List of top Mathematics Questions

Write \( \int \cot x \, dx \).

Let the probability mass function (p.m.f.) of a random variable X be \( P(X = x) = \binom{4{x} \left( \frac{5}{9} \right)^x \left( \frac{4}{9} \right)^{4-x} \), for \( x = 0, 1, 2, 3, 4 \), then E(X) is equal to _______.
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Write the joint equation of co-ordinate axes.

The solution of the differential equation \( \frac{d}{dt} \log \frac{x}{t} = x \) is _______.

\( \int 3 \cos^3 x \, dx = \).

If the corner points of the feasible solution are (0, 10), (2, 2), and (4, 0), then the point of minimum \( z = 3x + 2y \) is _______.

If y is a function of x and \( \log (x + y) = 2xy \), then the value of \( y'(0) = \).

In \( \triangle ABC \), if \( c^2 + a^2 - b^2 = ac \), then \( \angle B = \).

The area of the triangle with vertices (1, 2, 0), (1, 0, 2), and (0, 3, 1) in sq. unit is _______.

If \( p \wedge q \) is F, \( p \to q \) is F, then the truth values of p and q are _______ respectively.

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is

If the sum of the series \(\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ \)
is \(\frac{α}{β}\) , where α and β are co-prime, then α+3β is equal to ________

If the \(XZ\)-plane divides the straight line joining the points \((2,4,7)\) and \((3,-5,8)\) in the ratio \(α:1\),then the value of \(α\) is ?

Let a_n be the n^th term of the series 5 + 8 + 14 + 23 + 35 + 50 +.... and Sn = \(\displaystyle\sum_{k=1}^{n} a_k.\) Then S³⁰ - a⁴⁰ is equal to

A survey was conducted for 180 people in a city. 70 ate Pizza, 60 ate Burgers, and 50 ate Chips. Draw a pie diagram for the given information.

Show the following data by a frequency polygon:

Electricity Bill (₹)	Families (f)
200 - 400	240
400 - 600	300
600 - 800	450
800 - 1000	350
1000 - 1200	160

The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of the data:

No. of Mangoes	No. of Trees (f)
50 – 100	33
100 – 150	30
150 – 200	90
200 – 250	80
250 – 300	17

Solve the following simultaneous equations using Cramer’s Rule: \[ 4m + 6n = 54 \quad \text{and} \quad 3m + 2n = 28 \]

Fill in the boxes with the help of given information:

Tax invoice of services provided (Sample)
Food Junction, Khed-Shivapur, Pune
Invoice Date: 25 Feb., 2020

SAC	Food Items	Qty	Rate (₹)	Taxable Amount (₹)	CGST	SGST	Amount (₹)
9963	Coffee	1	20	20.00	2.5% = 0.50	2.5% = 0.50	21.00
9963	Masala Tea	1	10	10.00	2.5% = 0.25	2.5% = 0.25	10.50
9963	Masala Dosa	2	60	120.00	2.5% = 3.00	2.5% = 3.00	126.00
Total				150.00
Grand Total							₹157.50

Form a ‘Road Safety Committee’ of two, from 2 boys (B₁, B₂) and 2 girls (G₁, G₂). Complete the activity to write the sample space:

Observe the following table and find the Mean:

A courier service agent charged ₹590 to courier a parcel from Nashik to Nagpur. In the tax invoice, the taxable value is ₹500 on which CGST = ₹45 and SGST = ₹45. Find the rate of GST charged for this service.

Complete the following table using the given information:

Sr. No.	FV (₹)	Share is at	MV (₹)
1	100	Par	100
2	75	Premium ₹500	575
3	10	Discount ₹5	5
4	200	Discount ₹50	150

Complete the following activity to determine the nature of the roots of the quadratic equation \(x^2 + 2x - 9 = 0\):