In what ratio must pulses at ₹72 per kg be mixed with pulses ₹90 per kg so that the mixture be worth ₹80 per kg?

If \(A = \mathbb{R} - \left\{\frac{3}{2}\right\}\) and function \(f: A \rightarrow A\) is defined by \(f(x) = \frac{3x-2}{2x-3}\), then

If \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}-2 \hat{k}, \vec{c}=\hat{i}+3 \hat{j}-\hat{k}\), such that \(\vec{a}\) is perpendicular to \((\lambda \vec{b}+\vec{c})\), then the value of \(\lambda\) is :

A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successe, is:

A box contains 10 balls, each marked with one of the digits 0 to 9 .
If four balls are drawn successively with replacement from the box,
then the probability that none is marked with the digit \(0\) is :

The vector equation of line passing through (2, -1, 3) and perpendicular to the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+2}{2} \quad\) and \(\quad \frac{x+3}{-4}=\frac{y-5}{-3}=\frac{z+1}{2}\)
(Here \(\lambda\) is a parameter)

If a person \(A\) speaks the truth in \(80 \%\) cases and the person \(B\) speaks the truth in \(75 \%\) cases, then the probability that they contradict each other in a statement is:

If \(\int \frac{d x}{(x-1)^{3 / 4}(x+2)^{5 / 4}}=\alpha[1-g(x)]^\beta+c\), where \(c\) is a constant of integration, then which of the
following are true?
(A) \(\alpha=\frac{2}{3}\)
(B) \(\beta=\frac{3}{4}\)
(C) \(3 \alpha+4 \beta=5\)
(D) \(g(x)=\frac{3}{x+2}\)
Choose the correct answer from the options given below:

The plane \(x(1+2 \lambda)+y(2+\lambda)+z(3-\lambda)=0\) passes through the intersection of :

For a manufacturer, total cost function is given by \(C=\frac{x^2}{25}+2 x\). Which of the following are correct ?
A. 2.6 is the marginal cost when 5 units are produced.
B. \(\frac{2 x}{25}+2\) is the marginal cost function.
C. \(\frac{x}{25}+2\) is the average cost function.
D. 2.4 is the marginal cost when 5 units are produced.
E. \(\frac{x}{25}+1\) is the average cost function.
Choose the correct answer from the options given below:

Read the given passage and answer the question given below.
The sex linked recessive disease, which shows its transmission from unaffected carrier female to some of the male progeny has been widely studied. In this disease, a single protein that is a part of the cascade of proteins involved in the clotting of blood is affected. Due to this in an affected individual a simple cut will result in non-stop bleeding. The heterozygous female (carrier) for the disease may transmit it to sons. The possibility of a female becoming a sufferer of disease is extremely rare because mother of such a female has to be at least carrier and the father should be sufferer. The family pedigree of Queen Victoria shows a number of suffering descendents as she was a carrier of the disease.
Identify the genotype of queen Victoria. ('- gene for disorder)

Answer the question on the basis of passage given below :
A colloid is a heterogeneous system in which a substance is dispersed (dispersed phase) as fine particles in another substance called dispersion medium.
Their particle size is intermediate between that of pure solutions (less than 1 nm ) and suspensions (greater than 1000 nm ).
They are known for interesting properties such as enormous surface area, Tyndall effect, Brownian motion etc.
They are widely used in industries and day to day life.
Some prominent uses of colloids are those in smoke precipitators, purification of water, medicines, cleansers etc.
Stability of a colloid is intermediate between that of a solution and suspension. This stability can be attributed to _____________
A. Presence of charge on the particles of dispersed phase.
B. Prolonged mechanical stirring.
C. Solvation by the dispersion medium.
D. Brownian Motion.
E. Dialysis
Choose the correct answer from the options given below :

In Young's double slits experiment, if the ratio of the width of the two slits is 25 : 1, what is the ratio of intensity at the maxima and minima in the interference pattern?