, andtheir common difference =15( LCM of d_1 and d_2 )then common terms are9,24,39,54,69,84,99

Author admin Posted on Categories Uncategorized   Leave a comment on If the shortest distance of the parabola y^2=4x from the centre of the circle x^2+y^2-4x-16y+64=0 is d, then d^2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36

If the shortest distance of the parabola y^2=4x from the centre of the circle x^2+y^2-4x-16y+64=0 is d, then d^2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36

Ans. (3)Sol. Equation of normal to parabolay=mx-2m-m^3this normal passing through center of circle (2,8)8=2m-2m-m^3 or, m=-2So point P on parabola ⇒(am^2,-2am)=(4,4)And C=(2,8)PC=√(4+16)=√20d^2=20

Author admin Posted on Categories Uncategorized   Leave a comment on Permutation Word Problems with Solutions

Permutation Word Problems with Solutions

Learn to solve a great variety of permutation word problems with easy to follow explanations. The combination word problems will show you how to do the followings: Word problem #1 There are 18 students in a classroom. How many different eleven-person students can be chosen to play in a soccer team? Solution The order in which students are listed once the students are chosen does not distinguish one student from another. You need the number of combinations of 18 potential … Continue reading “Permutation Word Problems with Solutions”