Explore topic-wise InterviewSolutions in Current Affairs.

If tan theta +cot theta =2, find the value of tan^{​​​​2} theta + cot^{​​​​2} theta

Solve 24x < 100 when

(i) x is a natural number

(ii) x is an integer

If A and B are two events such that

$P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3}$ and $P(A\cap B)=\frac{1}{4},$ then find

(iii) $P\left(\frac{A^{\prime }}{B}\right).$

If the points $(0,2,5),(1,-2,4),(2,a,3)$ are collinear then which of the following is/are correct ?

The integral value(s) of $a$ for which the equation $[\frac{3}{2}+\frac{1}{50}]+[\frac{3}{2}+\frac{2}{50}]+[\frac{3}{2}+\frac{3}{50}]+\cdots +[\frac{3}{2}+\frac{49}{50}]=x^2+6x+a^2-7a+84,\forall x\in R$ have one positive and one negative root is/are

The number of words from the letters of the word 'Bharat' in which B and H will never come together, is

Decide, among the following sets, which sets are subsets of one and another:

A = {x: x ∈ R and x satisfy x² – 8x + 12 = 0},

B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.

If S is the focus of a parabola and PQ is any focal chord, then the semi-latus rectum of the parabola is

Find the values of other five trigonometric functions if , x lies in second quadrant.

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required. The conditional probability that $X\ge 6$ is given $X>3$ equals

• Add ful to the words given in brackets and complete the sentences.
  
  You must be ________________ to your friends. (help)
  
  
  
  Make a ________________ drawing. (colour)
  
  
  
  The puppy is so ________________. (play)
  
  
  
  Be ________________ while crossing the road. (care)
  
  


• Join the two words to make one word. Look at the example.

• Write five things you can do. Start with 'I can ______.'

1. I can ________________.

2. _____________________ .

3. ______________________.

4. ______________________.

5. ______________________.

6. I cannot ______________ but I can ______________.

7. I cannot ______________ but I can ______________.

8. I cannot ______________ but I can ______________.

• Give yourself a big star for being what you are.

The number of values of k for which the system of equations $(k+1)x+8y=4k,kx+(k+3)y=3k-1$ has infinitely many solution is

An urn contains 25 balls of which 10 balls bear a mark X and the remaining 15 bear a mark Y. A ball is drawn at random from the urn, its mark note down and it is replaced. If 6 balls are drawn in this way, find the probability that

The number of balls with X mark and Y mark will be equal.

If the letters of the word MATHEMATICS are arranged arbitrarily, the probability that C comes before E, E before H,H before I and I before S is

If $f\left(x\right)=4x^3-x^2-2x+1$ and $g\left(x\right)=\{\begin{array}{cc}min.\left\{f\right(t):0\le t\le x\};0\le x\le 1& \\ 3-x;1<x\le 2& \end{array}$ then the value of $\lambda$ lf $\frac{\lambda }{2}=g\left(\frac{1}{4}\right)+g\left(\frac{3}{4}\right)+g\left(\frac{5}{4}\right)$, is ___ .

The distances of the point (1,2,3) from the coordinate area are A, B, and C respectively now consider the following equations

$\left(1\right)A^2=B^2+C^2\text{(2)}{B}^2=2C^2\text{(3)}2A^2{C}^2=13B^2$

Which of these holds true?

The solution set of the inequation $\frac{3}{|x|+2}\ge 1$ is

Find the area of the region

If $f\left(x\right)=x^3-6x^2+9x+k=0$ has one root in $(1,3)$ then range of $k$ is

For the matrixshow
that A³ − 6A² + 5A +
11 I = O. Hence, find A^−1.

Let $\alpha$ and $\beta$ be the roots of $x^2-6x-2=0$ with $\alpha >\beta$ if $a_n={\alpha }^n-{\beta }^n$ for $n\ge 1$ then the value of $\frac{a_{10}-2a_8}{3a_9}=$

Prove that
sin 2x + 2sin 4x + sin 6x = 4cos² x
sin 4x

The area (in sq. units) bounded by the curve $y=\sqrt{x},2y-x+3=0,x$-axis, and lying in first quadrant is :