From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function
\(z=1.50 x+1.00 y\), the maximum value of \(z\) will be;-

A die is thrown 4 times and getting 3 is considered a success. The probability of 2 successes is :

The area of the smaller region enclosed by the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and the ne straight straight line \(\frac{x}{4}+\frac{y}{3}=1\) is \(a \pi+b\). The value of a + b is:

A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contains atleast 8 units of Vitamin A and 10 units of Vitamin C. Food 'I' contains 2 units/kg of Vitamin A and 1 unit/kg of Vitamin C while food 'II' contains 1 unit/kg of Vitamin A and 2 units/kg of Vitamin C. It costs ₹5 per kg to purchase food I and ₹7 per kg to purchase food II. If 'x' kg of food I is mixed with 'y' kg of food II, then the constraint pertaining to vitamin C contents will be:

The point at which the maximum value of \(x+y\), subject to constraints \(x+2 y \leq 70,2 x+y \leq 95, x \geq 0, y \geq 0\) is obtained, is :

If the tangent to the curve \(y^2 + 3x - 7 = 0\) at the point (h, k) is parallel to the line x - y = 4, then the value of k is:

The area of a triangle whose vertices are (-3,0), (3, 0) and (0, k) is 6. Then the value (or the values) of k will be:

Reaction of Phenol with conc. \(HNO _3\) gives

"Choose the reactions given by \(\text{Cr}_2\text{O}_7^{2-}\)
(A)\(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O}\)
(B) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{H}_2\text{S} \rightarrow 2\text{Cr}^{3+} + 3\text{SO}_4^{2-} + 7\text{H}_2\text{O}\)
(C) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{Sn}^{2+} \rightarrow 2\text{Cr}^{3+} + 3\text{Sn}^{4+} + 7\text{H}_2\text{O}\)
(D) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 3\text{Cr}^{3+} + 2\text{H}_2\text{O}\)
(E) \(\text{Cr}_2\text{O}_7^{2-} + 2\text{OH}^- \rightarrow 2\text{CrO}_4^{2-} + \text{H}_2\text{O}\)
Choose the correct answer from the options given below:"

Match List I with List - II.

List - I (Message Signal)	List - II (Band width)
(A) Speech	(I) 20 kHz
(B) TV Signal	(II) 2800 Hz
(C) Video for pictures	(III) 6 MHz
(D) Music	(IV) 4.2 MHz

Choose the correct answer from the options given below:

Value of \(\tan ^{-1} 2+\tan ^{-1} 3+\tan ^{-1} 4\) is equal to:

The person with karyotype 44+XXY is suffering from:

The critical points of \(f(x)=x^3+x^2+x+1\) are