The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(\sin |x|+\cos |x|) d x\), is equal to:

If \(A(3,2), B(1,-1)\) and \(C(2,1)\) are three vertices of a parallelogram \(A B C D\), then its area (in sq. units) is equal to

A die is thrown. If \(A\) is the event 'the number appearing is a multiple of 3 ' and \(B\) is the event 'the number appearing is even', then A and B are :

The point on the curve \(x^2=2 y\) in the I quadrant which is nearest to the point (0, 5) is:

Let \(A=\left[a_{i j}\right]_{3 \times 2}\) and \(B=\left[b_{i j}\right]_{3 \times 4}\) be two matrices.
Then the order of the matrix \(\left(A^T \cdot B\right)^T\) is :

If A is a skew-symmetric matrix, then which of the following statements is NOT true?
(A) A is singular if order of A is odd
(B) A is non-singular
(C) \(A^{2025}\) is a skew-symmetric matrix
(D) \(A^{2025}\) is a symmetric matrix
(E) all diagonal elements of A are zeros
Choose the correct answer from the option given below :

If the lines \(\frac{x-5}{5 \lambda+2}=\frac{2-y}{5}=\frac{1-z}{-1}\) and \(x=\frac{y+1 / 2}{2 \lambda}=\frac{z-1}{3}\) are perpendicular, then the value of \(\lambda\) is equal to

Match List-I with List-II

List-I (EM wave)	List-II (Production)
(A) Light	(I) Klystron valve or magnetron valve
(B) X-rays	(II) Rapid acceleration/deceleration of electrons in aerials
(C) Microwave	(III) Electrons in atoms move from higher to lower energy level
(D) Radiowave	(IV) Inner shell electrons/ fast-moving electrons decelerated by metal target

Choose the correct answer from the options given below:

Let \(N\) be set of natural numbers, then the function \(f : N \rightarrow N\), defined by
\(f(n)=\left\{\begin{array}{ll}\frac{n+1}{2} & ,\text { if } n \text { is odd } \\ \frac{n}{2} & , \text { if } n \text { is even }\end{array}\right.\) is

The chromosomal disorders are caused due to absence, excess or abnormal arrangement of one or more chromosomes. Failure of segregation of chromatids during cell division results in the gain or loss of chromosome(s), called aneuploidy.
Which of the following statements are correct with respect to the humans suffering from the disorder?
(A) One in every 800 live births shows this karyotype
(B) The affected individual has 45 chromosomes.
(C) Non-disjunction of chromosomes at the time of gamete formation causes this disorder.
(D) In this disorder, individual has 45 autosomes
Choose the correct answer from the options given below:

Plants can capture only 2-10% of the PAR and this small amount of energy sustains the entire world. Here PAR stands for:

In Young's double slit experiment, slits are illuminated by light of wavelength 650 nm. The slits are 0.13 cm apart and the screen is placed 1.2 m away. What will be the separation of the adjacent maxima?

Arrange the following electromagnetic waves in the increasing order of their energy.
(A) Ultraviolet rays
(B) Infrared rays
(C) Microwaves
(D) X-rays
(E) Gamma rays
Choose the correct answer from the options given below: