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If k is ratio of zeroes of the polynomial $4x^2-5x-3,$ then the value of ${(k+\frac{1}{k})}^{-2}$ is

The line y - x = 0, passes through the point ___.

The zeroes of the polynomial $x^2-x-12$ is

1. 0

I have a certain number of chocolates. My friend has 4 more than twice the number of chocolates I have. Which of the following equations depicts the relation between the number of chocolates with me and my friend?

(Assume $x$ as number of chocolates I have and $y$ as number of chocolates my friend has.)

where n, m are non-negative integers. Then x has a decimal expansion which ___________________

If (x-1) is a factor of ax - a, then find the value of a

You picked a card at random from a deck of 52, noted the suit of the card, and then replaced the card. You repeated this experiment 99 more times. Your observations are as shown below.

$\begin{array}{cc}\text{Suit}& \text{Frequency}\\ \text{Spades}& 23\\ \text{Diamond}& 26\\ \text{Club}& 21\\ \text{Heart}& 30\end{array}$

Find the probability of drawing
(i) Spades
ii) Diamonds
(iii) Clubs
(iv) Hearts.
Show that the sum of these probabilities is 1. [4 MARKS]

In the next six questions there is no negative marking. The best answer carries one mark while other answer choices carry less than one mark.

Q80. You are the chief manager of an important project. There are six fairly independent parts of the project requiring different mix of skill set and knowledge base. The six parts are handled by different team leaders. At this time four of the teams are progressing well with their assigned parts. However, two teams are behind schedule and if this state of affairs continues the project would have time overrun. Part of the problem lies in the fact that some staff members in these two behind schedule teams have left the organization without replacement. In the situation what action should you take?

1. Talk to the two teams to collectively analyses what is the problem.

2. Hold the two team leaders to be responsible for delay and think of replacing them.

3. Inform higher management about the developments and request filling the vacant positions.

4. Explore the possibility of outsourcing some part of the work.

∆ABC, in which angle A equal to 90 degree and AC equal to AC then find the angle

In Fig. X and Y are two points on equal sides AB and AC of a ΔABC such that AX = AY. Prove that XC = YB. [2 MARKS]

What is ${\frac{121}{169}}^{\frac{-3}{2}}$?

The supplement of a right angle is ___.

It is proposed to insert a circular curve of radius 300 m with a transition curve of 90 m length at each end. The spiral angle and central angle are respectively:

$(\text{Deflection angle = 40}{}^{\circ }\text{)}$

Question 1 (vi)

Without actually performing the long division, state whether $\frac{23}{2^3\times 5^2}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

In $\Delta ABC,\angle A={45}^{\circ },\angle B={60}^{\circ }$ and $\angle C={75}^{\circ }$. The angles of the triangle formed by joining the mid-points of the sides of this triangle are

Consider the following two statements:

Statement - 1: If two figures have same shape and same size then they are called congruent.

Statement - 2: If two figures have equal area they are called congruent.

Now, choose the correct option.

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively.

Three coins were tossed thirty times. Each time the number of heads occurring was noted as follows:

0, 1, 2, 2, 1, 2, 3, 1, 3, 0

1, 3, 1, 1, 2, 2, 0, 1, 2, 1

3, 0, 0, 1, 1, 2, 3, 2, 2, 0

The frequency distribution table for the given data will be

Which of the following is always irrational?

In the given figure, if $\angle ACB:\angle ABC=1:4,$

then ∠OAD is

The given figure shows a coloured region in a circle.

If the coloured part is compared with the full circle, what is the ratio of the coloured part to the full circle?

Find the area of an equilateral triangle having altitude h cm.

Four rational numbers between 3 and 4 are:

Factorise:

$x^2+\frac{12}{35}x+\frac{1}{35}$