Sign in
Please select an account to continue using cracku.in
↓ →
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
Let $$a_n$$ be the units place of $$1^2 + 2^2 + 3^2 + \ldots + n^2$$. Prove that the decimal $$0.a_1a_2a_3 \ldots a_n \ldots$$ is a rational number and represent it as $$\frac{p}{q}$$, where p and q are natural numbers.
(a) Find the positive integers m, n such that $$\frac{1}{m} + \frac{1}{n} = \frac{3}{17}$$. Also find the positive integers m, n, p such that $$\frac{1}{m} + \frac{1}{n} + \frac{1}{p} = \frac{3}{17}$$. Using this idea, prove that for any positive integer k we can find k distinct integers $$n_1, n_2, \ldots, n_k$$ such that $$\frac{1}{n_1} + \frac{1}{n_2} + \ldots + \frac{1}{n_k} = \frac{3}{17}$$.
Does there exist a positive integer which is a multiple of 2019 and whose sum of the digits is 2019 ? If no, prove it. If yes, give one such number.
.webp)
In a triangle XYZ, the medians drawn through X and Y are perpendicular. Then show that XY is the smallest side of XYZ.
Let $$\triangle PQR$$ be a triangle of area $$1 \text{ cm}^2$$. Extend QR to X such that $$QR = RX$$, RP to Y such that $$RP = PY$$ and PQ to Z such that $$PQ = QZ$$. Find the area of $$\triangle XYZ$$.
Find the real numbers x and y given that $$x - y = \frac{3}{2}$$ and $$x^4 + y^4 = \frac{2657}{16}$$.
.webp)
The difference of the eight digit number ABCDEFGH and the eight digit number GHEFCDAB is divisible by 481. Prove that $$C = E$$ and $$D = F$$.
ABCD is a parallelogram with area $$36 \text{ cm}^2$$. O is the intersection point of the diagonals of the parallelogram. M is a point on DC. The intersection point of AM and BD is E and the intersection point of BM and AC is F. The sum of the areas of triangles AED and BFC is $$12 \text{ cm}^2$$. What is the area of the quadrilateral EOFM?
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
91- 6303239042