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Find the distance between the points (3, -6), (-2, 2)

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h=-16t^2+24t+1$, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Prove the following trignometric identities:

$\frac{cos\theta }{1-sin\theta }=\frac{1+sin\theta }{cos\theta }$

Find the sum of 10 terms of the sequence 1,3,5,7,…

$MatrixA=\left(\begin{array}{ccccc}1& 1& 1& 1& 1\\ 1& 2& 3& 4& 5\\ 1& 3& 6& 10& 15\\ 1& 4& 10& 20& 35\\ 1& 5& 15& 35& 70\end{array}\right)$ is a ___ matrix of order ___

What is the simple interest if the sum of money is ₹ 4800 and the interest rate is 8.5% for time period of 2 years 3 months?

Question 1

Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.

Question 111

Solve the following

For what value of x is the perimeter of shape 186 cm?

Q. A shop is selling 135 black and 60 red t-shirts. All t-shirts are either size S (small), M (medium), or L (large). $30\%$ of the red t-shirts are of medium size and $25\%$ of them are L. Similarly, among black t-shirts, $20\%$ are size S and $23\%$ are size L. A boy picks a t-shirt at random. He gets a discount if the t-shirt is red and size L or if it is black and size S or M. What are the chances of his winning?

Q. एक दुकान 135 काले और 60 लाल टी-शर्ट बेच रही है। सभी टी-शर्ट या तो आकार में S (छोटे), M (मध्यम), या L (बड़े) हैं। लाल टी-शर्ट के $30\%$ मध्यम आकार के हैं और उनमें से $25\%$ L आकार के हैं। इसी तरह, काली टी-शर्ट में से $20\%$ S और $23\%$ L आकार के हैं। एक लड़का अनियोजित रूप से एक टी-शर्ट चुनता है। उसे छूट मिलती है यदि टी-शर्ट का रंग लाल और आकार L है, या यदि टी-शर्ट का रंग काला और आकार S अथवा M है। तो उसके जीतने की संभावना क्या है?

Question 2

A rectangular water tank of base $11m\times 6m$ contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.

Prove that $\frac{2}{\sqrt{7}}$ is irrational.

Question 128(i)

Predicting the ones digit, copy and complete this table and answer the questions that follow.

Powers Table

$\begin{array}{ccccccccccc}X& 1^x& 2^x& 3^x& 4^x& 5^x& 6^x& 7^x& 8^x& 9^x& {10}^x\\ 1& 1& 2& & & & & & & & \\ 2& 1& 4& & & & & & & & \\ 3& 1& 8& & & & & & & & \\ 4& 1& 16& & & & & & & & \\ 5& 1& 32& & & & & & & & \\ 6& 1& 64& & & & & & & & \\ 7& 1& 128& & & & & & & & \\ 8& 1& 256& & & & & & & & \\ \text{Ones digits of the powers}& 1& 2,4,6,8& & & & & & & & \end{array}$

Describe patterns you see in the ones digits of the powers.

The probability of getting at least one tail in 4 throws of a coin is__.

If the angle of elevation of a tower from a distance of 100 m from its foot is ${60}^{\circ }$, then the height of the tower is

Find the coordinates of the point which divides the line segment joining (-3,5) and (4, -9) in the ratio 1: 6 internally.

If A = {Whole numbers less than 5} and B = {Natural numbers less than 6}, then A and B are ________.

The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is

ABDE is a trapezium​ with $AE\parallel BD$ and $ED\perp BD$, and AC is drawn parallel to the side DE

Find the values of $\text{cot}\theta$ and $\text{cosec}\theta$ respectively, from the figure above.

The distance between the points (a, b) and (– a, – b) is:

Question 4

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

$\begin{array}{cc}\text{Number of students per teacher}& \text{Number of states/U.T}\\ 15-20& 3\\ 20-25& 8\\ 25-30& 9\\ 30-35& 10\\ 35-40& 3\\ 40-45& 0\\ 45-50& 0\\ 50-55& 2\end{array}$

Find the discriminant of the quadratic equation $3x^2–5x+2=0$ and hence, find the nature of the roots.

Prove that the difference of the squares of two consecutive natural is equal to their sum.

What type of decimal expansion does 29_{^{÷ 2^2×5×7 have?}}

For positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where

$0\le r$ $b$.

Question 82(iv)

Given below is a frequency distribution table. Read it and answer the questions that follow.

$\begin{array}{cc}Classinterval& Frequency\\ 10-20& 5\\ 20-30& 10\\ 30-40& 4\\ 40-50& 15\\ 50-60& 12\end{array}$

Which interval has a frequency of 10 ?