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Question 8
The quadratic equation $2x^2-\sqrt{5}x+1=0$ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere. [3 MARKS]

Question 91

Solve the following:

After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.

Question 92

Lemons were bought at Rs. 48 per dozen and sold at the rate of Rs. 40 per 10. Find the gain or loss per cent.

Question 27
The number of distinct prime factors of the largest 4-digit number is

(A) 2
(B) 3
(C) 5
(D) 11

In an AP, where the first term is 7 and the common difference is 4, ___ term of the AP will be five times the first term.
Represent this situation in the form of an equation, where $a$ = first term, $a_n$ = $n^{th}$ term and $d$ is the common difference.

In a $\Delta ABC,$ if $\angle A={30}^{\circ }andb:c=2:\sqrt{3},find\angle B.$

One angle of a parallelogram is twice the adjacent angle. Angles of the parallelogram are

If in certain code, STUDENT is written as RSTEDMS, then how would TEACHER be written in the same code?

In triangle ABC shown below, point G is the intersection of all the medians. If the length of AP is 18 cm, then the length of AG and GP respectively are:

$(cosec\theta -cot\theta {)}^2=$ ____________.

If p is a prime number ,then prove that √p is irrational.

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions $16cm\times 8cm\times 8cm$. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. $[use\pi -31.4]$

Two circle touch each other externally at C and AB is a common tangent to the circles. Then, $\angle$ACB = ______.

From an external point P, two tangents are drawn that touch the circle at points Q and R. The centre of the circle is O. The lines OQ and OR are drawn to complete the quadrilateral OQPR. The resulting quadrilateral is a ___.

$\Delta ABC$ is right angled at B and $5\times sinA=3$. Find cos C + tan A + cosec C.

Which of the following series forms an AP?

$\left(i\right)a–2d,a–d,a,a+d,a+2d$

$\left(ii\right)a,a+d,a+2d,a+3d,a+4d$

$\left(iii\right)a–3d,a–d,a+d,a+3d$

IF A and B ar eany two $2\times 2$ matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

Edward opened a Recurring deposit account in a bank. He deposited Rs 300 per month for 2 years. At the time of maturity he received Rs 7725. What was the rate of interest?

Find a, b, c and d, if $3\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=\left[\begin{array}{cc}a& 6\\ -1& 2d\end{array}\right]+\left[\begin{array}{cc}4& a+b\\ c+d& 3\end{array}\right]$

The range of values of x which satisfy $\frac{-1}{3}\le \frac{x}{2}-\frac{4}{3}<\frac{1}{6}$, where x ϵ R is .

If first term of an AP is 5, last term is 45 and the sum of the terms is 400, then the number of terms is in the AP is ___.

From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hollowed out. Find the total surface area of the remaining solid.
$[Use\pi =\frac{22}{7}]$

Which of the following is not a quadratic equation?

Prove that $\sin {80}^{\circ }\cos {10}^{\circ }$ + $\cos {80}^{\circ }sin{10}^{\circ }$ = 1

The present age of the father is 42 years and that of his son is 14 years. Find the ratio of:

Present age of father to the present age of son.

Find the median term of the following cumulative frequency distribution:
$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?

How will you make the following equations linear?

$\frac{5}{x-1}$ + $\frac{1}{y-2}$ = 2

$\frac{6}{x-1}$ - $\frac{3}{y-2}$ = 1

Which of the following is right angled triangle having three side given below

A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

If the volume of a hemisphere is four times its total surface area, what is its radius?

Two angles of a triangle are ${65}^{\circ }$ and ${45}^{\circ }$ then the third angle is:

If 15 % of x is equal to 65 % of y. Find the value of x: y.

If $\Delta ABC\sim \Delta PQR$ and AD and PM are corresponding medians of the two triangles, then

In the figure, lines PQ and RS intersect each other at point O; ray OA and ray OB bisect $\angle POR$ and $\angle POS$ respectively. If $\angle POA:\angle POB=2:7$, then find $\angle SOQ$ and $\angle BOQ$. [4 MARKS]

In fig., a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF. [3 MARKS]