The equation of the normal to the curve \(y=\frac{x-7}{(x-2)(x-3)}\) at (7,0) is:

In what ratio, water must be added to dilute honey costing ₹ 320 per liter so that the resulted syrup would be worth ₹ 280 per liter?

The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is:

If A is an invertible matrix of order 2 ; then \(\operatorname{det}\left(A^{-1}\right)\) is equal to:

Let \(f: R \rightarrow R\) be defined as \(f(x)=5 x^2\). Choose the correct answer :

A vector of magnitude 9, which is perpendicular to both the vectors \((4 \hat{i}-\hat{j}+8 \hat{k})\) and \((-\hat{j}+\hat{k})\) is

If \(\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|\), then x is equal to :

Match List I with List II

List I	List ll
(A) Down's syndrome	(I) 44 + XX/XY
(B) Klinefelter's syndrome	(II) 44 + XO
(C) Turner's syndrome	(III) 44 + XXY
(D) Normal human	(IV) 45 + XX/XY

Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Electronic Device)	List-II (Function)
(A) Stabilizer	(I) Used to convert a.c. voltage into d.c. voltage
(B) Filter	(II) Used either for stepping up or stepping down the a.c. voltage
(C) Rectifier	(III) Used for constant output voltage even when the input voltage or load current changes
(D) Transformer	(IV) Used to remove any ripple in the rectified output voltage

Choose the correct answer from the options given below:

The function \(f(x)=x^2-x+1\) is

If \(|\vec{a}-\vec{r}|=|\vec{a}|=|\vec{r}|=1\), then angle between \(\vec{a}\) and \(\vec{r}\) is

Which substance is produced by a cell in viral infection that protect other cells from further infection?

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, 3d series (Sc to Zn), 4d series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has Ac and elements from Rf to Cn. The two series of the inner transition metals; 4f (Ce to Lu) and 5f (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of s and p-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
Which of the following statements is correct?