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Solve for x if $4(2x+3{)}^2-(2x+3)-14=0$.

A chord of a circle of radius $28cm$ subtends a right angle at the center. What is the area of the minor sector?

In the rhombus ABCD, Side AD = 12 cm and $\angle B$ is ${135}^{\circ }$ as shown in figure. The height (DE) and the area of the rhombus will be equal to

If $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$, then $2A-B$ is

If ${\Delta }_1=\left|\begin{array}{cc}\omega & -{\omega }^2\\ -{\omega }^2& -\omega \end{array}\right|,{\Delta }_2=\left|\begin{array}{cc}-{\omega }^2& -\omega \\ \omega & {\omega }^2\end{array}\right|.$ Then the value of ${\Delta }_1\cdot {\Delta }_2=$

(where $\omega$ is a cube root of unity)

$\Delta ABC$ of dimesions $AB=4cm,BC=5cm$ and ∠B= 60^o is given.

A ray $BX$ is drawn from $B$ making an acute angle with $AB$.

5 points $B_1,B_2,B_3,B_4\&B_5$ are located on the ray such that $BB1=B1B2=B2B3=B3B4=B4B5$.

$B_4$ is joined to $A$ and a line parallel to $B_{4}A$ is drawn through $B_5$ to intersect the extended line $AB$ at $A^{\prime }$.

Another line is drawn through $A^{\prime }$ parallel to $AC$, intersecting the extended line $BC$ at $C^{\prime }$.

Find the ratio of the corresponding sides of $\Delta ABC$ and $\Delta A^{\prime }B{C}^{\prime }$.

Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60° and 45° respectively. If the height of the tower is $15$ m, then find the distance between the points.

Draw two congruent circles of radii 4.5 cm whose centres are 9 cm apart. Draw transverse common tangents.

The radius of a sphere is increased by $10\%$. Prove that the volume is increased by $33.1\%.$

Solve the linear equation $\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

The integral value of $k$ for which the equation $(k-12)x^2+2(k-12)x+2=0$ possesses no real solutions is ______.

The discriminant of quadratic equation is $2x^2+3x-5=0$ is ___

Obtain all other zeroes of , if two of its zeroes are .

A Ltd. invited applications for issuing 1,00,000 shares of ₹ 10 each at a premium of ₹ 1 per share. The amount was payable as follows:

Excess money paid on application is to be adjusted against the amount due on allotment and calls.

Rishabh, a shareholder, who applied for 1,500 shares and belonged to category (ii), did not pay allotment, first and second and final call money.

All the shares of Rishabh and Sudha were forfeited and were subsequently reissued at ₹ 7 per share fully paid.

Using the information from the given histogram which of the following is one of the points used to construct the corresponding ogive?

There are 35 students in a class of whom 20 are boys and 15 are girls. From these students one is chosen at random. What is the probability that the chosen student is a (i) boy, (ii) girl?

The value of $A\cdot \text{adj}\left(BCA\right),$ such that $|A|=2,|B|=3$ and $B=\text{adj}\left(C\right),$ where $A,B,C$ and $I_3$(identity) are all square matrices of order $3$, is

sin ${47}^o$ cos ${43}^o$ + cos ${47}^o$ sin ${43}^o$ = ?

(a) sin $4^o$ (b) cos $4^o$ (c) 1 (d) 0

If the area of a circle with radius $r$ is equal to the curved surface area of a cone with radius $r_1$ and slant height l then the value of $r_1$ in terms of r and l is:

The length of the minute hand of a clock is 14 cm. Find the area in

${cm}^2$ swept by the minute hand in 5 minutes.

If $132300=2^2\times 3^3\times 5^2\times a^b,$ then which of the following is true ?

A toy in shape of a sphere of radius 7cm is surmounted by a cone of height 11cm. Find the volume of the toy.

Two cones have the same volume and their base-radii are in the ratio 4 : 5. What is the ratio of their heights?

Question 22

Which of the following is different from the others?

(a) $20+(-25)$
(b) $(-37)-(-32)$
(c) $(-5)\times (-1)$
(d) $45÷(-9)$

Water in a canal, 4 m wide and 15 m deep is flowing with the speed of 12 km/h. Then the area of field it will irrigate in 20 minutes, if 10 cm of standing water is required for irrigation, is