List of practice Questions

How many chords can be drawn through 5 points on a circle ?

Two pipes A and B can fill a tank in 10 h and 15 h Respectively. Find the time taken to fill the tank when both the pipes are turned on simultaneously :

At what rate of interest 1,200 becomes ₹ 1,323 in 2 years where interest gets compounded annually:

Arun invests an amount of ₹4,000 at the rate of 2% simple interest per annum. For how many years did he invest the amount to double his sum?

What should replace the question mark ?
\(\frac{854\times 854 × 854-276 × 276 × 276}{854 \times854 + 854×276+276 × 276}=?\)

What is the maximum area of a rectangle which can be inscribed in a circle of radius 2 cm?

The diameter of the driving wheel of a bus is 140 m. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/h?

If the selling price is doubled, the profit triples. Find the profit % :

Arjun is twice as old as Shreya. Five years ago, his age was three times Shreya's age. Find the sum of their present ages:

A bag contains 6 white and 4 black ball. Two balls are drawn at random. Then the probability of getting balls of the same colour is ___.

A die is thrown. Find the probability of getting:
(A) A number greater then 6 and
(B) A number less than 3.

What does ICDS stand for?

Let \(y_c:\R \rightarrow(0,\infin)\) be the solution of the Bernoulli’s equation
\(\frac{dy}{dx}-y+y^3=0,\ \ \ \ \ \ \ y(0)=c \gt 0.\)
Then, for every 𝑐 > 0, which one of the following is true ?

Let A be a $n \times n$ matrix such that $| A |=2$ If the determinant of the matrix$\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot$ is $2^{84}$, then $n$ is equal to ____

A bullet from a gun is fired on a rectangular wooden block with velocity u. When the bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by \(\vec{E}\)=30(2𝑥̂ + 𝑦̂)sin [2𝜋 (5×10¹⁴𝑡 −\(\frac{10^7}{3}z\))] Vm⁻¹. Which of the following option(s) is(are) correct? [Given: The speed of light in vacuum, 𝑐 = 3 × 10⁸ ms⁻¹]

Let the circle \( S: x^2 + y^2 + 2gx + 2fy + c = 0 \) cut the circles \( x^2 + y^2 - 2x + 2y - 2 = 0 \) and \( x^2 + y^2 + 4x - 6y + 9 = 0 \) orthogonally. If the centre of the circle \( S = 0 \) lies on the line \( 2x + 3y - 2 = 0 \), then \( 2g + f = \)

If the line passing through the points \( (5,1,a) \) and \( (3,b,1) \) crosses the YZ plane at the point \( \left( 0, \frac{17}{2}, \frac{-13}{2} \right) \), then \( a + b = \):

In \( \triangle ABC \), the coordinates of the vertices are \( A(1,8,4) \), \( B(0,-11,4) \), and \( C(2,-3,1) \). If \( D \) is the foot of the perpendicular drawn from \( A \) to \( BC \), then the coordinates of \( D \) are:

The distance between two parallel planes \( ax + by + cz + d_1 = 0 \) and \( ax + by + cz + d_2 = 0 \) is given by \( \frac{|d_1 - d_2|}{\sqrt{a^2 + b^2 + c^2}} \). If the plane \( 2x - y + 2z + 3 = 0 \) has the distances \( \frac{1}{3} \) units from the planes \( 4x - 2y + 4z + \lambda = 0 \) and \( 2x - y + 2z + \mu = 0 \) respectively, then the maximum value of \( \lambda + \mu \) is:

Let \( S \) be the circumcircle of the triangle formed by the line \( x - 2y - 4 = 0 \) with the coordinate axes. If \( P(-2, -4) \) is a point in the plane of the circle \( S \) and \( Q \) is a point on \( S \) such that the distance between \( P \) and \( Q \) is the least, then \( PQ = \)

If the coordinates of the point of contact of the circles \( x^2 + y^2 - 4x + 8y + 4 = 0 \) and \( x^2 + y^2 + 2x = 0 \) is \( (a, b) \), then \( a + 2b \) is:

If the chord of contact of the point \( P(h, k) \) with respect to the circle \( x^2 + y^2 - 4x - 4y + 8 = 0 \) meets the circle in two distinct points and it also makes an angle \( 45^\circ \) with the positive X-axis in the positive direction, then \( (h, k) \) cannot be:

The equation of the pair of tangents drawn from the point \( (1, 1) \) to the circle \( x^2 + y^2 + 2x + 2y + 1 = 0 \) is:

If eight coins are tossed simultaneously, then the probability of getting at least six heads is: