The term anomers of glucose refers to

The pyrimidine bases present in DNA are

If $$A^2-A+1=0$$, then the inverse of $$A$$ is :

The system of equations $$\text{matrix}\alpha x+y+z=\alpha -1\text{cr}x+\alpha y+z=\alpha -1\text{cr}x+y+\alpha z=\alpha -1\text{cr}$$ has no solutions, if $$\alpha$$ is :

If $$a_1,a_2,a_3,........,a_n,.....$$ are in G.P., then the determinant $\Delta = \left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr {\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr {\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr } } \right|$ is equal to :

If $$a^2+b^2+c^2=-2$$ and f\left( x \right) = \left| {\matrix{ {1 + {a^2}x} & {\left( {1 + {b^2}} \right)x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {1 + {b^2}x} & {\left( {1 + {c^2}} \right)x} \cr {\left( {1 + {a^2}} \right)x} & {\left( {1 + {b^2}} \right)x} & {1 + {c^2}x} \cr } } \right|, then f$$(x)$$ is a polynomial of degree :

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

A random variable $$X$$ has Poisson distribution with mean $$2$$. Then $$P\left(X>1.5\right)$$ equals :

Let $$A$$ and $$B$$ two events such that P\left( {\overline {A \cup B} } \right) = {1 \over 6}, P\left( {A \cap B} \right) = {1 \over 4} and P\left( {\overline A } \right) = {1 \over 4}, where $$\overline{A}$$ stands for complement of event $$A$$. Then events $$A$$ and $$B$$ are :

The differential equation representing the family of curves $$y^2=2c\left(x+\sqrt{c}\right),$$ where $$c>0,$$ is a parameter, is of order and degree as follows:

If x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right), then the solution of the equation is :

If non zero numbers $$a,b,c$$ are in $$H.P.,$$ then the straight line {x \over a} + {y \over b} + {1 \over c} = 0 always passes through a fixed point. That point is :

If a vertex of a triangle is $$(1,1)$$ and the mid points of two sides through this vertex are $$(-1,2)$$ and $$(3,2)$$ then the centroid of the triangle is :

The line parallel to the $$x$$ - axis and passing through the intersection of the lines $$ax+2by+3b=0$$ and $$bx-2ay-3a=0,$$ where $$(a,b)$$ $$\ne$$ $$(0,0)$$ is :

If A = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right] and I = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right], then which one of the following holds for all $$n\ge 1,$$ by the principle of mathematical induction?

The value of $${}^{50}{C}_4+\sum _{r=1}^6{}^{56-r}{C}_3$$ is

If the coefficient of $$x^7$$ in {\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}} equals the coefficient of $$x^{-7}$$ in {\left[ {ax - \left( {{1 \over {b{x^2}}}} \right)} \right]^{11}}, then $$a$$ and $$b$$ satisfy the relation

If $$x$$ is so small that $$x^3$$ and higher powers of $$x$$ may be neglected, then {{{{\left( {1 + x} \right)}^{{3 \over 2}}} - {{\left( {1 + {1 \over 2}x} \right)}^3}} \over {{{\left( {1 - x} \right)}^{{1 \over 2}}}}} may be approximated as

If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of $${(1+\mathrm{y})}^m$$ are in A.P., then m and r satisfy the equation

\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx} is equal to