If \(f(x)=x^3 e^{-x}\), then the value of \(f^{\prime \prime}(1)\) is equal to

If \(X\) is normal distribution random variable with mean \(\mu=10\) and standard deviation \(\sigma=2, Z\) is standard normal variable and \(F(Z)\) is cumulative distribution function, then which of the following are true?
[Given that \(F(1.5)=0.9332, F(3)=0.9986, F(2.25)=0.9878\) and \(F(1)=0.8413\) ]
(A) \(P(X<13)=0.9332\)
(B) \(P(X>16)=0.9986\)
(C) \(P(12<X<14.5)=0.1465\)
(D) \(P(X>8)=0.8413\)
Choose the correct answer from the options given below:

The value of b for which the function \(f(x) = \sin x - bx + C\), where b and C are constants is decreasing for \(x \in R\) is given by

If the feasible region of an LPP is bounded and the corresponding objective function is \(Z =5 x -9 y\), then the objective
function attains :

The domain of the function \(\cos ^{-1}(2 x-3)\) is

The function \(f(x)=|x-3|, x \in R\) is:

A Bond has a coupon rate of 10\% per annum paid semi annually and the coupon payment made is ₹ 50 , so the face value of the bond is :

According to Gause's Competitive Exclusion Principle:

The ratio of the radii of two nuclei of mass numbers \( A_1 \) and \( A_2 \) respectively would be

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
"Maltose" disaccharide is composed of

Area of region bounded by the curves \(x=y^3, x=0\) between \(y=-1\) and \(y=2\) is :

Identify the correct statement for Zygote Intra-Fallopian Transfer (ZIFT).

Which of the following combinations should be used for better tuning of an LCR circuit used for communication?