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In a test of x questions , y( $<$ x) answers are correct. Assuming all questions were answered, the number of incorrect answers are

If median $AD$ of a triangle $ABC$ makes an angle $\frac{\pi }{6}$ with side $BC$, then the value of $(\cot B-\cot C{)}^2$ is equal to:

Draw a $\Delta ABC$ in which AB= 4 cm, BC = 6 cm and AC = 9 cm, construct a triangle similar to $\Delta ABC$ with scale factor $\frac{3}{2}$. Justify the construction. Are the two triangles congruent? Note that, all the three angles and two sides of the two triangles are equal.

Construct a triangle ABC, with AB=7 cm, BC= 8 cm and $\angle ABC={60}^o$. Locate by construction the point P such that:

(i) P is equidistant from B and C.

(ii) P is equidistant from AB and BC.

Measure and record the length of PB.

If the roots of the equation q$x^2$ + p$x$ + q = 0 where p, q are real, are complex, then the roots of the equation $x^2$ - 4q$x$ + $p^2$ = 0 are

If $S_n=n^{2}p$ and $S_{m_3}=m^{2}p,m\ne n$, in an A.P., prove that $S_p=p^3$.

A card is drawn at random from a pack of 52 cards. Find the probaility that the card drawn is

(i) a black king

(ii) either a black card or a king

(iii) black and a king

(iv) a jack, queen or a king

(v) neither a heart nor a king

(vi) spade or an ace

(vii) neither an ace nor a king

(viii) neither a red card nor a queen

(ix) other than an ace

(x) a ten

(xi) a spade

(xii) a black card

(xiii) the seven of clubs

(xiv) jack

(xv) the ace of spades

(xvi) a queen

(xvii) a heart

(xviii) a red card

(xix) neither a king nor a queen

If $(I+A{)}^7=x\cdot A+y\cdot I;A=\left[\begin{array}{cc}0& 3\\ 0& 0\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right].$ Then which of the following statement(s) is(are) correct

(where $x,y\in R$)

Question 14(i)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$

Construct a cumulative frequency table.

If A = {1,2,3,4,5},

B= {4,5,6,7,8} and C= {7,8,9,10,11}

Find :

(i) $A\cup B$ (ii) $A\cup C$

(iii) $B\cup C$

ΔABC is right angled at A, the value of tan B x tan C is:

The value of $\left|\begin{array}{ccc}3x& -x+y& -x+z\\ x-y& 3y& z-y\\ x-z& y-z& 3z\end{array}\right|$ equals to

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

The following images are __________ as they are identical.

Find the consecutive even integers whose squares have the sum 340.

If $A=\left[\begin{array}{ccc}2& -3& 9\end{array}\right],B=\left[\begin{array}{ccc}0& -1& 2\end{array}\right]\text{and}C=\left[\begin{array}{ccc}-2& -8& 6\end{array}\right]$, find A+B-C

What is the ratio of the base-radius and slant height of a cone made by rolling up a semicircle?

Choose the ogive curve for the given data.

$$\begin{array}{cc}Marks& Numberofstudents\\ >05& 48\\ >10& 45\\ >15& 39\\ >20& 30\\ >25& 18\\ >30& 10\end{array}$$

Find the volume (in cu ft) of the given decorative right circular cone.

Okay, now this guy is stuck. You need to help him out. What is the first thing to identify?

Find the surface area of a sphere whose radius is 21 cm.

1. 12

Find the sum of the squares of the first 9 natural numbers.

The x coordinate is known as __

Find the zeroes of the polynomial 3x^2-3√3+2 using middle term split

I don't think more information is needed

If $\Delta ABC$ and $\Delta BDE$ are equilateral triangles, where D is the mid point of BC, find the ratio of areas of $\Delta ABC$ and $\Delta BDE$

Aman invests Rs.29929 in shares of par value Rs.26 at $10\%$ premium. The dividend is 15% per annum. Calculate:

(i) the number of shares

(ii) the dividend received by him annually

(iii) the rate of interest he gets on his money.