\(\int_0^{\frac{\pi}{2}} \sin ^2 x d x\) is equal to:

The slope of the normal to the curve \(y=x^3-4 \sin x\) at \(x=0\) is:

If A is an invertible matrix of order 3 × 3 then the value of |adj(A)| is:

A plane meets the coordinates axes at A, B and C such that centroid of \(\triangle A B C\) is at the point (2, 3, 1). If the equation of the plane is 3x + 2y + 6z = k, then k is:

A Linear Programming Problem (LPP) consists of which of the following components?
(A) Decision variables
(B) The graphical compliment
(C) The objective function
(D) The linear constraints
Choose the correct answer from the options given below :

Let \(\left|\begin{array}{cc}3 x & -7 \\ 1 & 4\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & x\end{array}\right|\), then value of \(x\) is :

A card is picked at random from a pack of 52 playing cards. Given that the picked card is a queen, the probability of this card to be a card of spade is:

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Pick the incorrect statement from the following:

If \(x=4 t^2, y=8 t\), then \(\frac{d^2 y}{d x^2}\) is:

Identify the incorrect statement in reference to the latitudinal gradient in biodiversity.

Which types of bonds or interactions are found in the β-helix of protein?

Which one of the following factors can influence Hardy-Weinberg equilibrium?
A Natural selection
B. Genetic recombination
C. Gene flow
D. Mutation

A uniform wire of resistance 12 \( \Omega \) is cut into three pieces in the ratio of length 1 : 2 : 3. Now the three pieces are connected to form a triangle. A cell of emf 8 V and internal resistance 5 \( \Omega \) is connected across the highest of the three resistors. The current through the circuit is: