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Which of the following is $sin\theta$ from the unit circle?

How to remember the equations there is a lot of equations

Write the number of solutions of the following pair of linear equations:

$x+2y-8=0,2x+4y=16.$

Does HCF of two numbers only divides their LCM completely?

Write the zeros of the quadratic polynomial $f\left(x\right)=6x^2-3$.

In triangle ABC, D and E are points on AB and AC such that DE || BC. If AD = 4x-3, AE = 8x-7,
BD = 3x-1 and CE = 5x-3, find the value of x

Consider A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Find the cardinality of P(A).

If figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P.

If ∠POQ = 70^o, then ∠TPQ is equal to

Find values of a and b. 2x-3y=7. (a+b)x - (a+b-3)y=4a+b.

The informal source of credit does not include which one of the following?

What is the length of the third side in the triangle shown below?

For what value of m, the system of equations mx + 3y = m - 3 , 12x + my = m will have no solution

Show that 1.272727...=1.27 can be expressed in the form of p/q,where p and q are integers and q≠0

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [4 MARKS]

What are the minimum and maximum numbers of distinct real roots a quadratic equation can have ?

At 03:40, the hour hand and the minute hand of a clock form an angle of

Find the dimensions of the square whose area is equal to area of rectangle (with dimensions 5 cm $\times$ 4 cm) [Use construction]

From a point Q, the length of the tangent to a circle is $24cm$ and the distance of Q from the center is $25cm.$ The radius of the circle is ___ $cm.$

Ruhi’s mother is $26$ years older than her. The product of their ages (in years) $3$ years from now will be $360.$ Form a Quadratic equation so as to find Ruhi’s age

What is the discriminant of the equation $2x^2-5x-2=0$ ?

Question 28
Expand the following
(i) $(4a-b+2c{)}^2$

(ii) $(3a–5b–c{)}^2$

(iii) $(-x+2y-3z{)}^2$

An n-digit number is a positive number with exactly n digits. Atleast nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is

Two tangents are drawn from an external point P that touches the circle at points Q and R respectively. The centre of the circle is O. The lines OQ and OR are drawn to complete the quadrilateral OQPR. The resulting quadrilateral is a ________necessarily.

The locus of the mid points of the chords of the circle $x^2+y^2-ax-by=0$ which subtend a right angle at $(\frac{a}{2},\frac{b}{2})$ is :

In a circus, a motorcyclist performs his stunts in a hollow sphere.Neglect the thickness of sphere. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform stunts.(Take $\pi =\frac{22}{7}$)

Question 3
Does a quadratic equation with integral coefficient has integral roots. Justify your answer.

A man is watching a bulb glow which is 3 meters above him. If he is standing 3m away from the point directly below the bulb, what is the angle of elevation?

If general term of an AP is given by 2 + 4n then find its common difference.

The angles of a triangle are in A.P. If the greatest angle is three times the smallest angle, find the greatest angle in the triangle.

The product of $2^{\text{nd}}$ term and $4^{\text{th}}$ term of a G.P is 57600. If its $1^{st}$ term is 60, then find the G.P..

If x + a is a common factor of expressions $f\left(x\right)=x^2+px+qandg\left(x\right)=x^2+mx+n;$ show that : $a=\frac{n-q}{m-p}$

Question 5 (iii)
Rationalize the denominators of the following:

$\frac{1}{(\sqrt{5}+\sqrt{2})}$

Find the slope of the line which is perpendicular to :

(i) $x-\frac{y}{2}+3=0$

(ii) $\frac{x}{3}-2y=4$

Water is flowing at the rate of 2.52 km/hr through a cylindrical pipe into a cylindrical tank, the radius of the base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m. find the internal diameter of the pipe.

If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ =24 cmand OQ =25 cm. Find the radius of the circle.

A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.

Which of the following is a polynomial ?

(a) $x^2-5x+4\sqrt{x}+3$ (b) $x^{\frac{3}{2}}-x+x^{\frac{1}{2}}+1$

(c) $x^{\frac{3}{2}}-x+x^{\frac{1}{2}}+1$ (d) $\sqrt{2}{x}^2-3\sqrt{3}x+\sqrt{6}$

The area of a circle is the same as the area of a square. Their perimeters are in the ratio.

(a) 1 : 1 (b) $\frac{2}{\sqrt{\pi }}$ (c) $\pi$ : 2 (d) $\sqrt{\pi }$ : 2