The probability that a plant \(A\) survives is \(\frac{3}{4}\) and the probability that another plant \(B\) survives is \(\frac{1}{3}\).
The probability that only one of them survives is :

The area of the region bounded by the parabola \(y^2=x\) and the straight line 2y = x is

The relation \(R=\{(a, b):\) both \(a\) and \(b\) are either odd or even \(\}\) on the set \(\{1,2,4,5,7,8\}\) is

If \(f(x) = sin\) \(x - cos\) \(x\), \(x \in[0,2 \pi]\) then
(A) f(x) is increasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(B) f(x) is decreasing in \(\left(0, \frac{3 \pi}{4}\right)\)
(C) f(x) is decreasing in \(\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)\)
(D) f(x) is decreasing in \(\left(\frac{7 \pi}{4}, 2 \pi\right)\)
Choose the correct answer from the options given below:

If \(f(x)=-3 x^2\), then \(f(x)\) is:

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

The general solution of \(\frac{d y}{d x}=1+x^2+y^2+x^2 y^2\) is:
(given that \(C\) is the constant of integration)

A generator develops an e.m.f of 150 V and has a terminal potential difference of 125 V, when the armature current is 50 A, the resistance of armature will be

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Malignant malaria is caused by -

\(\int \sin x \sin 2 x \sin 3 x d x\) is equal to:

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Which of the following drugs are commonly used to quickly reduce the symptoms of allergy?

The minimum value of \(\left|\begin{array}{ccc}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{array}\right|, x \in R\) is

Which one of the following plays an important role in guiding the entry of pollen tube into the synergid?