The corner points of the feasible region of LPP \(x+y \leq 200, y \geq 4 x, x \geq 20, x \geq 0, y \geq 0\) are :
(A) \((20,180)\)
(B) \((40,180)\)
(C) \((20,80)\)
(D) \((40,80)\)
(E) \((40,160)\)

A small company manufactures necklaces and bracelets. The combined number of necklaces and bracelets it can handle per day is at the most 24 .A bracelet takes 1 hour to make and a necklace takes half hour to be made.Maximum number of hours available per day is 16 .If the number of necklaces and bracelets made per day is \(x\) and \(y\)
respectively then the time constraint for the L.P.P.is :

Area bounded by \(x=\frac{y^2}{4}\) and its latus rectum is:

If \(y=\left\{\log \left(x+\sqrt{x^2+1}\right)\right\}^2\) then \(\left(1+x^2\right) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}=\)

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4} \\ k, & x=\frac{\pi}{4}\end{array}\right.\)
is continuous at \(x=\frac{\pi}{4}\), then the value of \(k\) is:

The value of the determinant \(\left|\begin{array}{ccc}a+b & b+c & c+a \\ c & a & b \\ 1 & 1 & 1\end{array}\right|\) is :

Which of the following functions f(x) are differentiable at \(x = 0\)?
(A) \(|x|\)
(B) \(| x - 1|\)
(C) [x],where [t] denotes the greatest integer ≤ t
(D) \(| x + 1|\)
(E) \(x^2\)
Choose the correct answert from the option given below :

The number of years required for a sum of money to get tripple at the effective rate of \(4\%\) is : (Given \((1.04)^{28}=3\) )

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots \infty}}}\) then \(\frac{d y}{d x}\) equals to

Which one of the following hormones is essential for maintenance of the endometrium?

Arrange the following mixtures in increasing order of their resultant molarity
(A) 20 mL of 0.5 M HCl + 30 mL of 0.3 M HCl
(B) 30 mL of 0.3 M HCl + 30 mL of 0.3 M HCl
(C) 20 mL of 0.5 M HCl + 20 mL of 0.3 M HCl
(D) 20 mL of 0.3 M HCl + 30 mL of 0.5 M HCl
Choose the correct answer from the options given below:

Which of the following statements is/are true with respect to the MTP (Amendment) Act, 2017 enacted by the GOI?
(A) A pregnancy may be terminated on certain considered grounds within the first 12 weeks of pregnancy on the opinion of two government registered medical practitioners.
(B) This act intends to reduce illegal abortions and consequent maternal mortality and morbidity.
(C) If the continuation of pregnancy involves a risk to the life of a pregnant woman, it can be terminated by the opinion of 3 government registered medical practitioners.
(D) If there is a substantial risk that the child born will be seriously handicapped, pregnancy can be terminated even if lasted for more than 12 weeks, but fewer than 24 weeks by the opinion of two government registered medical practitioners.
Choose the correct answer from the options given below:

Arrange the following electromagnetic waves in decreasing order of their wavelength respectively.
A. Gamma Rays
B. UV Rays
C. Infrared Rays
D. X-Rays
E. Microwaves
Choose the correct answer from the options given below: