Which of the following are NOT correct regarding the equation of tangent and normal to the curve \(y=\frac{x-11}{(x-2)(x-3)}\) at the point, where it cuts the \(x\)-aris?
(A) The point of contact is \((11,0)\).
(B) The equation of tangent is \(x-72 y-11=0\).
(C) The equation of normal is \(7 2 x + y - 1 1 = 0\).
(D) The slope of the tangent at the given point of contact is \(\frac{1}{88}\).
Choose the correct answer from the options given below:

Consider the following hypothesis test:
\(H_0: \mu \leq 16\)
\(H_a: \mu>16\)
A sample of 25 provided a sample mean \(\bar{x}\) = 17 and a sample standard deviation S = 3.5, then the value of the test statistic in t-test is:

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where k > 0 is 30 sq. units, then the value of k is

For the linear programming problem,
Minimize (Z) =60x + 30y
subject to : \(2 x - y \geq-5 ; 3 x + y \geq 3 ; 2 x -3 y \leq 12; x , y \geq 0\)
the optimal value of \(z\) is

The value of \(\int_0^3|2 x-6| d x\) is :

Let \(R\) be the set of all real numbers and \(f: R \rightarrow\) Range \(f\) be given by \(f(x)=3 x^2+1\). Then \(f^{-1}\{1,2\}\) is :

The function \(f:[-1,1] \rightarrow \mathbb{R}\) (set of real numbers) given by \(f(x)=\frac{x}{x+3}\) is

If \(I=\int \frac{x^4+x^2+1}{x^2-x+1} d x=a x+\beta x^2+\gamma x^3+\delta\), where \(\delta\) is the constant of integration, then \((a+2 \beta+3 \gamma)\) equals

The biodiversity is ______ at lower altitudes and ______ with increasing higher latitudes.

Which of the following statements about d-block elements is correct?

Read the given passage carefully and answer the questions
Antibiotics have greatly improved our capacity to treat deadly diseases such as plague, whooping cough (kali khansi), diphtheria (gal ghotu) and leprosy (kusht rog), which used to kill millions all over the globe.
Streptokinase produced by the bacterium Streptococcus and modified by genetic engineering is used as a 'clot buster' for removing clots from the blood vessels of patients who have undergone myocardial infarction leading to heart attack. Microbes are diverse-protozoa, bacteria, fungi and microscopic animal and plant viruses, viroids and also prions that are proteinacious infectious agents. The puffed-up appearance of dough is due to the production of CO₂ gas. Similarly the dough, which is used for making bread, is fermented using baker's yeast (Saccharomyces cerevisiae). Primary sewage treatment basically involve physical removal of particles - large and small from the sewage through filtration and sedimentation. These are removed in stages; initially, floating debris is removed by sequential filtration. Then the grit (soil and small pebbles) are removed by sedimentation. All solids that settle form the primary sludge, and the supernatant forms the effluent. The effluent from the primary settling tank is taken for secondary treatment. The primary effluent is passed into large aeration tanks, where it is constantly agitated mechanically and air is pumped into it. This allows vigorous growth of useful aerobic microbes into flocs. While growing, these microbes consume the major part of the organic matter in the effluent.
Prions are made up of :

A galvanometer having a resistance of \( 8 \, \Omega \) is shunted by a wire of resistance \( 2 \, \Omega \). If the current is 1 A, the part of it passing through the shunt will be:

Arrange these in ascending order of wavelength while propagating through different medium.
(A) Light propagating in air
(B) Light propagating in water
(C) Light propagating in diamond
(D) Light propagating in glass
Choose the correct answer from the options given below :