\(x\)-axis, \(y=\cos x\) and \(y=\sin x, 0 \leq x \leq \frac{\pi}{2}\) is:

If X, Y, Z, W \& P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k respectively. The restrictions on n,k \& p so that PY + WY be defined are:

If \(y=x^{x \sin x}\) then \(\frac{d y}{d x}=\) ?

The value of \(\left|\begin{array}{ccc}x & x+y & x+y+z \\ 2 x & 3 x+2 y & 4 x+3 y+2 z \\ 3 x & 6 x+3 y & 10 x+6 y+3 z\end{array}\right|\) is

If \(A\) and \(B\) are symmetric matrices of order \(3 \times 3\) then the matrix \(2 A B-B A\) is :

If A and B are symmetric matrices of the same order, then which one of the following is true?

The corner points of the bounded feasible region for a linear programming problem (LPP) are \(\left(0, \frac{3}{2}\right),(1,2)\) and \((4,0)\).
If the objective function is \(Z=a x+b y\), where \(a\) and \(b\) are positive,
then the condition on \(a\) and \(b\) so that the maximum of \(Z\) occurs at \((1,2)\) and \((4,0)\) is :

If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), where \(|x|<1,|y|<1\) and \(x \neq y\), then

Match List-I with List-II

List-I (Quantity)	List-II (Variation with distance r)
(A) Electric field intensity (E) due to a single charge	(I) \( \propto \frac{1}{r} \)
(B) Electric field intensity due to electric dipole	(II) \( \propto \frac{1}{r^4} \)
(C) Electric potential (V) due to a single charge	(III) \( \propto \frac{1}{r^3} \)
(D) Electric field intensity due to a quadrupole	(IV) \( \propto \frac{1}{r^2} \)

Choose the correct answer from the options given below:

The correct decreasing order of acidic strengths of trioxides of nitrogen family is
A. \(\text{P}_2\text{O}_3\)
B. \(\text{N}_2\text{O}_3\)
C. \(\text{As}_2\text{O}_3\)
D. \(\text{Bi}_2\text{O}_3\)
E. \(\text{Sb}_2\text{O}_3\)
Choose the correct answer from the options given below:

The binomial distribution for which the mean is 5 and variance 4, is

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
What was the expected phenotypic ratio in any Mendelian monohybrid cross that had changed when F₁ (Rr) was self-pollinated in this cross?

If the value of the refractive index of a denser medium with respect to the rarer medium is 1.414, then the critical angle is: