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Question 8

ABCD is a cyclic quadrilateral. Find the angles of the cyclic quadrilateral.

In a plane rectangular coordinate system, there are three points $A(0,\frac{4}{3}),B(–1,0)$ and $C(1,0).$ The distance from point $P$ to line $BC$ is the geometric mean of the distances from this point to lines $AB$ and $AC.$ Then the locus of point $P$ is

Simplify $(3+\sqrt{3})(2+\sqrt{2})$ .

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.

1. 4

The value of determinant $\Delta =\left|\begin{array}{ccc}{x}^2+4& 2x& 1-x\\ 5x+1& 2x& 1\\ x+2& x& 2\end{array}\right|,(x\ne 0)$ is equal to

Question 7(ii)
In a class test containing 10 questions, 5 marks are awarded for every correct answer and (−2) marks are awarded for every incorrect answer and 0 for questions not attempted.
Reshma gets five correct answers and five incorrect answers, what is her score?

An equilateral ΔABC is inscribed in a circle with centre O. The measure of ∠BOC is :

The value of expression tan θ−cot θ at θ=30∘ is .

Find the area of quadrilateral ABCD, if AB || CD and AB = CD is as shown in figure :

Let $A=\{a,b,c,d\}$ and $B=\{b,d,f,g\}$. Find $A\Delta B.$

A trapezium with its parallel sides is in the ratio 16: 5 is cut from a rectangular whose sides measure 63 m and 5 m respectively. The area of the trapezium is $\frac{4}{15}$ of the rectangle. Find the difference between the lengths of the parallel sides of the trapezium.

S1: AM = $\frac{AP}{2}$, BN = $\frac{BP}{2}$

S2: OO' = AM + BN

Which of the above statements are true ?

Question 106

Simplify and write the result in decimal form:
$(1÷\frac{2}{9})+(1÷3\frac{1}{5})+(1÷2\frac{2}{3})$

What are the common factors of ​$3x^{3}y,5x{y}^{2}and15xy$?

The highest common factor between 7x²y⁵z³ and 12x²y³z is_______

In a class of $120$ students numbered from $1$ to $120$, all even numbered students opt for Physics, those whose numbers are divisible by $5$, opt for Chemistry and those whose numbers are divisible by $7$, opt for Maths. How many opt for none of the three subjects?

In the given figure, ABCD is a rhombus in which diagonals AC and BD intersect at O. Then measure of ∠AOB is.

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case:

(i) (ii) (iii) − 2x + 3 y = 6

(iv) x = 3y (v) 2x = − 5y (vi) 3x + 2 = 0

(vii) y − 2 = 0 (viii) 5 = 2x

When f(x) =$x^4$-2$x^3$+3$x^2$-ax+b is divided by x+1 and x-1, we get remainders 19 and 5 respectively. Find the remainder when f(x) is divided by x-3.

If transformations are done for the solid graph $f\left(x\right)$ to obtain the dashed graph $g\left(x\right)$, then $g\left(x\right)=$

Find the area of the triangle whose isdes are 42 cm, 34 cm and 20 cm in length. Hence, find the height corresponding to the longest side.

If (p+q)th term of G.P. is m and (p-q)th term is n, then pth term will be

Question 92 (xxvii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$(x+y{)}^4-(x-y{)}^4$

If the discriminant of the quadratic equation 4x² + px + 25 = 0; is 0, then find the value of p. Given $p>0.$

1. 59