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1. 70

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

The $\text{Brewster's angle}{i}_b$ for an interface should be :

Solve for x and y.

a^2x+b^2y=c^2,

b^2x+a^2y=d^2.

The diagonals of a quadrilateral ABCD intersect each other at the point O such that Show that ABCD is a trapezium.

If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 8 units then the other two vertices of the triangle are___

If ABCD is a cyclic quadrilateral. What will be the value of $x$ (in degrees)?

A man standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as ${60}^{\circ }$ and the angle of depression of the base of the hill as ${30}^{\circ }$. Calculate the distance of the hill from the ship and the height of the hill.

If $\alpha ,\beta ,\gamma$ are the zeros of the polynomial $x^3-6x^2-x+30$ then $(\alpha \beta +\beta \gamma +\gamma \alpha )$ = ?

(a) -1 (b) 1 (c) -5 (d) 30

In the shown diagram, if the angle between two chords AB and AC is ${65}^0$, then the angle between two tangents which are drawn at B and C is

A line segment $AB$ is divided in the ratio $m:n$ where $m$ and $n$ are co-prime, using a single ray $AX$. The number of arcs to be drawn on $AX$ is _____.

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.

If $\left[\begin{array}{cc}2x& x\\ y& 3y\end{array}\right]\left[\begin{array}{c}3\\ 2\end{array}\right]=\left[\begin{array}{c}16\\ 9\end{array}\right]$, then y =
___.

Question 9

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the coordinates of point B if AB and BC are parallel to the coordinate axes.

Degree of polynomial $x^p{y}^q{z}^r$ is

If 7x -15y = 4x + y , find the value of x : y. Hence, use componendo and dividendo to find the values of :

(i) $\frac{9x+5y}{9x-5y}$ (ii) $\frac{3x^2+2y^2}{3x^2-2y^2}$

In the figure, the $\angle ABC=30°$. If $CB=18m$ , then AB = and AC = .

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median drawn from B to AC, AB = 8cm and BC = 6 cm. Then, choose the correct option(s).

Find the value of ‘p’ for which the lines 2 + 3y – 7 = 0 & 4y + – 12 = 0 are ⊥ to each other.

In the figure below, two tangents are drawn from a point P to a circle meeting it at points A and C.

If $\angle AOC={120}^{\circ }$, what is the value of $\angle APC$?

In figure.6.17. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).

(i)

(ii)

If one root of the quadratic equation $3x^2+5a^{2}x+k=0$ is twice the reciprocal of the other root, then the value of $k$ is equal to

The quadratic equations $x^2+ax+b=0and{x}^2+bx+a=0$, have one common root and $a\ne b$, then