What's the highest score in the second innings of a Test by a batter who got a duck in the first?

What's the highest score in the second innings of a Test by someone who got a duck in the first? asked Mithun Ahmed from India
This question popped up in the middle of Yashasvi Jaiswal's sparkling second innings in Perth after he bagged a duck in the first knock. In the end, Jaiswal did not quite join them, but there are seven men who made a double-century and a duck in the same Test. And the only one of those whose double came in the second innings was the South African Dudley Nourse, with 0 and 231 against Australia in Johannesburg in December 1935.

Jaiswal was eventually out for 161, so the highest score by an Indian batter after a duck in the first innings remains Madhav Apte's 163 not out against West Indies in Port-of-Spain in February 1953. A few weeks ago Sarfaraz Khan followed a first-innings duck with 150 in the first Test against New Zealand in Bengaluru.

Nathan McSweeney took a catch from the 13th ball of his debut Test. Has anyone take one quicker than that? asked Manoj Arya via Twitter/X
Australia's new opener Nathan McSweeney caught Yashasvi Jaiswal on the 13th delivery of the first Test against India in Perth. We don't have ball-by-ball details for a lot of Tests, but McSweeney's early grab is certainly not a record: the fastest appears to have been by the former South Africa offspinner Hugh Tayfield, who caught Arthur Morris from the second ball of the match on his Test debut, against Australia in Johannesburg in 1949. Ian Chappell (for Australia in 1964) and the New Zealand wicketkeeper Robbie Hart (2002) both took a catch from the third ball of their debut Test.

The Indian slow left-armer Pragyan Ojha did take a catch from the first ball he was in the field for, against Sri Lanka in Kanpur in 2009, but India had batted first in that match (and scored 642!) so it wasn't at the very start of the match. Charles Davis, the doyen of the ball-by-ball scorecard, tells me that another slow left-armer, New Zealander Allen Lissette, also did this against West Indies in Dunedin in 1956.

Don Bradman scored a Test hundred every three innings, approximately speaking. Who holds the corresponding record in ODIs? asked Tim Sanderson from England
Don Bradman scored 29 hundreds in his 80 Test innings, a rate of better than one every three - he reached 100 in a staggering 36.25% of his Test innings. Next (of those who batted at least 30 innings) come a pair of West Indians: George Headley, with ten centuries in 40 innings (25%) and Clyde Walcott with 15 in 74 (20.27%). The leading current player is Kane Williamson, with 32 hundreds in 180 innings (17.77%), just ahead of Harry Brook (six in 35, or 17.14%).

There's something of a surprise leader in one-day internationals, with six tons in 30 innings, or 20%. It's Dawid Malan, the recently retired England left-hander. Virat Kohli is second at the moment, with 50 centuries from 283 innings (17.66%), but he's not far ahead of a clutch of current players: Rahmanullah Gurbaz (17.39%), Daryl Mitchell (17.14%), Babar Azam (16.23%) and Devon Conway (16.12%).

While Justin Greaves was in the nineties against Bangladesh there was a reviewed lbw appeal. If he'd been given out there would have been three dismissals in the nineties in that innings - has that actually ever happened in a Test? asked Marlon Spencer from Barbados
Justin Greaves had 92 when Mehidy Hasan tried an optimistic review in the first Test between West Indies and Bangladesh in Antigua on the weekend. Greaves survived, and went on to complete his maiden century, finishing with 115 not out.

Earlier in that innings, Mikyle Louis was out for 97 and Alick Athanaze for 90. This made it the 62nd Test innings to contain two nineties, some of them not outs - and there has still not yet been a case of three.

Pakistan's first innings against England in Karachi in 1973 actually contained two 99s, by Majid Khan and Mushtaq Mohammad. Later Dennis Amiss was also out one short of his hundred, making this the only Test to contain three 99s.

There have been 20 instances of two nineties in an innings in men's ODIs, and one in a T20 international (by Bermuda against Argentina in Buenos Aires in 2023). There have been no cases in women's Tests or T20s, but four in ODIs.

Gogumal Kishenchand of India played in five Test matches, and made a duck in each of them. Has anyone played more Tests while making a duck in all of them? asked Deepanjan Deb from India
A batter who mainly turned out for Gujarat and Baroda, Gogumal Kishenchand played four Tests for India in Australia in 1947-48, collecting a duck in all four second innings, and won one more cap against Pakistan in Lucknow in 1952, when he changed things around and was out for nought in the first innings.

Not surprisingly, this is the most Tests by anyone who collected a duck in all of them. Three other men had a career of three Tests with a duck in each: the Jack Edwards of Australia in the 1888 Ashes series in England, Johannes "Kodgee" Kotze of South Africa in the first decade of the 20th century, and the recent Afghanistan allrounder Mohammad Nabi. Two others who have done this but might yet appear again are Nabi's fellow Afghani Nijat Masood, who has played a Test this year, and Roy Kaia of Zimbabwe, who last featured in 2021.